Introduction

Recently there has been a surge in the investigation of topological insulators (TIs)1,2,3. TIs are characterized by topologically protected metallic surface or edge states with helical spin polarization residing inside an insulating bulk gap. These states have negligible elastic scattering and Anderson localization4,5, which may provide ideal dissipationless spin current for future electronic devices with low power consumption. To realize their potential applications, it is desirable for the TIs to have an energy gap as large as possible36. Using DFT bands as input, we construct the maximally localized Wannier functions and fit a tight-binding Hamiltonian with these functions. Figure 3(a) shows the DFT and fitted band structures, which are in very good agreement. Then, the edge Green's function of a semi-infinite Bi@H-Si(111) is constructed and the local density of state (DOS) of Bi zigzag edge is calculated, as shown in Fig. 3(b). Clearly, one sees gapless edge states that connect the upper and lower band edge of the bulk gap, forming a 1D Dirac cone at the center of Brillouin zone (Γ point). This indicates that the Bi@H-Si(111) is a 2D TI with a large gap of ~0.5 eV.

Figure 3
figure 3

Electronic structures of Bi@H-Si(111) and its edge state.

(a) Comparison of band structures for Bi@H-Si(111) calculated by DFT (black lines) and Wannier function method (green circles). (b) The Dirac edge states within the SOC-induced band gap. Scale bar is indicated on the right. (c) The partial DOS projected onto px, py and pz orbitals of Bi and the total DOS of neighboring Si atoms. (d) Top: The charge density redistribution induced by metal atom surface adsorption for Bi@H-Si(111) (isovalue = 0.02 e/Å3), illustrating saturation of Bi pz orbital. Bottom: Same as Top for the H-saturated freestanding planar Bi lattice.

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To further confirm the above topological edge-state results, we also calculated Z2 topology number. As the spatial inversion symmetry is broken in these systems, we used the method developed by ** in the same energy range, which effectively removes the pz bands away from the Fermi level, leaving only the px and py orbitals. We also analyzed the charge density redistribution [see upper panel of Fig. 3(d)], which clearly shows that charge redistribution induced by Si surface mainly happens to the pz orbital of Bi, in a similar way to the saturation of Bi pz orbital by using hydrogen [lower panel of Fig. 3(d)]. It has been shown that the free-standing planar hexagonal lattice of Bi is a topologically trivial insulator with Z2 = 0 (see Fig. S3). When it is placed onto the H-Si(111) surface or adsorbed with H, it becomes topologically nontrivial (Figs. S1 and S4). This originates from the intriguing orbital filtering effect imposed by the substrate or H saturation, which selectively remove the pz orbitals from the Bi lattice to realize the large-gap QSH phase.

Specifically, we can describe the Bi@H-Si(111) using a simplified (px, py) four-band model Hamiltonian in a hexagonal lattice as24,38,

in which , , , a1, a2 is the lattice vector, Vppσ (Vppπ) is the Slater-Koster parameter39 and σZ = ±1 is the spin eigenvalue.

Diagonalization of Eq. (1) in reciprocal space gives the band structures shown in Fig. 4, which shows typical four bands as a function of SOC strength. One sees that without SOC, this Hamiltonian produces two flat bands and two Dirac bands with a Dirac point formed at K point and two quadratic points at Γ point [Fig. 4(a)]. Inclusion of a small SOC (λ = 0.2t) opens one energy gap (ΔE1) at K point and two energy gaps (ΔE2) at Γ point [Fig. 4(b)], with both gaps topologically nontrivial24. With the increasing SOC strength, both ΔE1 and ΔE2 increase [Fig. 4(c)], which eventually leads to the formation of a different energy gap (ΔE3) between the upper and lower Dirac bands at Γ point when ΔE3 becomes smaller than both ΔE1 and ΔE2 [Fig. 4(d)]. As such, for sufficiently large SOC, ΔE3 replaces ΔE1 to be the global gap and correspondingly the global gap shifts from K to Γ point. Further increase of SOC will tend to decrease ΔE3, indicating that for sufficiently large SOC the band gap decreases with increasing SOC.

Figure 4
figure 4

Energy bands resulting from the four-band model [Eq. (1)] as a function of SOC strength (λ) scaled by t (t is the coupling strength between neighboring px and py orbitals).

Fermi energy is set to zero. The SOC induced energy gaps (ΔE1, ΔE2 and ΔE3) are indicated. The global gap transition from K point to Γ point driven by SOC can be clearly seen.

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Such interesting phenomenon has also been confirmed by the DFT results. By comparing Bi@H-Si(111) and Pb@H-Si(111), we see that given the correct Fermi energy, the global gap is located at Γ point for Bi@H-Si(111) [Fig. 2(c)], but at K point for Pb@H-Si(111) [Fig. 2(d)]. This is because the SOC strength in p orbital of Pb (~0.91 eV) is smaller than that of Bi (~1.25 eV)40. Meanwhile, the energy gap between the two py Dirac bands induced by SOC is actually larger for Pb@H-Si(111) (0.65 eV) than that of Bi@H-Si(111) (0.5 eV), suggesting that Pb may be a better choice to achieve large-gap QSH states on the substrate. This is in sharp contrast with the Kane-Mele model in graphene, for which an energy gap is opened at Dirac point that is in proportion to the strength of SOC19.

Besides Bi and Pb, we have also conducted calculations of other heavy elements adsorption on the Si surface, including Sb, Sn, Tl, In and Ga. It is found that Sb and Sn have a similar band structure with Bi and Sn, respectively (see Fig. S5 in Supplementary Information), but with a smaller energy gap resulting from their similar valence electron configurations but weaker SOC. Band structures of Tl, In and Ga@H-Si(111) are a bit different. As shown in Fig. 5, the Fermi level now sits further below the lower dispersive band that is mainly made of the heavy atom py orbital. This is due to the one (two) less valence electron compared to the Pb (Bi) group, i.e., [Xe].4f14.5d10.6s2.6p1 for Tl. Clearly, one sees that from Ga to Tl, the SOC gap between the lower Dirac band and dispersive band increases dramatically, from around 0.1 eV (for Ga) to 0.5 eV for (Tl), confirming the dependence of energy gap (ΔE2) on SOC as demonstrated in Fig. 4.

Figure 5
figure 5

Band structures of Ga, In, Tl@H-Si(111).

(a–b) Band structures of Ga@H-Si(11) without and with SOC, respectively. The Fermi level is set to zero. Band compositions around Fermi level are indicated. (c–d) Same as (a–b) for In@H-Si(111). (e–f) Same as (a–b) for Tl@H-Si(111).

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In summary, we demonstrate the possibility of ‘controlled’ growth of large-gap topological quantum phases on conventional substrate surfaces such as the important Si surface by a unique approach of substrate orbital filtering process combined with a proper choice of SOC. Its underlying physical principles are general, applicable to deposition of different metal atoms on different substrates11,27. It opens up a new and exciting avenue for future design and fabrication of room temperature topological surface/interface states based on current available epitaxial growth and semiconductor technology, where the metal overlayer is atomically bonded but electronically isolated from the underneath semiconductor substrate27.

Methods

Our electronic structure calculations based on density functional theory were performed by using a plane wave basis set41 and the projector-augmented wave method42, as implemented in the VASP code43. The exchange-correlation functional was treated with the generalized gradient approximation in Perdew-Burke-Ernzerhof format44. Calculations of Z2 triviality were carried out by using the full-potential linearized augmented plane-wave method implemented in the WIEN2K package45. Details for models and computations (Z2 invariant calculation results and band structures of Sb and Sn@H-Si(111)) are presented in Supplementary Information.