In the present STM and LEED experiments, we explored co-adsorption of Pb and Bi onto the Ge(111) and Si(111) surfaces in a wide range of adsorbate coverages, namely in the Ge(111) case we varied the concentration of Bi adsorption onto the β- 3 -Pb-Ge(111) substrate from 0.1 to 0.8 ML (see Supplementary Figure S1). In the most cases, the resultant PbBi layers display heterogeneous structures, where patches of the PbBi compounds are surrounded by patches of the bare Pb and Bi reconstructions or disordered surface regions (Supplementary Figure S1). The only well-defined PbBi compounds formed in the both systems contain 0.5 ML of Bi [monolayer, 7.2 ⋅ 10¹⁴ cm⁻² and 7.8 ⋅ 10¹⁴ cm⁻² for Ge(111) and Si(111), respectively] and the same concentration of Pb (see high-resolution STM images in Figures 1A,C, respectively). These compounds have two distinct phases, the 2 × 2-PbBi and 2 3 × 2 3 -PbBi (hereinafter referred to as 2 × 2 and 2 3 , respectively) as follows from the LEED patterns (Figures 1B,D). The attempt to fabricate recently predicted Pb₃Bi- 3 -Ge(111) phase (Qin et al., 2019; Li et al., 2020; Sun et al., 2021) through simultaneous adsorption of 1.00 ML Pb and 0.33 ML Bi onto the Ge(111) substrate resulted to the formation of β- 3 -Pb phase along with patches of the mixture of 2 3 and 2 × 2-PbBi phases containing mass transfer islands (see Supplementary Figure S2).

Among other varied parameters of Pb and Bi co-adsorption onto the Ge(111) and Si(111) surfaces, there were the growth temperature, typically between room-temperature (RT) and 350°C, and the order of the adsorbed elements, i.e., the PbBi phases can be built either by simultaneous deposition of Pb and Bi elements (followed by annealing) or using successive depositions with intermediate annealing after the deposition of the first adsorbate. General behavior of the PbBi/Ge(111) and PbBi/Si(111) systems was found to be very similar.

Based on experimental data (the surface concentration of each element and periodicity parameters) we conducted the comprehensive ab initio total-energy calculations to find the ground-state atomic models for the both phases, applying AIRSS method. The top views of the obtained lowest-energy models are displayed in Figures 2A,B, where one can see the presence of the distinct rhombus-like motif serving as a building block in both phases. The motif includes pair of Bi atoms and pair of Pb atoms, which all are located in the vicinities of the on-top (T1) sites on the bulk-truncated Ge(111) surface. In the rhombus, Bi dimer forms a short diagonal, while the two separated Pb atoms form a long rhombus diagonal, each being bonded to the bismuth atoms. One can see that in the 2 × 2-PbBi phase motifs are oriented in a single direction (Figure 2A), while in the 2 3 -PbBi phase motifs are arranged according to the C ₃ symmetry (Figure 2B), consequently their unit cells contain one and three rhombi, respectively. According to the total-energy calculations the 2×2-PbBi atomic model is more stable than the 2 3 -PbBi model by 10 meV per 1 × 1 unit cell. This relatively small energy difference accounts for the simultaneous growth of the two crystalline phases on Ge(111) surface with slight energetic favor for the 2 × 2 phase.

Simulated STM images of the 2×2-PbBi phase at the negative bias (or filled states) show the general honeycomb-like appearance (Figure 2C) (as it was also observed in experimental measurements (Figure 1A), although the detailed consideration reveals the 1D nature of STM pattern where bright protrusions are associated with Pb atoms forming a zig-zag charge chain. The positive bias (or empty states) STM simulation produces the very similar one-dimensional appearance of the pattern with bright protrusions associated with Pb-Pb bonds. The STM simulation of the 2 3 -PbBi phase (Figure 2E) at the negative bias gives a bright triangular appearance, while at the positive bias one may see the network-like structure with the big bright three-fold patterns connected by the small faint triangles around (Figure 2F).

It is worth noting that established PbBi-Ge(111) ground-state atomic models for two coexisting phases are akin to the recently discovered PbBi-Si(111) phases (Mihalyuk et al., 2021). For this reason, below we give a detailed comparison between the electronic structures of the 2 × 2-PbBi and 2 3 -PbBi phases on the Ge(111) with their counterparts on the silicon substrate.

Before we start the inspection of electronic properties of the considered systems, let us address the lattice symmetry issue, since it is indispensable for the proper understanding of the emerging electronic effects. The underlying Ge(111) substrate has a C _3v symmetry (plane-group p3m), while the rhombus-like motif has a C _1h symmetry (plane-group p1), arising from a particular arrangement of the constituent Pb and Bi atoms. So the presence of the PbBi rhombus on the Ge(111) substrate reduces the total symmetry of the system down to C _1h for the 2 × 2 case since it contains only one rhombus element bringing the structural anisotropy, but this does not happen in the case of the 2 3 -phase where all three rhombi are arranged in a C _3v symmetry manner (as shown in Figure 2B), and, thus, preserving the total C _3v symmetry of the structure.

Let us start our consideration with the electronic band structure of (Pb,Bi)/Ge(111)- 2 3 phase. Figure 3A shows the non-relativistic spectrum where the projections of Pb and Bi orbitals are shown by blue and orange circles, respectively. The spectrum has an insulating character with a bunch of the weakly-dispersive unoccupied surface bands propagating in the germanium band gap within the [0.2; 0.6] eV energy range above E _F . These bands are characterized by the contributions of both Pb and Bi orbitals. As expected the electronic dispersion of the spectrum has a clear isotropic character typical for the C _3v symmetry systems. Insulating character of the band structure is retained even after including SOC effect into band structure calculation, which will be discussed below.

One can trace the electronic character of the system from the structural considerations. Note that the geometry itself of the 2 3 -PbBi atomic model induces its insulating nature since all Pb atoms (accumulating the charges, as seen in the STM images in Figure 2D) in the unit cell are ordered as isolated clusters separated by non-metallic bismuth atoms around (see Figure 2D); as a result the weakly dispersive bands and zero density of states at the Fermi level are expected in the system.

Interesting that the 2 3 -PbBi compound grown on Si(111) surface, which atomic model is almost the same, has the qualitatively very similar dispersion character (Figure 3B) with no metallic bands and large gap around Fermi level. The higher position of the in-gap PbBi bands on Si(111) in contrast to Ge(111) is due to the fact that Si bulk gap almost two times larger than the Ge bulk gap. The discussed spectrum is calculated according to the corresponding model from Ref (Mihalyuk et al., 2021).

Now let us move to the (Pb,Bi)/Ge(111)-2 × 2 phase, which electronic spectrum is presented in Figure 4A along with analogous dispersions calculated for Si(111)-based system (Figure 4B); such a comparison allows us to trace the role of the supporting substrate on the resultant electronic properties. From the element-projected non-relativistic spectrum shown in Figure 4A one can see the highly dispersing S1 metallic surface band propagating within the germanium bulk gap and mainly filled by Pb states denoted in spectrum by blue colored circles. Intersection of the Fermi level gives rise to electron pocket around the M ̄ point. Another Bi-induced electronic band S2 (marked by orange circles) strongly hybridizes with the germanium bulk states and completely merged in the valence band area. Remarkably, the analogous spectrum for the Si-supported system Figure 4B qualitatively has a very different character showing the hybridization of S1 and S2 surface bands with each other resulting in appearance of 70 meV gap below the Fermi level in the middle of the M ̄ - K ̄ direction. The difference between spectra of silicon- and germanium-based structures is a bit unexpected, since their atomic models have almost identical adsorption geometry. In order to exclude the hybridization effects cased by the substrates we removed them from the structural model and calculated the spectra for 2 × 2-PbBi free-standing layers keeping their internal structure and lattice constants defined by the corresponding Ge(111)- or Si(111)-2 × 2 substrate (Figures 4C,D, respectively). One can see that the dispersion character of S1 and S2 bands qualitatively is the same either Ge or Si substrates support the PbBi layer, or not. One may conclude that substrates do not affect the character of the electronic spectra significantly, but rather it seems that the lattice constant of the system is a main issue. As known, the Ge(111) lattice constant a _Ge = 4.09 Å is by ≈ 6% larger than the silicon constant a _Si = 3.86 Å, therefore we decide to apply a 6% compressive/tensile strain to Ge/Si-derived free-standing atomic models to bring their lattice constants into line with the parameters of opposite model in order to see if the dispersions will be qualitatively changed under that factor. Figures 4E,F show the results of the strain test on electronic structure; from here one may see almost no changes in the character of the electronic structure, which is again a bit unexpected.

The last point that remains to be explored is the geometry of the rhombus itself, which is apparently expected to determine the principal features of the electronic spectrum. Figure 5 give the comprehensive comparison between silicon- and germanium-based models of the 2 × 2 phase. It is worth to note that PbBi rhombi on both substrates are not equilateral and have the buckling geometry, i.e., the heights of Pb₁ and Pb₂ atoms with respect to the position of Bi atoms are slightly different due to the different relief of the underlying substrates. In spite of ≈6% difference between Ge(111) and Si(111) surface unit cell parameters one may see that rhombus parameters such as Bi-Bi, Pb-Bi bondlengths and inside obtuse angle denoted as α are changed insignificantly, while Pb-Pb bondlength and angle of the zig-zag Pb chain denoted as β are changed crucially and, thus, deserve special consideration.

In order to scrutinize the bond strengths within rhombi and between rhombi and Ge (Si) substrates, we conducted a chemical-bonding analysis using Crystal Orbital Hamilton Populations method, which results are summarised in Table 1. One can see that among various bonds in the system the strongest are those between Pb (Bi) atoms and nearest substrate atoms, wherein the strength of Pb-Si and Bi-Si interactions is a bit larger than Pb-Ge and Bi-Ge interactions, which is consistent with the shorter bond lengths in the Si case, and longer in the Ge case. However, as we showed above in Figure 4, the interaction of the PbBi atomic layer with underlying substrate does not qualitatively affect the dispersion of the PbBi bands near the Fermi level. Within the distorted rhombus, the Bi-Bi bond is a bit weaker in the Ge-supported structure, whereas the bonds between Bi atoms and two differently located Pb atoms are stronger in this structure in comparison with the Si case. The weakest bond in the PbBi atomic layer is the Pb-Pb one and its length defines the proximity of neighboring rhombi or density of motifs packing. Remarkably, among all other bonds that one has almost the double difference in energy values between Ge and Si cases (see Table 1).

With motivation to estimate the impact of Pb-Pb interaction on principal characteristics of electronic spectrum of free-standing PbBi layer we applied a 6% compressive strain to the lattice vectors of Ge-derived unit cell but keeping all parameters of PbBi rhombus unchanged (unlike to the previous strain test, where the uniform changing of all rhombus parameters also took the place). In the result the Pb-Pb distances and angle in the Pb-Pb “zig-zag chain” became almost the same (d _Pb-Pb = 3.993 Å and β = 150.73°) as in the Si-derived cell. This structural transformation dramatically changed the electronic spectrum (see the red dispersion curves in Figure 4E) shaping it to the character very similar to the Si-derived case (Figure 4D). However, under the uniform 6% compression the Pb-Pb bond length is almost the same, d _Pb-Pb = 4.084 Å like in the former structure, while the β angle is equal to that the undeformed structure, 142.26°. Thus, one can conclude that change in the β angle of the Pb-Pb zig-zag chain is a key factor responsible for a significant decrease in hybridization between the rhombi (decrease in the Pb-Pb bond strength) and, as a result, an increase in hybridization within PbBi rhombi leading to the modification of the electronic band structure near the Fermi level.

Let us finally examine the impact of spin-orbit coupling effect on the electronic properties of 2 3 -PbBi and 2 × 2-PbBi phases. Figures 6A,B display relativistic spin-projected spectra for both phases, from which one can see that dispersion character did not change substantially in comparison with non-relativistic spectra shown in Figure 3A and Figure 4A. The spectrum of 2 3 -PbBi (Figure 6A) demonstrates relatively small band splitting going over the entire k space; the bands have isotropic character with helical behaviour of spin components typical for the system with C _3v symmetry. The electronic band structure of 2 × 2-PbBi phase Figure 6B in the presence of SOC shows only tiny spin splitting in contrast to the related Si-based phase where spin-splitting is huge (Mihalyuk et al., 2021). The geometry of 2×2-PbBi atomic model as noticed above is characterized by a C _1h symmetry and that, as seen in the Fermi contours in Figure 6C, it shapes the electronic band structure as a quasi-one-dimensional metallic system with highly anisotropic constant energy contours (elongated along each third K ̄ - M ̄ - K ̄ side of the hexagonal 2 × 2 Brillouin zone (Figure 6C). The 1D character of 2 × 2-PbBi electronic structure may be unambiguously confirmed by calculating the spectrum within rectangular 2 × 2 3 unit-cell, which takes into account the C _1h character of the model. Due to the Brillouin zone folding the spin-split bands, dispersing along the K ̄ - M ̄ - K ̄ direction of hexagonal 2 × 2 BZ (Figure 6C), appear in the X ̄ - Γ ̄ - X ̄ direction of the own rectangular 2 × 2 3 surface BZ as shown in Figure 6D.