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<journal-id journal-id-type="publisher-id">Front. Phys.</journal-id>
<journal-title>Frontiers in Physics</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Phys.</abbrev-journal-title>
<issn pub-type="epub">2296-424X</issn>
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<article-id pub-id-type="publisher-id">1270602</article-id>
<article-id pub-id-type="doi">10.3389/fphy.2023.1270602</article-id>
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<subj-group subj-group-type="heading">
<subject>Physics</subject>
<subj-group>
<subject>Review</subject>
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<title-group>
<article-title>Fabrication and quantum sensing of spin defects in silicon carbide</article-title>
<alt-title alt-title-type="left-running-head">Luo et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fphy.2023.1270602">10.3389/fphy.2023.1270602</ext-link>
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<contrib-group>
<contrib contrib-type="author" equal-contrib="yes">
<name>
<surname>Luo</surname>
<given-names>Qin-Yue</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
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<contrib contrib-type="author" equal-contrib="yes">
<name>
<surname>Li</surname>
<given-names>Qiang</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="fn" rid="fn1">
<sup>&#x2020;</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wang</surname>
<given-names>Jun-Feng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Pei-Jie</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
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<contrib contrib-type="author">
<name>
<surname>Lin</surname>
<given-names>Wu-Xi</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
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<contrib contrib-type="author">
<name>
<surname>Zhao</surname>
<given-names>Shuang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
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<contrib contrib-type="author">
<name>
<surname>Hu</surname>
<given-names>Qi-Cheng</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
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<contrib contrib-type="author">
<name>
<surname>Zhu</surname>
<given-names>Zi-Qi</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Xu</surname>
<given-names>Jin-Shi</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
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<xref ref-type="aff" rid="aff6">
<sup>6</sup>
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<contrib contrib-type="author" corresp="yes">
<name>
<surname>Li</surname>
<given-names>Chuan-Feng</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Guang-Can</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
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<aff id="aff1">
<sup>1</sup>
<institution>College of Physics</institution>, <institution>Sichuan University</institution>, <addr-line>Chengdu</addr-line>, <addr-line>Sichuan</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>CAS Key Laboratory of Quantum Information</institution>, <institution>University of Science and Technology of China</institution>, <addr-line>Hefei</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Institute of Advanced Semiconductors and Zhejiang Provincial Key Laboratory of Power Semiconductor Materials and Devices</institution>, <institution>ZJU-Hangzhou Global Scientific and Technological Innovation Center</institution>, <addr-line>Hangzhou</addr-line>, <addr-line>Zhejiang</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>State Key Laboratory of Silicon Materials and Advanced Semiconductors</institution>, <institution>School of Materials Science and Engineering</institution>, <institution>Zhejiang University</institution>, <addr-line>Hangzhou</addr-line>, <country>China</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>CAS Center for Excellence in Quantum Information and Quantum Physics</institution>, <institution>University of Science and Technology of China</institution>, <addr-line>Hefei</addr-line>, <country>China</country>
</aff>
<aff id="aff6">
<sup>6</sup>
<institution>Hefei National Laboratory</institution>, <institution>University of Science and Technology of China</institution>, <addr-line>Hefei</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2071619/overview">Gang-Qin Liu</ext-link>, Chinese Academy of Sciences (CAS), China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2047510/overview">Panyu Hou</ext-link>, National Institute of Standards and Technology (NIST), United States</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2400852/overview">Ning Wang</ext-link>, Huazhong University of Science and Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Jun-Feng Wang, <email>jfwang@scu.edu.cn</email>; Jin-Shi Xu, <email>jsxu@ustc.edu.cn</email>; Chuan-Feng Li, <email>cfli@ustc.edu.cn</email>
</corresp>
<fn fn-type="equal" id="fn1">
<label>
<sup>&#x2020;</sup>
</label>
<p>These authors have contributed equally to this work</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>26</day>
<month>09</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>11</volume>
<elocation-id>1270602</elocation-id>
<history>
<date date-type="received">
<day>01</day>
<month>08</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>08</day>
<month>09</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Luo, Li, Wang, Guo, Lin, Zhao, Hu, Zhu, Xu, Li and Guo.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Luo, Li, Wang, Guo, Lin, Zhao, Hu, Zhu, Xu, Li and Guo</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>In the past decade, color centers in silicon carbide (SiC) have emerged as promising platforms for various quantum information technologies. There are three main types of color centers in SiC: silicon-vacancy centers, divacancy centers, and nitrogen-vacancy centers. Their spin states can be polarized by laser and controlled by microwave. These spin defects have been applied in quantum photonics, quantum information processing, quantum networks, and quantum sensing. In this review, we first provide a brief overview of the progress in single-color center fabrications for the three types of spin defects, which form the foundation of color center-based quantum technology. We then discuss the achievements in various quantum sensing, such as magnetic field, electric field, temperature, strain, and pressure. Finally, we summarize the current state of fabrications and quantum sensing of spin defects in SiC and provide an outlook for future developments.</p>
</abstract>
<kwd-group>
<kwd>spin defects</kwd>
<kwd>fabrication</kwd>
<kwd>quantum sensing</kwd>
<kwd>silicon carbide</kwd>
<kwd>high pressure</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Quantum Engineering and Technology</meta-value>
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</front>
<body>
<sec id="s1">
<title>1 Background and introduction</title>
<p>Solid-state color centers have been one of the leading systems in quantum technology [<xref ref-type="bibr" rid="B1">1</xref>&#x2013;<xref ref-type="bibr" rid="B5">5</xref>]. Color centers exist in many materials, including diamond [<xref ref-type="bibr" rid="B1">1</xref>&#x2013;<xref ref-type="bibr" rid="B5">5</xref>], silicon carbide (SiC) [<xref ref-type="bibr" rid="B1">1</xref>&#x2013;<xref ref-type="bibr" rid="B5">5</xref>], hexagonal boron nitride [<xref ref-type="bibr" rid="B6">6</xref>], and gallium nitride [<xref ref-type="bibr" rid="B7">7</xref>, <xref ref-type="bibr" rid="B8">8</xref>]. There are five primary types of color centers in diamond, including nitrogen-vacancy (NV) centers and group-IV color centers, such as silicon-vacancy centers, germanium-vacancy centers, lead-vacancy centers, and tin-vacancy centers [<xref ref-type="bibr" rid="B9">9</xref>]. In particular, the NV center in diamond has been the most studied solid-state spin defect. Its spin state can be initialized and controlled by laser and microwave, respectively [<xref ref-type="bibr" rid="B1">1</xref>&#x2013;<xref ref-type="bibr" rid="B3">3</xref>]. It has been used in various quantum technologies, such as 1.3-km spin&#x2013;photon entanglement [<xref ref-type="bibr" rid="B10">10</xref>], ten-qubit quantum register [<xref ref-type="bibr" rid="B11">11</xref>], and high-sensitivity nanoscale quantum sensing [<xref ref-type="bibr" rid="B12">12</xref>], for its excellent properties, such as large optically detected magnetic resonance (ODMR) contrast [<xref ref-type="bibr" rid="B13">13</xref>] and long spin coherence time [<xref ref-type="bibr" rid="B14">14</xref>] at room temperature. However, the lack of established nanotechnology of diamond and visible-range fluorescence of the NV center limits its wider applications, such as long-distance quantum sensing and spin-photon entanglement [<xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B15">15</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>]. Additionally, while color centers in hexagonal boron nitride have been used in quantum photonics and quantum information processing [<xref ref-type="bibr" rid="B6">6</xref>], their coherence time is limited to a few microseconds at present [<xref ref-type="bibr" rid="B6">6</xref>]. These limitations have motivated scientists to search for other color centers in different host materials.</p>
<p>SiC is a wide-bandgap semiconductor material with mature inch-scale growth and micro- and nano-fabrication technologies [<xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B15">15</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>]. It has been widely applied in high-power and high-temperature electronic devices. SiC has approximately 250 known polytypes with the hexagonal 4H&#x2013;SiC and 6H&#x2013;SiC and the cubic 3C&#x2013;SiC being the most widely used polytypes [<xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B15">15</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>]. Since the coherent control of divacancy center spin in 4H&#x2013;SiC at room temperature was first realized in 2011, color centers in SiC have drawn much attention and become one of the promising platforms for quantum information [<xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B15">15</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>]. There are two types of color centers in SiC: one is room-temperature stable bright single-photon sources, and the other is the spin defects. The fluorescence range of these bright single photon sources covers from the visible range to the telecom range, with the fluorescence counts reaching greater than 1 Mcps [<xref ref-type="bibr" rid="B18">18</xref>, <xref ref-type="bibr" rid="B19">19</xref>]. Due to the mature doping technology, integrated SiC p&#x2013;n junction single-photon diodes are also fabricated [<xref ref-type="bibr" rid="B18">18</xref>]. Similar to NV centers in diamond, there are also three main types of spin defects in SiC: silicon-vacancy centers [<xref ref-type="bibr" rid="B1">1</xref>, <xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B20">20</xref>], divacancy centers [<xref ref-type="bibr" rid="B1">1</xref>, <xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>], and nitrogen-vacancy centers [<xref ref-type="bibr" rid="B1">1</xref>, <xref ref-type="bibr" rid="B4">4</xref>, <xref ref-type="bibr" rid="B21">21</xref>&#x2013;<xref ref-type="bibr" rid="B24">24</xref>]. <xref ref-type="fig" rid="F1">Figures 1A, B, C</xref> show the atom configurations of the three main types of spin defects in SiC, respectively.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Atom configurations of the three main types of spin defects in silicon carbide. <bold>(A)</bold> Silicon-vacancy center [<xref ref-type="bibr" rid="B20">20</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature Communications [<xref ref-type="bibr" rid="B20">20</xref>], copyright (2015). <bold>(B)</bold> Divacancy center [<xref ref-type="bibr" rid="B15">15</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature [<xref ref-type="bibr" rid="B15">15</xref>], copyright (2011). <bold>(C)</bold> Nitrogen-vacancy centers [<xref ref-type="bibr" rid="B24">24</xref>], reprinted with permission from AAAS.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g001.tif"/>
</fig>
<p>All three types of spin defects have achieved efficient fabrication of single spin and have been applied in various quantum technology applications [<xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B22">22</xref>], including integrated quantum photonics [<xref ref-type="bibr" rid="B18">18</xref>, <xref ref-type="bibr" rid="B25">25</xref>], quantum information processing [<xref ref-type="bibr" rid="B15">15</xref>&#x2013;<xref ref-type="bibr" rid="B17">17</xref>], quantum networks [<xref ref-type="bibr" rid="B26">26</xref>, <xref ref-type="bibr" rid="B27">27</xref>], and quantum sensing [<xref ref-type="bibr" rid="B24">24</xref>]. In quantum photonics, nanopillars [<xref ref-type="bibr" rid="B25">25</xref>] and solid immersion lenses [<xref ref-type="bibr" rid="B17">17</xref>] have been used to enhance the silicon-vacancy center count several times. Photonic crystal cavities realize an 80-fold selective Purcell enhancement of the zero-phonon line (ZPL) for silicon-vacancy centers [<xref ref-type="bibr" rid="B28">28</xref>]. Most recently, the silicon carbide-on-insulator on-chip integrated nanophotonic cavity has efficiently enhanced the emission of a single silicon-vacancy center and the frequency conversion [<xref ref-type="bibr" rid="B29">29</xref>]. Moreover, silicon-vacancy centers can be integrated into nano-fabricated waveguide devices. In addition, the photonic crystal cavity also realizes a 50-fold Purcell enhancement of a single divacancy center [<xref ref-type="bibr" rid="B30">30</xref>]. In the quantum information process, coherent control of single silicon-vacancy and divacancy centers has been realized, demonstrating their longer coherence times of approximately 1&#xa0;ms [<xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B17">17</xref>]. The coherence time of divacancy centers has been extended to greater than 5&#xa0;s using the dynamical decoupling methods and an isotopically purified SiC sample [<xref ref-type="bibr" rid="B31">31</xref>]. High-fidelity nuclear quantum registers have been demonstrated using a single silicon-vacancy center [<xref ref-type="bibr" rid="B32">32</xref>] and divacancy center [<xref ref-type="bibr" rid="B33">33</xref>]. The spin defects have advantages in long-distance quantum networks for their near-infrared fluorescence [<xref ref-type="bibr" rid="B26">26</xref>, <xref ref-type="bibr" rid="B27">27</xref>, <xref ref-type="bibr" rid="B34">34</xref>, <xref ref-type="bibr" rid="B35">35</xref>]. A high-fidelity spin-photon interface has been realized in a single silicon-vacancy center [<xref ref-type="bibr" rid="B26">26</xref>] and divacancy center [<xref ref-type="bibr" rid="B27">27</xref>, <xref ref-type="bibr" rid="B34">34</xref>, <xref ref-type="bibr" rid="B35">35</xref>]. Moreover, the charge depletion technology has been found to narrow optical linewidths by more than 50-fold, approaching the lifetime limit [<xref ref-type="bibr" rid="B34">34</xref>]. Optical Rabi oscillations of single divacancy centers have also been realized [<xref ref-type="bibr" rid="B35">35</xref>]. All three spin defects have been widely used in high-sensitivity multiple quantum sensing, including magnetic field [<xref ref-type="bibr" rid="B36">36</xref>], electric field [<xref ref-type="bibr" rid="B37">37</xref>], temperature [<xref ref-type="bibr" rid="B38">38</xref>], strain [<xref ref-type="bibr" rid="B39">39</xref>], and pressure [<xref ref-type="bibr" rid="B40">40</xref>].</p>
<p>Given the rapid development of SiC-based quantum technologies, in this review, we discuss recent progress in the fabrication and quantum sensing of spin defects in SiC. We begin by focusing on the advances in single and ensemble fabrication methods of the three spin defects. Then, we discuss the achievements of the SiC-based multiple quantum sensing applications under atmospheric environments and high pressure. Finally, the conclusions and outlook of SiC spin defect fabrication and quantum sensing are discussed.</p>
</sec>
<sec id="s2">
<title>2 Fabrication of the three spin defects in SiC</title>
<p>Spin defects in SiC, such as the silicon-vacancy center, divacancy center, and nitrogen-vacancy centers, exhibit excellent spin and optical properties for quantum technologies [<xref ref-type="bibr" rid="B41">41</xref>&#x2013;<xref ref-type="bibr" rid="B43">43</xref>]. Efficient and controllable fabrication technologies are very important to fully realize their potential in various SiC-based quantum technologies. In this section, we first review the progress in the fabrication of three spin defects in SiC, respectively. Currently, four methods, including electron or neutron irradiation [<xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B20">20</xref>], ion implantation [<xref ref-type="bibr" rid="B44">44</xref>, <xref ref-type="bibr" rid="B45">45</xref>], focused ion beam implantation [<xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B47">47</xref>], and laser writing [<xref ref-type="bibr" rid="B48">48</xref>], have been used in the fabrication of three types of spin defects in SiC.</p>
<sec id="s2-1">
<title>2.1 Silicon-vacancy centers</title>
<p>The silicon-vacancy center is a paramagnetic defect consisting of a missing silicon atom in the SiC lattice [<xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B20">20</xref>]. The negatively charged silicon-vacancy center has the spin state <italic>S</italic> &#x3d; 3/2. There are two types of silicon-vacancy centers in 4H&#x2013;SiC: V1 and V2, and their corresponding ZPLs are 861&#xa0;nm (V1) and 915&#xa0;nm (V2), respectively [<xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B20">20</xref>, <xref ref-type="bibr" rid="B44">44</xref>&#x2013;<xref ref-type="bibr" rid="B46">46</xref>]. There are three types of silicon-vacancy centers in 6H&#x2013;SiC, the ZPLs of which are at 865&#xa0;nm (V1), 887&#xa0;nm (V2), and 908&#xa0;nm (V3), respectively [<xref ref-type="bibr" rid="B49">49</xref>]. Due to its spin state, which can be coherently controlled at room temperature, the V2 in 4H&#x2013;SiC has become the most studied type of silicon-vacancy center [<xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B20">20</xref>, <xref ref-type="bibr" rid="B44">44</xref>&#x2013;<xref ref-type="bibr" rid="B46">46</xref>]. The zero-field-splitting <italic>D</italic> of V2 is 35&#xa0;MHz.</p>
<p>In order to isolate single silicon-vacancy centers, most of the experiments use commercially available high-purity SiC samples [<xref ref-type="bibr" rid="B17">17</xref>, <xref ref-type="bibr" rid="B20">20</xref>, <xref ref-type="bibr" rid="B44">44</xref>&#x2013;<xref ref-type="bibr" rid="B46">46</xref>]. High-energy electron and neutron irradiations are used to generate single silicon-vacancy centers, and a confocal scanning microscopy image is shown in <xref ref-type="fig" rid="F2">Figure 2A</xref> [<xref ref-type="bibr" rid="B17">17</xref>]. This method can generate silicon-vacancy centers throughout the sample. Particularly, F. Fuchs et al. used neutron irradiation (0.18&#xa0;MeV&#x2013;2.5&#xa0;MeV) in a fission reactor to generate single silicon-vacancy centers [<xref ref-type="bibr" rid="B20">20</xref>]. The irradiation dose is varied over more than eight orders of magnitude, from 1 &#xd7; 10<sup>9</sup> to 5 &#xd7; 10<sup>17</sup>&#xa0;cm<sup>&#x2212;2</sup>. The single silicon-vacancy center can be observed at the level of 1 &#xd7; 10<sup>9</sup>&#xa0;cm<sup>&#x2212;2</sup>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Confocal images of silicon-vacancy centers on SiC by using different methods. <bold>(A)</bold> PL confocal map of irradiation on 4H&#x2013;SiC using 2&#xa0;MeV electrons after annealing [<xref ref-type="bibr" rid="B17">17</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B17">17</xref>], copyright (2015). <bold>(B)</bold> PL image of the ion implantation confocal map after annealing at 600&#xb0;C for 1&#xa0;h [<xref ref-type="bibr" rid="B45">45</xref>], copyright (2019), American Chemical Society. <bold>(C)</bold> PL image of focused ion implantation using Si<sup>2&#x2b;</sup> [<xref ref-type="bibr" rid="B46">46</xref>], copyright (2017), American Chemical Society. <bold>(D)</bold> PL image of laser writing at an energy from 7.4 to 13&#xa0;nJ [<xref ref-type="bibr" rid="B48">48</xref>], copyright (2019), American Chemical Society.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g002.tif"/>
</fig>
<p>Compared to irradiation, ion implantation allows color centers&#x2019; predetermined location fabrication [<xref ref-type="bibr" rid="B44">44</xref>, <xref ref-type="bibr" rid="B45">45</xref>]. Carbon, hydrogen, and helium ions are demonstrated to generate shallow single silicon vacancies over a wide dose ranging from 10<sup>11</sup>&#xa0;cm<sup>&#x2212;2</sup> to 10<sup>14</sup>&#xa0;cm<sup>&#x2212;2</sup>. With the same energy, helium ions have better implantation conversion efficiency than carbon and hydrogen ions [<xref ref-type="bibr" rid="B45">45</xref>]. After using the optimized annealing, the conversion yield can be further increased more than 2 times. High-concentration silicon ensemble defects contribute to higher sensitivity in magnetic or temperature sensing [<xref ref-type="bibr" rid="B45">45</xref>]. To generate single silicon-vacancy center arrays, a polymethyl methacrylate (PMMA) layer, usually several hundred nanometers thick, should be deposited on the SiC surface by spin coating. Electron-beam lithography (EBL) is then employed to make an array of apertures with a specific separation [<xref ref-type="bibr" rid="B44">44</xref>]. Then, holes are made before ion implantation. The stopping and range of ions in matter (SRIM) simulation shows that carbon atoms can be blocked by the PMMA layer, which leads to the generation of defects only in the SiC layer below the holes of PMMA layer. By contrast, 20&#xa0;keV helium and hydrogen ions can penetrate through the 200-nm PMMA layer. After implantation, the PMMA layer is removed in acetone, and the apertures are also cleaned by isopropanol ultrasonication. By using 30&#xa0;keV carbon ions, the single defect generation ratio is approximately 34% &#xb1; 4%, and the conversion yield of the implanted carbon ions into the silicon-vacancy defects is approximately 19% &#xb1; 4% [<xref ref-type="bibr" rid="B44">44</xref>]. Furthermore, by adding the annealing process (temperature at 600&#xb0;C for 1&#xa0;h), the conversion yield can be improved to approximately 78% &#xb1; 5%, which is approximately four times higher than unannealed results and leads to less residual radiation damage [<xref ref-type="bibr" rid="B45">45</xref>]. <xref ref-type="fig" rid="F2">Figure 2B</xref> shows the confocal image of the silicon-vacancy center array after annealing. This method can realize the on-demand generation of single silicon-vacancy centers [<xref ref-type="bibr" rid="B45">45</xref>]. However, since the ion implantation creates residual radiation damage, this method may degrade its effect on the coherence properties of silicon-vacancy centers.</p>
<p>As is mentioned in ion implantation, the determination of the location needs a PMMA mask, making it inconvenient to integrate with photonic devices [<xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B47">47</xref>, <xref ref-type="bibr" rid="B50">50</xref>]. Focused ion beam (FIB) implantation provides a method for three-dimensional silicon-vacancy center engineering, which needs no mask, and vacancies are generated by ion collision [<xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B47">47</xref>]. The depth of defects is determined and can be predicted by SRIM simulation based on the ion energy and the relationship between the ion energy loss in a particular implanted material and the depth of implantation, while the lateral distribution is controlled by the focused ion beam with nanometer resolution implemented by predesigned computer files [<xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B47">47</xref>]. The focused ion spot scale is a nanometer, and the implantation dose that determines the vacancy number can be precisely controlled by the beam current and the residence time [<xref ref-type="bibr" rid="B17">17</xref>]. So far, there are hydrogen (H<sup>&#x2b;</sup>, 1.7&#xa0;MeV) [<xref ref-type="bibr" rid="B47">47</xref>], silicon (Si<sup>2&#x2b;</sup>, 35&#xa0;keV) [<xref ref-type="bibr" rid="B46">46</xref>], and helium (He<sup>2&#x2b;</sup>, 30&#xa0;keV with a dose of 1&#xd7;10<sup>13</sup>&#xa0;cm<sup>-2</sup>) [<xref ref-type="bibr" rid="B50">50</xref>] ions used in focused ion beam implantation. The Si<sup>2&#x2b;</sup> and He<sup>2&#x2b;</sup> implantations need the annealing process to restore the lattice damage caused by implantation at 650&#xb0;C in air for 6&#xa0;h and 500&#xb0;C for 2&#xa0;h in a vacuum, respectively. In addition, in the He<sup>2&#x2b;</sup> ion implantation process, post-annealing at 600&#xb0;C in vacuum is adopted to remove the interstitial defects and reduce background fluorescence. <xref ref-type="fig" rid="F2">Figure 2C</xref> presents the PL confocal scan of focused Si<sup>2&#x2b;</sup> beam implantation. By optimizing the dose at 20 ions per spot, focused He<sup>2&#x2b;</sup> and Si<sup>2&#x2b;</sup> ion beam implantation can achieve a conversion yield of approximately 6.95% and 3.9% and a generation rate for a single silicon-vacancy center of approximately 35% and 38%, respectively [<xref ref-type="bibr" rid="B46">46</xref>, <xref ref-type="bibr" rid="B50">50</xref>].</p>
<p>All the aforementioned methods inevitably cause residual damage to the lattice, which may degrade the defects&#x2019; optical and spin properties. Femtosecond (fs) laser writing minimizes the damage to the crystal lattice and is convenient to realize on-demand location vacancy center generation in 4H&#x2013;SiC and 6H&#x2013;SiC [<xref ref-type="bibr" rid="B48">48</xref>, <xref ref-type="bibr" rid="B51">51</xref>, <xref ref-type="bibr" rid="B52">52</xref>]. A femtosecond pulsed laser with a central wavelength of 790&#xa0;nm and a duration time of 250 fs is used [<xref ref-type="bibr" rid="B48">48</xref>]. An objective is used to focus the laser beam onto the sample that is fixed on the three-dimensional highly precise translation stage. Before laser writing, samples need to be cleaned using Piranha solution to remove organic contaminants [<xref ref-type="bibr" rid="B18">18</xref>&#x2013;<xref ref-type="bibr" rid="B20">20</xref>]. Generally, the separation between arrays is 5&#xa0;&#x3bc;m, and laser energy from several to hundreds of nanojoules is performed per pulse for each line. <xref ref-type="fig" rid="F2">Figure 2D</xref> shows the confocal image after different energy laser writing. Experimental results get an optically stable single V<sub>Si</sub> yield of up to 30% and a lateral position accuracy of 80&#xa0;nm without post-annealing, which is sufficient for coupling V<sub>Si</sub> centers to optical structures, such as multi-mode waveguides, solid immersion lenses, or nanopillars. However, to enhance the photostability and yield, an extra annealing process can be employed. Moreover, the pulse laser can also be used to ablate 4H&#x2013;SiC nanoparticles with silicon-vacancy centers [<xref ref-type="bibr" rid="B53">53</xref>].</p>
</sec>
<sec id="s2-2">
<title>2.2 Divacancy centers</title>
<p>Divacancy centers in SiC consist of a missing Si atom adjacent to a missing C atom, and the neutrally charged divacancy centers have spin state <italic>S</italic> &#x3d; 1 [<xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>]. Divacancy centers exist in three polytypes of SiC: 4H&#x2013;, 6H&#x2013;, and 3C&#x2013;SiC [<xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B54">54</xref>]. There are seven types of divacancy centers in 4H&#x2013;SiC, named PL1&#x2013;PL7. Similarly, there are also six types of divacancy centers in 6H&#x2013;SiC, named QL1&#x2013;QL6. There is only one type of divacancy center in 3C&#x2013;SiC. Since the ODMR contrast and coherence time of the divacancy centers in 4H&#x2013;SiC are larger than those of divacancy centers in 6H&#x2013;SiC, most experiments focus on the divacancy centers in 4H&#x2013;SiC [<xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B54">54</xref>]. The basic method for generating divacancy centers by irradiation is the same as for generating silicon-vacancy centers. Using 2&#xa0;MeV electrons with a dose ranging from 5 &#xd7; 10<sup>12</sup>&#xa0;cm<sup>&#x2212;2</sup> (for generation single divacancy centers) to 1 &#xd7; 10<sup>15</sup>&#xa0;cm<sup>&#x2212;2</sup> to generate Si and C vacancies uniformly, followed by annealing at 750&#xb0;C or 850&#xb0;C (for neutral VV<sup>0</sup>) for 30&#xa0;min in Ar gas, enables Si and C vacancies to migrate and form divacancies [<xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B27">27</xref>]. As shown in <xref ref-type="fig" rid="F3">Figures 3A, 3B</xref>, this method has been used to generate single divacancy centers in 4H&#x2013; and 3C&#x2013;SiC [<xref ref-type="bibr" rid="B16">16</xref>, <xref ref-type="bibr" rid="B27">27</xref>]. However, the position of the divacancy center is random.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Confocal images of divacancy centers on SiC by using different methods and materials. <bold>(A)</bold> Irradiation at 10<sup>13</sup>&#xa0;cm<sup>&#x2212;2</sup> fluence at a depth of 20&#xa0;&#xb5;m into the 4H&#x2013;SiC membrane [<xref ref-type="bibr" rid="B16">16</xref>]. Not all spots are isolated single defects, reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B16">16</xref>], copyright (2015). <bold>(B)</bold> PL scan of 3C&#x2013;SiC by irradiation [<xref ref-type="bibr" rid="B27">27</xref>], copyright (2017), American Physical Society. <bold>(C)</bold> 30&#xa0;keV carbon ion implantation on 4H&#x2013;SiC [<xref ref-type="bibr" rid="B55">55</xref>], copyright (2021), China Science Publishing &#x26; Media Ltd. <bold>(D)</bold> Laser writing PL confocal image. No dots are observed under 28.8&#xa0;nJ [<xref ref-type="bibr" rid="B56">56</xref>], reprinted with permission from Almutairi AFM et al., Copyright (2022), AIP Publishing LLC.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g003.tif"/>
</fig>
<p>Similar to silicon-vacancy center generation using ion implantation, divacancy centers can be fabricated in the same way. A 200-nm-thick positive electron-beam photoresist PMMA layer is spin-coated onto the sample surface. EBL is performed to create a mask, on which an array of apertures with a separation distance of 2&#xa0;&#x3bc;m and a diameter of 50 &#xb1; 10&#xa0;nm are produced [<xref ref-type="bibr" rid="B55">55</xref>]. 30&#xa0;keV&#xa0;C<sup>&#x2b;</sup> with a dose of 1.02 &#xd7; 10<sup>15</sup>&#xa0;cm<sup>&#x2212;2</sup> are implanted, making approximately 20 ions per spot. The results are shown in <xref ref-type="fig" rid="F3">Figure 3C</xref>. After removing the mask in acetone solution with an ultrasonic bath, the sample is annealed at 900&#xb0;C for 30&#xa0;min in vacuum [<xref ref-type="bibr" rid="B55">55</xref>]. To reduce background fluorescence, the sample was cleaned again in a mixture of concentrated sulfuric acid and hydrogen peroxide with a ratio of 3:1 [<xref ref-type="bibr" rid="B23">23</xref>]. This method generates different types of divacancy centers. The coherent manipulation of single PL6 divacancy center spins in 4H&#x2013;SiC with a high readout contrast (30%) and a high photon count rate (150&#xa0;kcps) at room temperature is demonstrated [<xref ref-type="bibr" rid="B55">55</xref>]. The coupling between a single divacancy spin and a nearby silicon nuclear spin is also observed.</p>
<p>As divacancy centers generated by electron irradiation are randomly distributed, ion implantation with a PMMA mask causes residual lattice damage, and shallow color centers limit some applications, laser writing is adopted. Using a high-purity 4H&#x2013;SiC sample as the host material, with a laser wavelength of 1,030&#xa0;nm, and writing in an argon atmosphere [<xref ref-type="bibr" rid="B56">56</xref>], the procedure for generating divacancy centers is the same as that for silicon-vacancy centers. As presented in <xref ref-type="fig" rid="F3">Figure 3D</xref>, divacancy centers in the same row are formed with the same laser energy of 230, 115, 57.7, and 28.8 nJ, respectively [<xref ref-type="bibr" rid="B56">56</xref>]. The post-annealing method is performed from 500&#xb0;C to 1,000&#xb0;C in a step of 100&#xb0;C for 30&#xa0;min in argon gas. Results show that the optimized annealing temperature is 800&#xa0;&#xb0;C [<xref ref-type="bibr" rid="B56">56</xref>].</p>
</sec>
<sec id="s2-3">
<title>2.3 Nitrogen-vacancy center</title>
<p>The N<sub>C</sub>V<sub>Si</sub> center in SiC consists of a nitrogen impurity substituting a carbon atom (N<sub>C</sub>) and a silicon vacancy (V<sub>Si</sub>) adjacent to it [<xref ref-type="bibr" rid="B21">21</xref>&#x2013;<xref ref-type="bibr" rid="B24">24</xref>]. It can be observed in three polytypes of SiC: 4H&#x2013;, 6H&#x2013;, and 3C&#x2013;SiC [<xref ref-type="bibr" rid="B21">21</xref>&#x2013;<xref ref-type="bibr" rid="B24">24</xref>, <xref ref-type="bibr" rid="B57">57</xref>, <xref ref-type="bibr" rid="B58">58</xref>]. The negatively charged state NV center has a spin state of 1. In n-type 4H&#x2013;SiC, 12&#xa0;MeV proton irradiation with a dose of 1 &#xd7; 10<sup>14</sup>&#xa0;cm<sup>-2</sup> and post-annealing at 900&#xb0;C can create NV centers [<xref ref-type="bibr" rid="B21">21</xref>]. High-energy protons and electrons can cause point defects, while heavy ions generate large residual lattice damage [<xref ref-type="bibr" rid="B21">21</xref>]. Except for n-type 4H&#x2013;SiC with a nitrogen concentration of 10<sup>18</sup>&#xa0;cm<sup>&#x2212;3</sup>, high-purity semi-insulting 4H&#x2013;SiC (nitrogen concentration &#x3d; 3 &#xd7; 10<sup>15</sup>&#xa0;cm<sup>&#x2212;2</sup>) is also used in NV center generation. Various ions, such as 240&#xa0;keV hydrogen, 2&#xa0;MeV nitrogen, 4&#xa0;MeV silicon, and 7&#xa0;MeV iodine ion beams, are utilized for irradiation to generate the NV center ensemble, as shown in <xref ref-type="fig" rid="F4">Figure 4A</xref> [<xref ref-type="bibr" rid="B59">59</xref>]. Then, all samples are annealed in Ar gas (1 &#xd7; 10<sup>5</sup>&#xa0;Pa) at different temperatures for 30&#xa0;min and naturally cooled down to room temperature. Results show that 1,000&#xb0;C is the optimal annealing temperature to generate NV centers [<xref ref-type="bibr" rid="B59">59</xref>].</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Confocal images of NV centers in 4H&#x2013;SiC by using different methods and calculations of PL integrated intensity as a function of vacancy centers per area. <bold>(A)</bold> PL integrated intensity of the NV centers as a function of vacancy centers per area [<xref ref-type="bibr" rid="B59">59</xref>], reprinted with permission from Sato SI et al., Copyright (2019), AIP Publishing LLC. <bold>(B)</bold> PL images of the NV center ensemble by carbon ion implantation after annealing at 1,050&#xb0;C [<xref ref-type="bibr" rid="B22">22</xref>], copyright (2020), American Physical Society. <bold>(C)</bold> Confocal scan image of the single NV center array [<xref ref-type="bibr" rid="B22">22</xref>], copyright (2020), American Physical Society. <bold>(D)</bold> Confocal scan image of single NV centers at a low dose (10<sup>10</sup>/cm<sup>2</sup>) [<xref ref-type="bibr" rid="B23">23</xref>], copyright (2020), American Chemical Society.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g004.tif"/>
</fig>
<p>In addition, as shown in <xref ref-type="fig" rid="F4">Figure 4B</xref>, 30&#xa0;keV nitrogen ion implantation (dose 1 &#xd7; 10<sup>14</sup>&#xa0;cm<sup>&#x2212;2</sup>) can create shallow single NV center ensemble at a depth of 60&#xa0;nm in a bulk high-purity 4H&#x2013;SiC epitaxy layer sample. After annealing under optimal conditions at 1,050&#xb0;C for 2&#xa0;h, NV centers&#x2019; concentration can increase by six times. Using the masked implantation methods, the single NV center array is generated. <xref ref-type="fig" rid="F4">Figures 4C, 4D</xref> show confocal images of the single NV center array by nitrogen ion implantation. The single defect generation efficiency is around 30%, and the conversion yield of the implanted nitrogen ions into the NV center is approximately 4.3% [<xref ref-type="bibr" rid="B22">22</xref>]. The NV centers are proven as a three-energy-level electronic structure system. Both the excitation and the emission polarization degrees are approximately 90% for <italic>c</italic>-axis NV centers [<xref ref-type="bibr" rid="B60">60</xref>].</p>
</sec>
</sec>
<sec id="s3">
<title>3 Quantum sensing</title>
<p>Color centers in SiC have been applied to various quantum sensing fields, such as magnetic field, electric field, temperature, strain, and pressure [<xref ref-type="bibr" rid="B36">36</xref>&#x2013;<xref ref-type="bibr" rid="B40">40</xref>]. They have some advantages, including high sensitivity and high spatial resolution under ambient conditions. Combined with mature micro- and nano-fabrication and growth technologies of SiC, SiC color center-based quantum sensing will have widespread applications [<xref ref-type="bibr" rid="B36">36</xref>&#x2013;<xref ref-type="bibr" rid="B40">40</xref>]. <xref ref-type="fig" rid="F5">Figure 5</xref> shows the Hamiltonian of the spin defects&#x2019; spin state and their relevant physical parameters [<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B61">61</xref>, <xref ref-type="bibr" rid="B62">62</xref>]. The spin state S is 1 for the divacancy and NV centers in SiC, and it is 3/2 for the silicon-vacancy centers in SiC. The electron gyromagnetic ratio <italic>&#x3b3;</italic> is 2.8&#xa0;MHz/G. The first item is zero-field splitting (ZFS), and <italic>D</italic> is related to temperature and pressure, which can be used for temperature sensing and pressure sensing [<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B62">62</xref>]. The second item is the Zeeman splitting, which can be used for magnetic field sensing, and the last item is the Stark effect, which can be used for electric field and strain [<xref ref-type="bibr" rid="B3">3</xref>, <xref ref-type="bibr" rid="B62">62</xref>]. We then discuss the progress of these various quantum sensing methods in detail.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Spin Hamiltonian of the spin defects in SiC and related quantum sensing physical quantities for each term of the Hamiltonian.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g005.tif"/>
</fig>
<sec id="s3-1">
<title>3.1 Magnetic field sensing</title>
<p>Since these color centers in SiC are spin defects, one of the main quantum sensing is magnetic field sensing through measuring the Zeeman splitting [<xref ref-type="bibr" rid="B36">36</xref>]. SiC offers a platform for wafer-scale quantum sensing at room temperature, benefiting from its mature fabrication and generation technologies. Continuous wave ODMR is the most useful and simplest magnetic field detection method [<xref ref-type="bibr" rid="B36">36</xref>, <xref ref-type="bibr" rid="B63">63</xref>&#x2013;<xref ref-type="bibr" rid="B66">66</xref>]. The ODMR magnetic field sensitivity is [<xref ref-type="bibr" rid="B63">63</xref>] <inline-formula id="inf1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mo>&#x2248;</mml:mo>
<mml:mfrac>
<mml:mi>h</mml:mi>
<mml:mrow>
<mml:mi>g</mml:mi>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mfrac>
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:msqrt>
<mml:mi>R</mml:mi>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>, where <italic>h</italic> is the Planck constant, <italic>C</italic> is the ODMR contrast, <italic>R</italic> is the count rate of detected photons, and <inline-formula id="inf2">
<mml:math id="m2">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>&#x3bd;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the linewidth of the ODMR spectra. By measuring the evolution of the ODMR spectra with respect to the polar angle <italic>&#x3b8;</italic> and the strength of the magnetic field, we can get the polar angle of the external magnetic field [<xref ref-type="bibr" rid="B66">66</xref>]. The strength and angle sensitivity are approximately 10&#xa0;&#x3bc;T/Hz<sup>1/2</sup> and 0.5&#xb0;/Hz<sup>1/2</sup>, respectively [<xref ref-type="bibr" rid="B66">66</xref>]. Moreover, both the ODMR contrast and frequency of the divacancy center vary with the off-axis magnetic field angle and strength, paving the way for SiC-based all-optical magnetic field imaging and sensing [<xref ref-type="bibr" rid="B67">67</xref>]. Additionally, the coherence time also decreases with the polar angle <italic>&#x3b8;</italic> of the magnetic field. All optical methods require no RF system, which makes it easier for practical uses and more stable in complex environments. Simin et al. found a sharp variation of the photoluminescence intensity in the vicinity of level anticrossing (1.25&#xa0;mT) of the silicon-vacancy center as shown in <xref ref-type="fig" rid="F6">Figure 6A</xref>, giving the basis for all-optical sensing of the magnetic field as shown in <xref ref-type="fig" rid="F6">Figure 6B</xref> [<xref ref-type="bibr" rid="B68">68</xref>]. The DC magnetic field sensitivity is better than 100&#xa0;nT/Hz<sup>1/2</sup> within a volume of 3 &#xd7; 10<sup>&#x2212;7</sup>&#xa0;mm<sup>3</sup> for isotopically purified 4H&#x2013;<sup>28</sup>SiC at room temperature [<xref ref-type="bibr" rid="B68">68</xref>]. Since it does not need a microwave, it will be easier to improve the sensitivity by using larger-volume samples. Using three Helmholtz coil pairs, silicon-vacancy centers-based vector magnetometry can be realized.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Magnetometry sensitivity maps and set-up images. <bold>(A)</bold> Experimental results of the angle evolution of V<sub>si</sub> ODMR spectra under an external magnetic field of <italic>B</italic> &#x3d; 0.8&#xa0;mT [<xref ref-type="bibr" rid="B66">66</xref>], copyright (2015), American Physical Society. <bold>(B)</bold> Lock in signal in-phase <italic>Ux</italic> and quadrature <italic>Uy</italic> as a function of sub-&#x3bc;T magnetic fields. The magnetic field increases in the sub-&#x3bc;T level every 125&#xa0;s [<xref ref-type="bibr" rid="B68">68</xref>], copyright (2016), American Physical Society. <bold>(C)</bold> The magnetometry sensitivity as a function of laser power and Rabi frequency [<xref ref-type="bibr" rid="B64">64</xref>], copyright (2020), American Physical Society. <bold>(D)</bold> Pulsed ODMR spectra in the same magnetic field and at the same angle but using different pulse sequences. (a) Sweep pulse. (b) A <italic>&#x3c0;</italic> pulse before the sweep pulse. (c) A <italic>&#x3c0;</italic> pulse before and after the sweep pulse [<xref ref-type="bibr" rid="B36">36</xref>], copyright (2016), American Physical Society. <bold>(E)</bold> The shot-noise-limited sensitivity map in magnetometry after thermal quenching [<xref ref-type="bibr" rid="B65">65</xref>], copyright (2021), American Physical Society. <bold>(F)</bold> Images of the fiber-integrated probe. The probe consists of a multi-mode fiber tip, a copper wire, and a SiC sample pasted on the fiber tip. b, c, d, and e are pictures of the probe at different angles [<xref ref-type="bibr" rid="B69">69</xref>], copyright (2023), Optica Publishing Group.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g006.tif"/>
</fig>
<p>The linewidth of the ODMR is fundamentally limited by the dephasing time <italic>T</italic>
<sub>2</sub>
<sup>&#x2217;</sup> of the spin defects [<xref ref-type="bibr" rid="B63">63</xref>]. The laser- and MW-dependent power broadening also affects the ODMR linewidth [<xref ref-type="bibr" rid="B63">63</xref>, <xref ref-type="bibr" rid="B64">64</xref>]. Increasing the ODMR contrast and decreasing the ODMR linewidth will generate higher sensitivity. Wang J. F. et al. investigated the ODMR contrast and linewidth as functions of laser power and the microwave (MW) power of the divacancy center at room temperature [<xref ref-type="bibr" rid="B64">64</xref>]. The results show that the ODMR contrast decreases with the laser power, while the ODMR linewidth only slightly increases as the laser power increases [<xref ref-type="bibr" rid="B64">64</xref>]. Both the ODMR contrast and the linewidth increase with the MW power. Finally, they present a two-dimensional experimental magnetic field sensitivity image as a function of laser and MW power as shown in <xref ref-type="fig" rid="F6">Figure 6C</xref>. The sensitivity increases by approximately 10 times (4&#xa0;&#x3bc;T/Hz<sup>1/2</sup>) for the optimized laser and MW power range [<xref ref-type="bibr" rid="B64">64</xref>]. In order to further decrease the linewidth of the ODMR, the pulsed ODMR spectra are used in the experiments as shown in <xref ref-type="fig" rid="F6">Figure 6D</xref> [<xref ref-type="bibr" rid="B36">36</xref>]. The linewidth can be reached at approximately 500&#xa0;kHz, which causes a sensitivity of 200&#xa0;&#x3bc;T/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B36">36</xref>].</p>
<p>The ODMR contrast is one of the main factors limiting the SiC defects&#x2019; sensitivity. Recently, a study found that the ODMR contrast and count rate can increase approximately ten and two times by using thermally quenched methods as shown in <xref ref-type="fig" rid="F6">Figure 6E</xref> [<xref ref-type="bibr" rid="B65">65</xref>]. After optimizing the laser and microwave power broadening of the ODMR, the experimental sensitivity can increase to approximately 3.5&#xa0;nT/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B65">65</xref>]. However, all the previous magnetometers use the confocal system, which is not suitable for applications in practical environments. To further increase the capability of the magnetometer and make it compatible with practical environments, it needs to integrate the silicon-vacancy center-based magnetometer with optical fiber [<xref ref-type="bibr" rid="B69">69</xref>, <xref ref-type="bibr" rid="B70">70</xref>]. SiC is a technology-friendly semiconductor material, which has mature growth and fabrication techniques. SiC-based magnetic field sensing is compatible with the semiconductor industry and could be widely used. Moreover, since the wavelengths of the spin defects in SiC are near-infrared, they are useful for long-distance magnetometry. Quan W. K. et al. realized the fiber-integrated SiC-based magnetometer [<xref ref-type="bibr" rid="B69">69</xref>, <xref ref-type="bibr" rid="B70">70</xref>]. As shown in <xref ref-type="fig" rid="F6">Figure 6F</xref> they pasted a pasted a 100-&#xb5;m-diameter sample on a fiber tip and realized an efficient coupling of the silicon-vacancy and divacancy centers with the fiber. After optimizing the laser and MW powers broadening the linewidth of ODMR peaks, they obtained a sensitivity of 12.3&#xa0;&#x3bc;T/Hz<sup>1/2</sup> and 3.9&#xa0;&#x3bc;T/Hz<sup>1/2</sup>, respectively [<xref ref-type="bibr" rid="B69">69</xref>, <xref ref-type="bibr" rid="B70">70</xref>]. It has been used to sense external magnetic field strength and angle.</p>
</sec>
<sec id="s3-2">
<title>3.2 Temperature sensing</title>
<p>The basic principle of SiC-based temperature sensing is that the ground zero-field-splitting (ZFS) <italic>D</italic> of the divacancy center decreases with the temperature [<xref ref-type="bibr" rid="B38">38</xref>, <xref ref-type="bibr" rid="B71">71</xref>, <xref ref-type="bibr" rid="B72">72</xref>]. The three types of divacancy centers&#x2019; <italic>D</italic> parameters in 4H&#x2013;SiC decrease when the temperature increases, and PL5 and PL6 divacancy centers&#x2019; ZFS linearly decrease around room temperature with a slope of approximately &#x2212;109.5 and 100&#xa0;kHz/Hz<sup>1/2</sup> as shown in <xref ref-type="fig" rid="F7">Figure 7A</xref>, respectively. Those values are approximately 1.5 times larger than that of the NV centers in diamond [<xref ref-type="bibr" rid="B38">38</xref>, <xref ref-type="bibr" rid="B73">73</xref>]. On this basis, the Ramsey methods have been used to measure the temperatures and the results are shown in <xref ref-type="fig" rid="F7">Figure 7B</xref>. The dephasing time <italic>T</italic>
<sub>2</sub>
<sup>&#x2a;</sup> is approximately 2&#xa0;&#x3bc;s, and it does not change as the temperature decreases from 300&#xa0;K to 20&#xa0;K [<xref ref-type="bibr" rid="B38">38</xref>]. The change of the Ramsey oscillation frequency is due to the change of the temperature, which can be used for temperature sensing. The sensitivity is<disp-formula id="e1">
<mml:math id="m3">
<mml:mrow>
<mml:mi>&#x3b7;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msqrt>
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<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mrow>
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<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
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</mml:mrow>
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<mml:mrow>
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<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mfrac>
</mml:msqrt>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>D</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>T</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>d</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msqrt>
<mml:mi>t</mml:mi>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the photon counts in the dark and bright spin states per shot, respectively [<xref ref-type="bibr" rid="B38">38</xref>, <xref ref-type="bibr" rid="B74">74</xref>]. <italic>dD/dT</italic> is the slope of the divacancy centers&#x2019; ZFS with temperature, and <italic>T</italic>
<sub>
<italic>d</italic>
</sub> is the coherence time. The sensitivity is approximately 206&#xa0;mK/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B38">38</xref>]. Since the PL5 is a basal divacancy center with a large transverse strain E, it can protect the temperature sensor against magnetic field noise [<xref ref-type="bibr" rid="B38">38</xref>]. This is useful for practical environments. Moreover, it can also be used to sense higher temperatures. The experiments show that both the value of ZFS and ODMR contrast of the ZFS of the PL5 divacancy centers decrease as the temperature increases from 300&#xa0;K to 600&#xa0;K. The dephasing time <italic>T</italic>
<sub>2</sub>
<sup>&#x2a;</sup> decreases with temperature [<xref ref-type="bibr" rid="B75">75</xref>]. A Ramsey-based temperature sensing at approximately 450&#xa0;K is realized, and the sensitivity is approximately 880&#xa0;mK/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B75">75</xref>]. Moreover, the anti-Stokes excited counts obviously increases as temperature ranges from 300 to 500&#xa0;K, which is suitable for all fast optical temperature sensing applications [<xref ref-type="bibr" rid="B76">76</xref>].</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>ODMR, Ramsey, and TCPMG measurements under different temperatures. <bold>(A)</bold> ODMR resonant frequency as a function of temperature [<xref ref-type="bibr" rid="B38">38</xref>]. The blue line is a linear fitting to the data, copyright (2017), American Physical Society. <bold>(B)</bold> Ramsey oscillation under three representative temperatures [<xref ref-type="bibr" rid="B38">38</xref>], copyright (2017), American Physical Society. <bold>(C)</bold> The ground-state (GS) and excited-state (ES) ZFS as a function of temperature [<xref ref-type="bibr" rid="B77">77</xref>], reprinted with permission from Macmillan Publishers Ltd.: Scientific Reports [<xref ref-type="bibr" rid="B77">77</xref>], copyright (2016). <bold>(D)</bold> The TCPMG-N pulse sequences and corresponding coherence time experimental results [<xref ref-type="bibr" rid="B73">73</xref>], copyright (2023), the Royal Society of Chemistry.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g007.tif"/>
</fig>
<p>Except for the ground-state ZFS, the excited-state ZFS can also be used for temperature sensing [<xref ref-type="bibr" rid="B77">77</xref>, <xref ref-type="bibr" rid="B78">78</xref>]. The ground-state ZFS of the silicon-vacancy centers in SiC does not change as the temperature decreases from 320&#xa0;K to approximately 20&#xa0;K, which is due to Kramers&#x2019; theorem [<xref ref-type="bibr" rid="B76">76</xref>, <xref ref-type="bibr" rid="B77">77</xref>, <xref ref-type="bibr" rid="B79">79</xref>]. The half-integer spin system is insensitive to fluctuations in strain, temperature, and electric field [<xref ref-type="bibr" rid="B79">79</xref>]. However, as shown in <xref ref-type="fig" rid="F7">Figure 7C</xref>, the excited-state ZFS is found to have a large thermal shift of 2.1&#xa0;MHz/K in 4H&#x2013;SiC, and the sensitivity is approximately 100&#xa0;mK/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B77">77</xref>]. Combined with the 4H&#x2013;SiC p&#x2013;n diode using proton beam writing, the temperature change induced by an injected current is measured [<xref ref-type="bibr" rid="B78">78</xref>]. The results pave the way for practical applications inside SiC power devices like thermometers. In order to further increase the sensitivity, the coherence time needs to be further increased. The thermal Carr&#x2013;Purcell&#x2013;Meiboom&#x2013;Gill (TCPMG) methods are performed on the PL6 divacancy center at room temperature [<xref ref-type="bibr" rid="B73">73</xref>]. As shown in <xref ref-type="fig" rid="F7">Figure 7D</xref>, the coherence time linearly increases with the pulse numbers, and the longest coherence time is approximately 21&#xa0;&#x3bc;s, which is 10 times higher than <italic>T</italic>
<sub>2</sub>
<sup>&#x2a;</sup>. The corresponding sensitivity is 13.4&#xa0;mK/Hz<sup>1/2</sup>, which is approximately 15 times higher than that of the Ramsey results [<xref ref-type="bibr" rid="B73">73</xref>]. In order to apply the SiC-based thermometer to practical environments, fiber-coupled PL5 divacancy center thermometers are prepared. A 100-&#x3bc;m-diameter SiC with divacancy centers is pasted on the fiber tips. The ODMR and Ramsey methods are used for wide-range and highly precise temperature sensing, respectively. The sensitivity can reach approximately 163&#xa0;mK/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B70">70</xref>].</p>
</sec>
<sec id="s3-3">
<title>3.3 Electric field sensing</title>
<p>The basic principle of electric field sensing of spin defects in SiC is the Stark effect. For divacancy centers, their Hamiltonian (the defects are <bold>
<italic>z</italic>
</bold>-axis) is as follows [<xref ref-type="bibr" rid="B39">39</xref>]:<disp-formula id="e2">
<mml:math id="m6">
<mml:mrow>
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<mml:mo>&#x3d;</mml:mo>
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<mml:msub>
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<mml:mi>z</mml:mi>
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<mml:msub>
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</mml:msub>
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<mml:mi>y</mml:mi>
</mml:msub>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>g</mml:mi>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>B</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
<mml:mo>&#xb7;</mml:mo>
<mml:mi mathvariant="bold-italic">B</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
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<mml:mi>x</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where <italic>h</italic> is Planck&#x2019;s constant; <italic>D</italic>, <italic>Ex</italic>, and <italic>Ey</italic> are the zero-magnetic-field splitting parameters, g is the electron g factor, <italic>&#x3bc;</italic>
<sub>
<italic>B</italic>
</sub> is the Bohr magneton, <bold>
<italic>B</italic>
</bold> is the magnetic field, and <bold>
<italic>&#x3c3;</italic>
</bold> is the vector of spin-1 Pauli matrices. <italic>D</italic> can be written as <inline-formula id="inf5">
<mml:math id="m7">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
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<mml:mn>0</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mo>&#x2225;</mml:mo>
</mml:msub>
<mml:mi>F</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf6">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
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<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
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<mml:msubsup>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mn>0</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mo>&#x22a5;</mml:mo>
</mml:msub>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <italic>D</italic>
<sup>0</sup> and <italic>E</italic>
<sup>0</sup>
<sub>
<italic>x,y</italic>
</sub> terms are the crystal-field splittings in the absence of applied strain and electric fields and <inline-formula id="inf7">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mo>&#x22a5;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf8">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>d</mml:mi>
<mml:mo>&#x2225;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the Stark coupling parameters of the ground-state spin to an electric field F [<xref ref-type="bibr" rid="B39">39</xref>].</p>
<p>In order to detect the AC electric field, the &#xb1; <italic>V</italic>
<sub>mem</sub> pulses are applied across a 53-&#x3bc;m-thick SiC membrane sample with divacancy centers (see <xref ref-type="fig" rid="F8">Figure 8A</xref>). The Hahn-echo pulse scheme is used for T<sub>2</sub>-limited AC electric field sensing [<xref ref-type="bibr" rid="B39">39</xref>]. During the free evolution periods, <italic>V</italic>
<sub>mem</sub> pulses can cause an electric field-induced phase shift of the spin superposition. Five types of divacancy centers, including both basal and c-axis-oriented, are used to measure the electric field both at 20&#xa0;K and 300&#xa0;K [<xref ref-type="bibr" rid="B39">39</xref>]. The fits use exponentially decaying sine curves, and fitted frequencies are spin&#x2013;electric field coupling parameters. Experimentally measured and calculated Stark parameters for the PL1&#x2013;PL6 ground-state-spin Hamiltonians in 4H&#x2013;SiC are shown in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Experimental setup and measurements under different electric fields. <bold>(A)</bold> Schematic of the SiC sample and the voltage applied on the sample for electric field measurement (upper part) and experimental results by utilizing the pulse sequence (lower part) [<xref ref-type="bibr" rid="B39">39</xref>], copyright (2014), American Physical Society. <bold>(B)</bold> Pulse sequence used in measurement (upper part) and the normalized PL at different electric fields (lower part) [<xref ref-type="bibr" rid="B37">37</xref>], reproduced from [<xref ref-type="bibr" rid="B37">37</xref>], CC BY 4.0. <bold>(C)</bold> R shift as a function of the electric field. The points are experimental results, and the black line is the fitting by using the model [<xref ref-type="bibr" rid="B37">37</xref>], reproduced from [<xref ref-type="bibr" rid="B37">37</xref>], CC BY 4.0. <bold>(D)</bold> EOCC contrast as a function of the electric field under different temperatures by using silicon-vacancy centers [<xref ref-type="bibr" rid="B37">37</xref>], reproduced from [<xref ref-type="bibr" rid="B37">37</xref>], CC BY 4.0.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g008.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Experimentally measured and calculated Stark parameters for the PL1&#x2013;PL6 ground-state-spin Hamiltonians in 4H&#x2013;SiC [<xref ref-type="bibr" rid="B39">39</xref>], copyright (2014), American Physical Society.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Defect<bold>/</bold>configuration</th>
<th colspan="2" align="center">Experiment</th>
<th colspan="2" align="center">Theory</th>
</tr>
<tr>
<th align="center">
<italic>d</italic>
<sub>&#x22a5;</sub>
</th>
<th align="center">
<italic>d</italic>
<sub>&#x7c;&#x7c;</sub>
</th>
<th align="center">
<italic>d</italic>
<sub>&#x22a5;</sub>
</th>
<th align="center">
<italic>d</italic>
<sub>&#x7c;&#x7c;</sub>
<sup>
<italic>a</italic>
</sup>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">NV center</td>
<td align="center">17</td>
<td align="center">0.35</td>
<td align="center">0.76</td>
<td align="left"/>
</tr>
<tr>
<td align="left">PL1 (hh)</td>
<td align="left"/>
<td align="center">2.65</td>
<td align="center">5.2</td>
<td align="center">0.38</td>
</tr>
<tr>
<td align="left">PL2 (kk)</td>
<td align="left"/>
<td align="center">1.61</td>
<td align="center">4.2</td>
<td align="center">0.23</td>
</tr>
<tr>
<td align="left">Ratio of PL1: NV</td>
<td align="left"/>
<td align="center">7.6:1</td>
<td align="center">6.8:1</td>
<td align="center">0.5:1</td>
</tr>
<tr>
<td align="left">Ratio of PL2: NV</td>
<td align="left"/>
<td align="center">4.6:1</td>
<td align="center">5.5:1</td>
<td align="center">0.3:1</td>
</tr>
<tr>
<td align="left">PL3 (hk)</td>
<td align="center">32.3</td>
<td align="center">&#x3c;3</td>
<td align="center">0.41</td>
<td align="left"/>
</tr>
<tr>
<td align="left">PL4 (kh)</td>
<td align="center">28.5</td>
<td align="center">0.44</td>
<td align="center">0.79</td>
<td align="left"/>
</tr>
<tr>
<td align="left">PL5</td>
<td align="center">32.5</td>
<td align="center">&#x3c;3</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">PL6</td>
<td align="left"/>
<td align="center">0.96</td>
<td align="left"/>
<td align="left"/>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="Tfn1">
<label>
<sup>a</sup>
</label>
<p>Calculated with only the atom-distortion effect.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Except for the spin methods, all-optical method electrometry is also realized. The optical charge conversion (OCC) rate between the bright and dark charge states of both divacancy and silicon-vacancy centers is strongly modulated by the applied microwave (megahertz to gigahertz) electric field and, therefore, can be used to detect the electric field through changes in photoluminescence (PL). G. Wolfowicz et al. characterized OCC transient decays by resetting the charge state with 405&#xa0;nm illumination followed by a 976-nm pump laser (pulse sequence is shown at the top of <xref ref-type="fig" rid="F8">Figure 8B</xref>) [<xref ref-type="bibr" rid="B37">37</xref>]. As shown in <xref ref-type="fig" rid="F8">Figure 8B</xref>, the decay can be fitted by an exponential decay function: <italic>f</italic>(<italic>t</italic>) is exp (&#x2212;(<italic>Rt</italic>)<sup>n</sup>), where R is the decay time. The electric field-induced changed <italic>R</italic> is <inline-formula id="inf9">
<mml:math id="m11">
<mml:mrow>
<mml:mo>&#x394;</mml:mo>
<mml:mi>R</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x394;</mml:mo>
<mml:msub>
<mml:mi>R</mml:mi>
<mml:mi>&#x221e;</mml:mi>
</mml:msub>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2329;</mml:mo>
<mml:mrow>
<mml:mrow>
<mml:mfrac>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mtext>sat</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mtext>sat</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mrow>
<mml:mo>&#x232A;</mml:mo>
</mml:mrow>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf20">
<mml:math id="m20">
<mml:mrow>
<mml:mo>&#x2329;</mml:mo>
<mml:mo>&#x232A;</mml:mo>
<mml:mi mathvariant="normal">t</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> corresponds to a time average over an oscillation of the RF electric field, <italic>E</italic>
<sub>sat</sub> is the root-mean-square amplitude of the saturation electric field, and &#x394;<italic>R</italic>
<sub>&#x221e;</sub> is the maximum <italic>R</italic> shift when <italic>E</italic>
<sub>sat</sub> changes [<xref ref-type="bibr" rid="B37">37</xref>]. They found in this sample &#x394;<italic>R</italic>
<sub>&#x221e;</sub> &#x3d; 27 &#xb1; 1% and <italic>E</italic>
<sub>sat</sub> &#x3d; 158 &#xb1; 20&#xa0;V/cm for the divacancy center. <xref ref-type="fig" rid="F8">Figure 8C</xref> presents the <italic>R</italic> shift as a function of the electric field. The OCC sensitivity increases with the 976&#xa0;nm laser power. As shown in <xref ref-type="fig" rid="F8">Figure 8D</xref>, the OCC methods can also be used for silicon-vacancy center-based electric field sensing for a wide temperature range. The optimized measured OCC sensitivity can reach 41 &#xb1; 8 (V/cm)<sup>2</sup>/Hz<sup>1/2</sup> [<xref ref-type="bibr" rid="B37">37</xref>]. The AC electric field can also be used to coherently drive the spin state of divacancy centers (Rabi oscillator) in 6H&#x2013;SiC [<xref ref-type="bibr" rid="B80">80</xref>]. Most recently, the NV center ensembles in 4H&#x2013;SiC were used to sense an artificial AC radio-frequency field centered at &#x223c;900&#xa0;kHz with a resolution of 10&#xa0;kHz [<xref ref-type="bibr" rid="B24">24</xref>]. The experiments pave the way for the SiC spin defects based on high-sensitivity and high-spatial resolution electric field sensing.</p>
</sec>
<sec id="s3-4">
<title>3.4 Strain sensing</title>
<p>Electrical field and strain interactions with spin defects are intertwined, so the spin defects can also be used to detect the strain. The <italic>D</italic> and <italic>E</italic>
<sub>
<italic>x,y</italic>
</sub> in Eq. <xref ref-type="disp-formula" rid="e2">2</xref> are also related to strain as follows: <inline-formula id="inf10">
<mml:math id="m12">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mi>D</mml:mi>
<mml:mn>0</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mo>&#x2225;</mml:mo>
</mml:msub>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>; <inline-formula id="inf11">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msubsup>
<mml:mi>E</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mn>0</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mo>&#x22a5;</mml:mo>
</mml:msub>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mrow>
<mml:mi>x</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>y</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <italic>D</italic>
<sup>0</sup> and <italic>E</italic>
<sup>0</sup>
<sub>
<italic>x,y</italic>
</sub> terms are the crystal-field splitting in the absence of applied strain and electric fields, <inline-formula id="inf12">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mo>&#x2225;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf13">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>e</mml:mi>
<mml:mo>&#x22a5;</mml:mo>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the strain-coupling parameters, and <bold>
<italic>&#x3b5;</italic>
</bold> is the effective strain field [<xref ref-type="bibr" rid="B39">39</xref>]. In order to detect strain, a 4H&#x2013;SiC membrane with divacancy centers is placed on the top of a piezo actuator, which applies strain to the SiC membrane as it stretches (<xref ref-type="fig" rid="F9">Figure 9A</xref>). The strain can affect the ZPL of the six types of divacancy centers in 4H&#x2013;SiC. The ZPLs of the c-axis-oriented divacancy centers bifurcate as the strain increases, reflecting the reduction of the C<sub>3v</sub> symmetry due to the strain.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>ODMR measurements and Hahn-echo pulse sequence and corresponding results. <bold>(A)</bold> DC ODMR results for strain sensing at a temperature of 20&#xa0;K. By utilizing the opposite voltage, a 0.8&#xa0;MHz shift is observed [<xref ref-type="bibr" rid="B39">39</xref>], copyright (2014), American Physical Society. <bold>(B)</bold> The Hahn-echo pulse sequence used to measure the strain [<xref ref-type="bibr" rid="B39">39</xref>], copyright (2014), American Physical Society. <bold>(C)</bold> Hahn-echo results for PL1&#x2013;PL4 without external magnetic field [<xref ref-type="bibr" rid="B39">39</xref>], copyright (2014), American Physical Society.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g009.tif"/>
</fig>
<p>Strain also affects the spin states. Transverse strain shifts the ODMR of the PL2 for approximately 0.8 MHz, with a 300&#xa0;V piezo value [<xref ref-type="bibr" rid="B39">39</xref>]. The DC strain sensing is limited by <italic>T</italic>
<sub>2</sub>
<sup>&#x2a;</sup>, which is the inhomogeneous spin-dephasing time (approximately 1.5&#xa0;&#x3bc;s). It can also be used to detect AC strain. The Hahn-echo pulse scheme is used for <italic>T</italic>
<sub>2</sub>-limited AC strain sensing, as shown in <xref ref-type="fig" rid="F9">Figure 9B</xref>. The corresponding AC strain sensing data are shown in <xref ref-type="fig" rid="F9">Figure 9C</xref>.</p>
</sec>
<sec id="s3-5">
<title>3.5 High-pressure sensing</title>
<p>High-pressure technologies have been widely applied in physics, geophysics, and material sciences, inducing many unusual and important phenomena at high pressures [<xref ref-type="bibr" rid="B81">81</xref>&#x2013;<xref ref-type="bibr" rid="B83">83</xref>]. In the last few decades, pressure-induced high-critical-temperature (<italic>T</italic>
<sub>c</sub>) superconductivity has drawn much attention [<xref ref-type="bibr" rid="B82">82</xref>, <xref ref-type="bibr" rid="B83">83</xref>]. For example, the <italic>T</italic>
<sub>c</sub> of lanthanum hydride increases to 250&#xa0;K at 170&#xa0;GPa [<xref ref-type="bibr" rid="B82">82</xref>, <xref ref-type="bibr" rid="B83">83</xref>]. However, measuring the local magnetic field in the diamond anvil cell (DAC) is still a great challenge due to the micrometer-sized sample chamber [<xref ref-type="bibr" rid="B84">84</xref>&#x2013;<xref ref-type="bibr" rid="B87">87</xref>]. It is important to generate new methods to overcome the challenges. The ZFS of the NV centers linearly increases with a slope of 14.6&#xa0;MHz/GPa at high pressure [<xref ref-type="bibr" rid="B88">88</xref>]. Using the ODMR of the NV centers in diamond, the pressure-induced magnetization of the Fe particles and the Meissner effect of superconductors have been measured [<xref ref-type="bibr" rid="B84">84</xref>&#x2013;<xref ref-type="bibr" rid="B87">87</xref>]. However, the NV centers have four axes, and their ZFS decreases with temperature, which makes it a little difficult to analyze the ODMR spectra [<xref ref-type="bibr" rid="B84">84</xref>&#x2013;<xref ref-type="bibr" rid="B87">87</xref>]. Similar to NV centers in diamond, defects in silicon carbide (SiC) could also be used to measure the magnetic properties of materials at high pressure [<xref ref-type="bibr" rid="B40">40</xref>, <xref ref-type="bibr" rid="B89">89</xref>]. SiC is a widely used semiconductor, which has mature inch-scale growth and micro/nano-fabrication technologies.</p>
<p>The silicon-vacancy center in SiC has only a single axis, and the ODMR has only two resonant peaks at an external magnetic field. Moreover, it also has a temperature-independent ZFS. The two superior properties make it convenient to analyze the ODMR spectra [<xref ref-type="bibr" rid="B40">40</xref>, <xref ref-type="bibr" rid="B76">76</xref>]. Recently, Wang J. F. et al. realized a magnetic detection under high pressures using designed silicon-vacancy centers in SiC [<xref ref-type="bibr" rid="B40">40</xref>]. As presented in <xref ref-type="fig" rid="F10">Figure 10A</xref>, two high-quality single-crystal 4H-SiC cubes are used to fabricate SiC anvils with 200-&#xb5;m-diameter culets. A 100-nm-deep high-density shallow silicon-vacancy center is generated (20keV He implantation) for magnetic detection. The ZFS increases with the pressure with a slope of 0.31&#xa0;MHz/GPa (<xref ref-type="fig" rid="F10">Figure 10B</xref>), which is obviously smaller than the coefficient of 14.6&#xa0;MHz/GPa for NV centers in diamond. The coherence time <italic>T</italic>
<sub>2</sub> remains invariable up to 25&#xa0;GPa. Then, a tiny Nd<sub>2</sub>Fe<sub>14</sub>B sample is placed on the culet surface, and using the ODMR of the shallow silicon-vacancy centers, the pressure-induced magnetic phase transition is observed and presented in <xref ref-type="fig" rid="F10">Figure 10C</xref>. The phase transition range is from 6&#xa0;GPa to 10&#xa0;GPa, which is consistent with previous results [<xref ref-type="bibr" rid="B87">87</xref>]. Finally, they used the ODMR methods to measure the Meissner effect of a well-known superconductor YBa<sub>2</sub>Cu<sub>3</sub>O<sub>6.6</sub> (<xref ref-type="fig" rid="F10">Figure 10D</xref>) and map the <italic>T</italic>
<sub>c</sub>&#x2013;pressure phase diagram. The <italic>T</italic>
<sub>c</sub> increases as the pressure increases to approximately 17.1&#xa0;GPa (<xref ref-type="fig" rid="F10">Figure 10E</xref>), which is consistent with the results obtained by AC susceptibility methods in the DAC [<xref ref-type="bibr" rid="B40">40</xref>]. The experiments prove that the silicon-vacancy center is an excellent quantum sensor at high pressure.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>
<bold>(A)</bold> Schematic of the SiC anvil cell [<xref ref-type="bibr" rid="B40">40</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B40">40</xref>], copyright (2023). <bold>(B)</bold> The <italic>D</italic> shifts under different pressure. The red line shows that the <italic>D</italic> value has a linear dependence on pressure [<xref ref-type="bibr" rid="B40">40</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B40">40</xref>], copyright (2023). <bold>(C)</bold> The magnetometry of the Nd<sub>2</sub>Fe<sub>14</sub>B sample by using silicon-vacancy centers under compression (blue) and decompression (red) processes, respectively [<xref ref-type="bibr" rid="B40">40</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B40">40</xref>], copyright (2023). <bold>(D)</bold> ODMR splitting as a function of temperature under 9.0&#xa0;GPa. The mutation point shows the superconducting transition [<xref ref-type="bibr" rid="B40">40</xref>], reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B40">40</xref>], copyright (2023). <bold>(E)</bold> The YBa<sub>2</sub>Cu<sub>3</sub>O<sub>6.6</sub> phase diagram [<xref ref-type="bibr" rid="B40">40</xref>]. By measuring <italic>T</italic>c under different pressures, the <italic>T</italic>c&#x2013;pressure phase diagram can be obtained. The orange part is in the superconducting phase, and the white part is in the normal state, reprinted with permission from Macmillan Publishers Ltd.: Nature Materials [<xref ref-type="bibr" rid="B40">40</xref>], copyright (2023). <bold>(F)</bold> Optical image of the culet surface (left) and the fluorescence scanning confocal image of the sample (right), respectively [<xref ref-type="bibr" rid="B89">89</xref>], copyright (2022), American Chemical Society. <bold>(G)</bold> The D shift as a function of pressure. The red line is a linear fitting to the data [<xref ref-type="bibr" rid="B89">89</xref>], copyright (2022), American Chemical Society.</p>
</caption>
<graphic xlink:href="fphy-11-1270602-g010.tif"/>
</fig>
<p>Divacancy centers can also be used in quantum sensing at high pressure. As shown in <xref ref-type="fig" rid="F10">Figure 10F</xref>, a tiny SiC sample with high-concentration divacancy centers is placed in the DAC chamber. The ZPLs of the PL5 and PL6 are also blueshifted with pressure. The ZFS D of the PL5, PL6, and PL7 linearly increases with pressure with coefficients of 25.1, 11.8, and 23.6&#xa0;MHz/GPa, respectively (<xref ref-type="fig" rid="F10">Figure 10G</xref>). The ZFS E of PL5 values keep stable at 17&#xa0;MHz as the pressure increases to 8&#xa0;GPa. The ODMR contrast decreases with the pressure. The pressure sensing sensitivity of the divacancy center ensemble at room temperature is <inline-formula id="inf14">
<mml:math id="m16">
<mml:mrow>
<mml:mrow>
<mml:mi mathvariant="italic">&#x3B7;</mml:mi>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3c0;</mml:mi>
<mml:mfrac>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>D</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mi>K</mml:mi>
<mml:msqrt>
<mml:msubsup>
<mml:mi>T</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
</mml:msubsup>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>, where <italic>K</italic> &#x3d; (1 &#x2b; 2(<italic>a</italic>
<sub>0</sub> &#x2b; <italic>a</italic>
<sub>1</sub>)/(<italic>a</italic>
<sub>0</sub> - <italic>a</italic>
<sub>1</sub>)<sup>2</sup>)<sup>&#x2212;1/2</sup>, where <italic>a</italic>
<sub>0</sub> &#x3d; <italic>I</italic> &#xd7; <italic>&#x3c4;</italic>, <italic>a</italic>
<sub>1</sub> &#x3d; <italic>I</italic> &#xd7; <italic>&#x3c4;</italic> &#xd7; (1 - <italic>c</italic>), and <inline-formula id="inf15">
<mml:math id="m17">
<mml:mrow>
<mml:msubsup>
<mml:mi>T</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>&#x2a;</mml:mo>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> is the dephasing time [<xref ref-type="bibr" rid="B88">88</xref>, <xref ref-type="bibr" rid="B89">89</xref>]. Here, <italic>I</italic> is the photon count, <italic>&#x3c4;</italic> is the Rabi readout duration time, and <italic>c</italic> is the ODMR contrast. The calculated pressure sensing sensitivity is 0.28 <inline-formula id="inf16">
<mml:math id="m18">
<mml:mrow>
<mml:mtext>MPa</mml:mtext>
<mml:mo>/</mml:mo>
<mml:msqrt>
<mml:mtext>Hz</mml:mtext>
</mml:msqrt>
</mml:mrow>
</mml:math>
</inline-formula> [<xref ref-type="bibr" rid="B89">89</xref>]. The coherence time <italic>T</italic>
<sub>2</sub> of PL5 decreases quickly as the pressure increases from ambient pressure to approximately 5&#xa0;GPa, and then, it slowly declines as the pressure increases up to 36.1&#xa0;GPa [<xref ref-type="bibr" rid="B89">89</xref>]. The PL6 can also be applied to detect the pressure-induced magnetic phase transition of a Nd<sub>2</sub>Fe<sub>14</sub>B magnet [<xref ref-type="bibr" rid="B89">89</xref>]. The experiments pave the way for the applications of silicon-vacancy centers and divacancy centers in SiC in quantum sensing at high pressures and give quantum platforms for <italic>in situ</italic> magnetic detection at high pressures.</p>
</sec>
</sec>
<sec id="s4">
<title>4 Conclusion and outlook</title>
<p>In this review, we focused on the fabrication of three spin defects and various quantum sensing of the spin defects in SiC. We first summarize four main methods used to generate the three spin defects: electron or neutron irradiation, ion implantation, focused ion implantation, and laser writing, discussing the specific advantages of the efficiency and position accuracy of these methods. On this basis, we discuss the progress in various quantum sensing fields, including magnetic field, temperature, electric field, strain, and high pressure. We introduce the basic working principles, sensing sensitivities, and spatial resolutions of these quantum sensing methods.</p>
<p>Because of the low counts of the single-spin defects, one of the challenges in spin defect fabrication is the on-demand generation with high spatial accuracy, which will be beneficial for coupling with the photonic structures. For quantum sensing, there are some methods to further increase the sensitivity. The first one is using photonic structures, such as nanopillars [<xref ref-type="bibr" rid="B25">25</xref>], solid immersion lenses [<xref ref-type="bibr" rid="B17">17</xref>], ring resonators, and photonic crystal cavities [<xref ref-type="bibr" rid="B29">29</xref>], to increase the counts of the spin defects. The second is using the isotope purification SiC sample or dynamical decoupling methods to increase the coherence time [<xref ref-type="bibr" rid="B31">31</xref>]. The third is optimizing the generation method to increase the concentration of spin defects. Combining nano SiC samples with an atomic force microscope (AFM), spin defects can be used to realize nanoscale quantum sensing imaging [<xref ref-type="bibr" rid="B53">53</xref>, <xref ref-type="bibr" rid="B90">90</xref>]. Various SiC spin defect-based quantum sensing have high sensitivity and spatial resolution, opening up wide applications in physics, biology, and materials science. With the progress of this technology, quantum sensing will extend the range of applications and make them more feasible in practical environments.</p>
</sec>
</body>
<back>
<sec id="s5">
<title>Author contributions</title>
<p>Q-YL: Writing&#x2013;original draft, Writing&#x2013;review and editing. QL: Writing&#x2013;original draft, Writing&#x2013;review and editing. J-FW: Writing&#x2013;original draft, Writing&#x2013;review and editing, Funding acquisition, Supervision. P-JG: Writing&#x2013;original draft. W-XL: Writing&#x2013;original draft. SZ: Writing&#x2013;original draft. Q-CH: Writing&#x2013;original draft. Z-QZ: Writing&#x2013;original draft. J-SX: Writing&#x2013;original draft, Writing&#x2013;review and editing, Funding acquisition, Supervision. C-FL: Writing&#x2013;original draft, Writing&#x2013;review and editing, Funding acquisition, Supervision. G-CG: Writing&#x2013;review and editing, Supervision.</p>
</sec>
<sec id="s6">
<title>Funding</title>
<p>The authors declare financial support was received for the research, authorship, and/or publication of this article. This work was supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0301400), the National Natural Science Foundation of China (Grant Nos. 11975221, 61905233, U19A2075, and 11821404), Anhui Initiative in Quantum Information Technologies (Grant No. AHY060300), and the Fundamental Research Funds for the Central Universities (Grant No. WK2470000026).</p>
</sec>
<ack>
<p>J-FW also acknowledges financial support from the Science Specialty Program of Sichuan University (Grant No. 2020SCUNL210).</p>
</ack>
<sec sec-type="COI-statement" id="s7">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The authors declare that they were editorial board members of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.</p>
</sec>
<sec sec-type="disclaimer" id="s8">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
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