Quantum anomalous Hall effect in stanene on a nonmagnetic substrate

Since the quantum anomalous Hall (QAH) effect was realized in magnetic topological insulators, research on the effect has become a hot topic. The very harsh realizing requirements of the effect in experiments, however, hinder its practical applications. Based on ab initio methods, we find that nonmagnetic $\mathrm{Pb}{\mathrm{I}}_2$ films are ideal substrates for the two-dimensional honeycomb stanene. The QAH effect with a pretty large band gap (up to 90 meV) can be achieved in the functionalized $\mathrm{stanene}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructure. Despite van der Waals interactions in the heterostructure, band inversions are found to be happening between Sn $(s$ and $p_{x,y}$ ) and $\mathrm{Pb}\left(p_{x,y}\right)$ orbitals, playing a key role in determining the nontrivial topology and the large band gap of the system. Having no magnetic atoms is imperative to triggering the QAH effect. A very stable rudimentary device having QAH effects is proposed based on the $\mathrm{Sn}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructure. Our results demonstrate that QAH effects can be easily realized in the $\mathrm{Sn}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructures in experiments.

Figure 1

(a) Total energy of the $\mathrm{Pb}{\mathrm{I}}_2$ monolayer as a function of the lattice constant. Side (b) and top (c) views of half-H-passivated stanene grown on the $\mathrm{Pb}{\mathrm{I}}_2$ monolayer. “$d$” in (b) gives the distance between the stanene and the substrate. The solid black and dashed red lines in (c) denote the $3\times 3$ and $1\times 1$ unit cells, respectively. The structure shown in (b), (c) is the most stable configuration for the heterostructure.

Figure 2

The band structures of the $\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructure (a) without and (b) with SOC. The red and blue curves express the spin-up and spin-down bands, respectively. (c) Magnification of the band structure of (b) around the $E_F$. (d) The band evolution mechanism of the $\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructure from the case without SOC to the case with SOC. The orbital component analysis is with respect to the Γ point. The small arrows in (d) show the spin directions.

Figure 3

(a) FM and 120° AFM orders considered for the $\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructure. The small blue arrows represent the spin directions. The unit cell for the 120° AFM orders is displayed by the green lines. (b) Band structures for the $\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructure with SOC by using DFT methods (solid black curves) and Wannier interpretation (open magenta circles). The blue dots denote the Berry curvatures [in atomic units (a.u.)] for the whole valence bands. (c) The corresponding distribution of Berry curvature in the 2D momentum space. (d) The electric field effect on the band gap of the heterostructure.

Figure 4

(a) The $\mathrm{Pb}{\mathrm{I}}_2/\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ sandwiched heterostructure. (b) Band structures for the $\mathrm{Pb}{\mathrm{I}}_2/\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ sandwiched heterostructure with SOC by using DFT methods (solid black curves) and Wannier interpretation (open magenta circles). The blue dots denote the Berry curvatures [in atomic units (a.u.)] for the whole valence bands. (c), (d) The schematic diagrams to realize the QAH effect in $\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ heterostructures and $\mathrm{Pb}{\mathrm{I}}_2/\mathrm{SnH}/\mathrm{Pb}{\mathrm{I}}_2$ sandwiched heterostructures, respectively. The green arrows in (c), (d) indicate the edge currents. The H-passivated stanene overlayers can give rise to a magnetic moment of $1{\mu }_B$ per unit cell with the FM ground state as shown in Fig. 3.