Band inversion induced large-gap quantum spin Hall states in III-Bi-monolayer/${\mathrm{SiO}}_2$

We extend the $p_x-p_y$ large-gap scenario to the band inversion systems and exemplify the mechanism with a family of III-Bi honeycomb monolayers on $\mathrm{Si}{\mathrm{O}}_2$, which can be the next generation of large-gap quantum spin Hall (QSH) systems. First, it suggests a topological gap of the same order as the current record kept of bismuthene/SiC(0001). Second, the band inversion mechanism in which these QSH insulators originate is qualitatively distinct from the Kane-Mele paradigm. Our work demonstrates that the $p_x\text{−}{p}_y$ scenario can be utilized to promote large-gap QSH states with both Kane-Mele and band inversion mechanisms, providing an efficient building principle for future topological device construction.

Figure 1

$\mathrm{III}\text{−}\mathrm{V}\text{−}\mathrm{monolayer}/\mathrm{Si}{\mathrm{O}}_2$. (a) Crystalline structures of $\mathrm{Tl}\mathrm{Bi}/\alpha \text{−}\mathrm{Si}{\mathrm{O}}_2$ in top and side view. A similar but enlarged plot can be found in the Supplemental Material [30]. (b) Electronic structures of $\mathrm{Tl}\mathrm{Bi}/\alpha \text{−}\mathrm{Si}{\mathrm{O}}_2$. (c), (d) Projection of Bloch bands on bonding/antibonding states without (c) and with (d) the SOC of $\mathrm{Tl}\mathrm{Bi}/\alpha \text{−}\mathrm{Si}{\mathrm{O}}_2$. (e) The zigzag edge states of $\mathrm{Tl}\mathrm{Bi}/\alpha \text{−}\mathrm{Si}{\mathrm{O}}_2$. (f)–(j) The same plot for $\mathrm{Tl}\mathrm{Bi}/\beta \text{−}\mathrm{Si}{\mathrm{O}}_2$.

Figure 2

Model Hamiltonian. (a) Spinless (dashed red line) and spinful (solid blue line) band structures with the basis $p$. (b) Landau levels as a function of a perpendicular magnetic field, with two zoomed-in plots on the right showing the conduction band bottom and valence band top evolution in an energy range of 10 meV. (c) Zigzag edge states are calculated from a nanoribbon with bulk bands as (a). (d) Comparison of spinful band structure (dashed red line) and band structure with vanishing $\langle p_{x/y,\sigma }|\mathit{L}·\mathit{S}|p_{z,\sigma }\rangle$ (solid blue line). (e), (f) The same as (b), (c), but with vanishing $\langle p_{x/y,\sigma }|\mathit{L}·\mathit{S}|p_{z,\sigma }\rangle$. (g)–(i) The same as (a)–(c), but with the basis $p_{x,y}$. The six zoomed-in plots on the right-hand side correspond to the edge Dirac points denoted by the red arrows in (c), (f), and (i) under magnetic fields $B_x=10$ T ($B_z=10$ T). They are gapped as long as $p_z$ orbital is active. The energy and momentum ranges of these subplots are shown on the right of each.

Figure 3

Magnetic responses of $\mathrm{III}\text{−}\mathrm{V}\text{−}\mathrm{monolayer}/\mathrm{Si}{\mathrm{O}}_2$. (a) $\mathrm{Tl}\mathrm{Bi}/\alpha \text{−}\mathrm{Si}{\mathrm{O}}_2$. (b) $\mathrm{Tl}\mathrm{Bi}/\beta \text{−}\mathrm{Si}{\mathrm{O}}_2$. The insets are zoomed-in plots in an energy range of 5 meV and a $k$ range of 0.05/Å.