Since the discovery of graphene (Geim and Novoselov, 2007), there has been an increasing amount of research on two-dimensional (2D) materials (Miro et al., 2014; Ren et al., 2024). The wide application of the unique properties and advantages of 2D materials has made them highly regarded research in the field of materials science (Tang et al., 2022; Wang et al., 2023; Su et al., 2022; Su et al., 2023; Sun et al., 2022). For example, due to the extremely thin thickness of transition metal dichalcogenides (TMDs), their light absorption performance is outstanding, suggesting potential applications in fields such as solar cells and optoelectronic devices (Zhao et al., 2024; Ren et al., 2019). The AlN monolayer also has outstanding strength and stiffness in the plane direction compared with the bulk one (Ren et al., 2021a; Ren et al., 2021b). In addition, the larger specific surface area exposes more catalytic active sites; therefore, 2D materials present excellent photocatalytic and electrocatalytic properties.

Wu et al. (2020) prepared IrPdPtRhRu high-entropy alloy (HEA) nanoparticles with a mean diameter of 5.5 ± 1.2 nm by a facile one-pot polyol method, which possesses a lattice constant of 3.856 Å. The HAADF-STEM configurations of the IrPdPtRhRu HEAs and the corresponding energy-dispersive X-ray (EDX) images of each element suggest the solid-solution alloys obtained by homogeneous distribution. The duration of the IrPdPtRhRu was evaluated in both acidic (0.05 M H₂SO₄) and alkaline (1.0 M KOH) electrolytes, which proves the hydrogen evolution reaction (HER) ability of the IrPdPtRhRu HEA NPs.

High throughput computing method investigations are conducted to develop new 2D materials, expand their application, and develop more novel mechanical, optical, and electronic properties (Ren et al., 2022a; Sun and Schwingenschlögl, 2021; Haastrup et al., 2018). For example, Luo used particle swarm optimization to structure boron carbon compounds, and the results show that boron carbon compounds have strong B–C bonds and thermal stability and can maintain structural stability even above 2,000 K (Luo et al., 2011). Lu proposed a CaP₃ monolayer with a direct bandgap of approximately 1.15 eV, and the electron mobility obtained is as high as 19,930 cm²⋅V⁻¹⋅s⁻¹ (Lu et al., 2018). Yuan predicted the monolayered penta-RuS₄ through first-principle calculations, and interestingly, this monolayered penta-RuS₄ structure exhibits unique anisotropic secondary energy dispersion (Yuan et al., 2017). Jing presented a monolayered GeP₃ crystal that has an indirect bandgap of 0.55 eV. The double-layer GeP₃ possesses a decreased bandgap of 0.43 eV. It is noteworthy that the GeP₃ monolayer can transform the indirect bandgap into the direct bandgap under the condition of biaxial strain. Meanwhile, GeP₃ also has remarkable light absorption ability and can be widely used in optoelectronics (Jing et al., 2017).

Jin proposed a novel Janus MoTe monolayer using density functional theory (DFT). The results indicate that the monolayered Janus MoTe presents relatively wide spatial extension and low binding energy. Furthermore, the time for electron–hole recombination is approximately 1.31 ns, making it a potential photocatalyst for water splitting (Jin et al., 2018). More recently, researchers used the B₂P₆ present Janus structure and proved that B₂P₆ is an indirect bandgap semiconductor with an excellent hydrogen production efficiency of 28.2% and an outstanding photocatalyst (Sun and Schwingenschlögl, 2020a) that also can be tuned by external strain (Ren et al., 2021c). For a B₂P₆ monolayer, the HER and oxygen evolution reactions (OERs) can be induced respectively at different surfaces because the energy levels of the two surfaces exhibit staggered band energy, thereby separating the photogenerated electrons and holes. Such a Janus structure of the B₂P₆ monolayer exhibits intrinsic differences by atomic adsorption on different surfaces (Ren et al., 2022b).

A CS monolayer was proposed with strong absorption of solar radiation and conversion efficiencies as high as 20.1% (Sun and Schwingenschlögl, 2020b), which also presents decent band edge positions for the redox reaction in water splitting used as a photocatalyst. A CN monolayer shows a wide bandgap of approximately 6 eV as a potential power device (Ren et al., 2023a). The wide bandgap and extremely strong elastic modulus of the CN monolayer enable it to maintain the potential for photocatalytic water splitting even under large strains. Thus, B- or C-atom-based new materials are proposed to possess novel electronic and optical performances for use in nanodevices.

In this investigation, a novel monolayered C₂B₆ system is proposed by the elemental mutation method considering the prototype of the Li _x B _y structure. Using the first-principle calculations, the C₂B₆ monolayer possesses excellent stability by phonon spectrum and ab initio molecular dynamics (AIMD) calculations. Then, the electronic feature is investigated by band structure and carrier mobility. The optical performance of the C₂B₆ monolayer is addressed by light absorption spectrum and photocurrent testing.

All first-principle simulations were performed using the Vienna ab initio simulation package (VASP) (Oganov and Glass, 2006) using the DFT (Grimme et al., 2010; Van de Walle and Martin, 1989; Grest et al., 1981). The projector augmented wave potentials (PAW) were used in the calculations to demonstrate the core electrons (Kresse and Furthmüller, 1996a; Kresse and Furthmüller, 1996b; Blöchl, 1994). The Perdew–Burke–Ernzerhof (PBE) functional was conducted by the generalized gradient approximation (GGA) method (Kresse and Joubert, 1999; Perdew et al., 1996). The Heyd–Scuseria–Ernzerhof hybrid functional was explored to calculate a more accurate band structure and light absorption spectrum (Heyd et al., 2005; Heyd et al., 2003). The spin effect is not explored in the calculations because it has almost no effect on the electronic properties of the studied system, which is proved by the band structure demonstrated in Supplementary Figure S1 in Supporting Information. The energy cut-off was 550 eV. The Monkhorst–Pack k-point grid was set as 17 × 17 × 1 in the first Brillouin zone. The density functional perturbation theory (DFPT) was considered to obtain the phonon spectra by the PHONOPY code (Togo and Tanaka, 2015; Togo et al., 2008). Furthermore, the convergence for force was set as 0.01 eV Å⁻¹, while the energy of the calculated system is set as 0.01 meV. The photocurrent of the C₂B₆ monolayer is calculated by Nanodcal software based on non-equilibrium Green’s function (NEGF) theory.

First, the crystal structure of the C₂B₆ monolayer is predicted as a puckered unit-cell with the space group of Pca ₂₁ , using the elemental mutation method from the prototype of the Li _x B _y structure (Ren et al., 2022c), shown in Figure 1A. The optimized lattice parameters of the x and y in unit-cell of the C₂B₆ monolayer are 5.218 Å and 3.310 Å, respectively, which is comparable with the CS monolayer (Lv et al., 2020). The C–B bond and the C–C bonds are obtained as 1.59 Å and 1.32 Å, respectively.

The simulated STM configuration of the C₂B₆ monolayer is demonstrated in Figure 1B, which can provide a reference for experimental observations. The cohesive energy of the C₂B₆ monolayer is calculated as 6.516 eV/atom, which is obtained by (2E _C + 6E _B – E _CB)/8, where E _C, E _B, and E _CB are the total energies of a C atom, a B atom, and the C₂B₆ monolayer, respectively. The calculated cohesive energy of the C₂B₆ monolayer is comparable with the predicted Li _x B _y system (approximately 4.11–5.53 eV/atom) (Ren et al., 2022c) and the CB monolayer (approximately 6.13 eV/atom) (Ren et al., 2023a). It is also larger than that of the V–VI system (approximately 3.37–3.81 eV/atom) (Ren et al., 2022a), suggesting the stability of the C₂B₆ monolayer. The thermal stability of the C₂B₆ monolayer is estimated by the AIMD calculations using the Nosé−Hoover heat bath scheme (Nosé, 1984). The supercell of the C₂B₆ monolayer is constructed on a 7 × 4 × 1 grid to ensure the lattice translational constraints contain 192 atoms (Ren et al., 2020a). The C₂B₆ monolayer is relaxed at 300 K within 10 ps. After the completed simulations, the atomic structure of the C₂B₆ monolayer is still unscathed, as shown in the insets of Figure 1C. The temperature and energy of the AIMD for the C₂B₆ monolayer are also convergent, as shown in Figure 1C, which further provides evidence of stability. The C₂B₆ monolayer is also stable under 600 K, while the structure can be melted down at the temperature of 1,000 K, as demonstrated in the Supplementary Figures S2A, B, respectively.

The dynamic stability of the C₂B₆ monolayer is investigated by phonon spectra, calculated in Figure 2A. One can see that there is no imaginary frequency in the phonon spectra of the C₂B₆ monolayer, implying the dynamic stability of the C₂B₆ system. The highest frequency of the optical branch can reach 45 THz, as shown in Figure 2A. Such maximal optical branch frequency is also comparable with the prototype (Li _x B _y system), suggesting applications as efficient thermoelectric functional devices that can be tuned by the phononic crystal structure (Ren et al., 2020b). There are 24 degeneracy points at the Γ point. The lattice vibration mode of the C₂B₆ system at the Γ point for these 24 degeneracy configurations is studied, as shown in Figure 2B. All these optical phonons at the Γ point can be demonstrated as Equation 1: Γ optic = 4 A g   R + A u   R + 3 B 1 g   IR + 3 B 1 u   R + 2 B 2 g   R + 3 B 2 u   IR + B 3 g   IR + 2 B 3 u   R , (1) where R, IR, and IN represent the optical phonon mode with Raman active, infrared active, and inactive, respectively. Interestingly, A_2g, A_u, B_3g, A_2u, and B_1g are out-of-plane vibration modes, and the others are a combined form.

Then, the band structure of the C₂B₆ monolayer is investigated, as shown in Figure 3, by PBE and HSE06 methods. The C₂B₆ monolayer is a semiconductor with an indirect bandgap with the conduction band minimum (CBM) located between the M and Y points, while the valence band maximum (VBM) is set between the X and M points, demonstrated in Figure 3A. More interestingly, even though the wider bandgap is obtained by the HSE06 functional, it still presents as small as 0.671 eV, smaller than the As₂X₃ system (Zhao et al., 2023). It is worth noting that the ultra-narrow bandgap is also reported in the PbN/CdO heterostructure (approximately 0.128 eV). Such an ultra-narrow bandgap in the C₂B₆ monolayer facilitates rapid charge transitions and can serve as a potential efficient nanoelectronic device, optical device, and catalyst (Wang et al., 2017; Huang et al., 2024). The projected band structure of the C₂B₆ monolayer is calculated by the HSE06 in Figure 3B. The B atoms make an obvious and significant contribution to the energy band compared with the C atoms. The density of states (DOS) of the C₂B₆ monolayer is calculated in Figure 3C, which further proves that most of the energy level of the C₂B₆ system contributions come from B atoms.

The carrier mobility is further explored, considering the ultra-narrow bandgap of the C₂B₆ monolayer for promising applications in nanodevices. The carrier mobilities of the electrons and holes in transport directions (x and y demonstrated in Figure 1A) are calculated by the Bardeen–Shockley theory demonstrated as Equation 2 (Van de Walle and Martin, 1989): μ = e ℏ 3 C / k B T m * m x * m y * D 2 , (2) where e is the elementary charge, ℏ represents Planck’s constant, and k _B is the Boltzmann constant. The effective mass of the carriers, electrons, and holes is explained by m*, and the effective mass is obtained using Equation 3: m * = ℏ 2 d 2 E k   d k 2 − 1 , (3) where the wave vector is represented by the k. Electronic energy is demonstrated by the E _k . C is the elastic modulus of the C₂B₆ monolayer calculated by C = [∂² E/∂((l–l ₀ )/l ₀ )²]/S ₀, where the free energy is E, and the original lattice constant and the difference by the strain are l and l ₀ , respectively. S ₀ is the area of the C₂B₆ monolayer. The energy of the C₂B₆ monolayer under applied uniaxial is demonstrated in Figure 4A. One can see that the sensitivity of energy of the C₂B₆ monolayer to external strain in the y direction is significantly higher than that in the x direction, suggesting the higher elastic modulus of the y direction. Furthermore, D is used to show the potential constant of the C₂B₆ monolayer, which is calculated by D = ΔE _edge/((l–l ₀ )/l ₀), where the ΔE _edge is the difference of the band edge by uniaxial strain along the transport directions. As shown in Figure 4B, when the strain is applied in the y direction, the CBM and the VBM can be increased linearly. Meanwhile, the CBM and the VBM of the C₂B₆ monolayer can be decreased linearly by the strain along the x direction, suggesting the external strain is an effective measure to tune the electronic properties of the C₂B₆ monolayer.

The calculated effective mass and deformation potential constant elastic modulus are demonstrated in Table. 1. It is worth noting that the effective mass of the C₂B₆ monolayer along the y direction is as low as 0.406 m*, suggesting higher carrier mobility. The sensitivity of edge energy to strain along x and y directions is similar for electrons and holes. The apparent mechanical anisotropy obtained from the elastic modulus of the C₂B₆ monolayer is calculated as 183 N⋅m⁻¹ and 377 N⋅m⁻¹, respectively, in the x and y directions. Thus, the pronounced anisotropic carrier mobility of the C₂B₆ monolayer is also obtained such that electrons 360 cm²⋅V⁻¹⋅s⁻¹ and 205 cm²⋅V⁻¹⋅s⁻¹ mobility in the x and y directions, respectively. More importantly, the C₂B₆ monolayer possesses ultrahigh hole mobility in the y direction of approximately 6,342 cm²⋅V⁻¹⋅s⁻¹. The difference of the carrier between the electron and hole in the y direction is also approximately 30 times, suggesting excellent promotion to separate the excited carriers. In addition, the electrons and holes show a favorable transport along the x and y directions, respectively. The obtained carrier mobility of the C₂B₆ monolayer is even higher than other popular 2D materials, such as the GaPS₂Se₂ monolayer (530 cm²⋅V⁻¹⋅s⁻¹) (Zhang Y. et al., 2022), the B₂P₆ monolayer (5,888 cm²⋅V⁻¹⋅s⁻¹) (Ren et al., 2021c), and MoSi₂N₄ (2,169 cm²⋅V⁻¹⋅s⁻¹) (Ren et al., 2023b) and is comparable with a Li₂B₆ monolayer (6,800 cm²⋅V⁻¹⋅s⁻¹) (Kai et al., 2018).

The light absorption performance of the C₂B₆ monolayer is further investigated by the absorption coefficient (α), which is calculated by Equation 4 (Zhang L. et al., 2022). α ω = 2 ω c ε 1 2 ω + ε 2 2 ω 1 / 2 − ε 1 ω 1 / 2 , (4) where the ε ₁(ω) is the real part of the dielectric constant, and the ε ₂(ω) is the imaginary part. ω represents the angular frequency, and c is the speed of light in a vacuum. It is worth noting that ε ₂(ω) can be calculated by Equation 5 (Zhang et al., 2008): ε 2 q → O u ^ , ℏ ω = 2 e 2 π Ω ε 0 ∑ k , v , c ∣ Ψ k c u ^ ⋅ r Ψ k v 2 × δ E k c − E k v − E , (5) where Ψ k , E k , and u ^ are used to explain the wave function, energy, and unit vector of the electric field of the incident light, respectively. Then, the superscripts (v and c) in the Ψ k and E k demonstrate the conduction and valence bands, respectively. Furthermore, ε(ω) = ε ₁(ω) + iε ₂(ω) can be used to calculate the complex dielectric function, and the Kramers–Kronig relation can define the real parts ε ₁ and ε ₂.

The obtained light absorption spectrum of the C₂B₆ monolayer is explained in Figure 5. The C₂B₆ monolayer shows excellent optical properties in the visible and near-ultraviolet regions with an absorption peak of approximately 3.566 × 10⁵ cm⁻¹ and a wavelength of approximately 106 nm. The novel absorption coefficient at the visible light range is also obtained at approximately 9.578 × 10⁴ cm⁻¹ with a wavelength of approximately 450 nm. Such an optical absorption peak of the C₂B₆ monolayer is also higher than other reported 2D materials, such as a CdO/arsenene heterostructure (8.47 × 10⁴ cm⁻¹) (Ren et al., 2021d), GaN (4.00 × 10⁴ cm⁻¹) (Ren et al., 2020c), and Mg(OH)₂ (3.49 × 10⁴ cm⁻¹) (Ren et al., 2019).

The excellent carrier mobility and the optical performance of the C₂B₆ monolayer suggest potential applications as a photocurrent device. The model of the C₂B₆ monolayer used as a photocurrent nanodevice is illustrated in Figure 6A with two electrodes. The C and B atoms at the central region are excited by the linearly polarized light in the z direction and can induce the photon-generated carriers with the photocurrent flowing to the electrodes as I _ph, which can be obtained as Equation 6 (Qin et al., 2024; Li et al., 2024): J ph = i e h ∫ Tr  Γ G < ph + f E ( G > ph − G < ph d E , (6) where Γ = i Σ R − Σ L is the coupling of the center area and electrodes in the C₂B₆ monolayer. Σ L is the interactive self-energy of the left electrode, and the Σ R is interactive self-energy of the right one. f(E) is the Fermi−Dirac distribution. Green’s functions for photon−electron interactions are presented by G > ph . J _ph is normalized by I _ph = J _ph/eI _ω, and the I _ω demonstrates the photon flux. The calculated unit for the photocurrent is a0 2/photon, where the a⁰ ₂ is used to explain the Boreal radius. The photocurrent is also dependent on the photon energy and polarization angle of the C₂B₆ monolayer; thus, the photocurrent C₂B₆ monolayer is calculated with a different angle and intensity of light incidence in Figure 6B. One can see that the maximal I _ph of the C₂B₆ monolayer is approximately 0.24 a⁰ ₂/photon with the energy and the polarization angle of approximately 1.2 eV and 90°, respectively. Note that the anisotropy of carrier mobility also implies different photocurrents in the x and y directions. The obtained maximal I _ph of the C₂B₆ monolayer along the y direction is demonstrated in Figure 6C as approximately 0.012 a⁰ ₂/photon at the polarization angle of 90° with the energy of approximately 2.4 eV. The obtained photocurrent of the C₂B₆ is comparable with the other reported 2D materials, for example, MoSSe (0.88 a⁰ ₂/photon) (Cui et al., 2024), WSe₂/MoSe₂ (0.65 a⁰ ₂/photon) (Sun et al., 2023) and MoS₂/WSSe (0.71 a⁰ ₂/photon) (Sun et al., 2023) linearly polarized lights.

Furthermore, the dependence of the photocurrent of the C₂B₆ on angle and energy is also different along the x and y directions compared with Figures 6B, C. The photocurrent of the C₂B₆ can be decreased with increasing energy, and the vertical illumination method can obtain the maximal photocurrent along the x direction. Differently, the optimum photocurrent of the C₂B₆ can be induced by the horizontal irradiation method. With increasing energy, there is no unified trend of change for the photocurrent of the C₂B₆ along the y direction. Thus, the photocurrent direction can be effectively controlled by adjusting the incident angle, another promising attribute for a photoelectric device. When the C₂B₆ monolayer is illuminated, the photogenerated electrons can move quickly to the conduction band due to the narrow bandgap, inducing the valence band with photogenerated holes. Under the drive of a photocurrent, photogenerated electrons and holes can be rapidly separated due to the strong anisotropy of the mobility, implying that C₂B₆ is a potential high-efficiency photocatalyst.

In summary, a C₂B₆ monolayer is proposed with inherent stability. The puckered crystal structure of the C₂B₆ monolayer presents semiconductor properties with an ultranarrow indirect bandgap of approximately 0.671 eV, while the ultrahigh hole mobility is calculated as 6,342 cm²⋅V⁻¹⋅s⁻¹ in the suitable direction. The calculated anisotropic carrier mobility of the electrons and holes in the C₂B₆ monolayer demonstrates the advantages of carrier separation for use as a photocatalyst. Finally, the excellent light absorption and the photocurrent are also addressed, demonstrating the potential applications for photocatalytic, photovoltaic and optical and cold chain electronic devices.