Quantum Spin Hall Effect in Two-Dimensional Crystals of Transition-Metal Dichalcogenides

We propose to engineer time-reversal-invariant topological insulators in two-dimensional crystals of transition-metal dichalcogenides (TMDCs). We note that, at low doping, semiconducting TMDCs under shear strain will develop spin-polarized Landau levels residing in different valleys. We argue that gaps between Landau levels in the range of 10–100 K are within experimental reach. In addition, we point out that a superlattice arising from a moiré pattern can lead to topologically nontrivial subbands. As a result, the edge transport becomes quantized, which can be probed in multiterminal devices made using strained 2D crystals and/or heterostructures. The strong $d$ character of valence and conduction bands may also allow for the investigation of the effects of electron correlations on the topological phases.

Figure 1

Top view of the 2D lattice of TMDC. The unit cell and Brillouin zone are shown in the right panel. $M$ corresponds to the transition-metal atom, and $X$ to the chalcogen atoms.

Figure 2

(a) Low-energy spectrum of a semiconducting transition-metal dicalchogenide around the $K$ and $K^{\prime }$ points of the first Brillouin zone described by the continuum-limit Hamiltonian in Eq. (3). The inset shows the orientation of the stress tensor field discussed through the text with respect to the lattice. (b) Schematic representation of the LLs induced in the valence band when strain is applied. (c) A superlattice can be also used to create a topologically nontrivial subband structure. A triangular superlattice produces replicas of $K$ and $K^{\prime }$ by mixing the valence and conduction band states at the mini-Dirac points as indicated by the arrows. (d) Highest valence subbands of a $20\times 20$ $M{X}_2$ superlattice with $\mathrm{\Delta }=1\mathrm{eV}$, $v=6.6\mathrm{eV}\mathrm{A}$, $V_s=-0.1\mathrm{eV}$, and $V_g=0.05\mathrm{eV}$, where $V_s$, $V_g$ are the scalar and gauge potentials discussed through the text. Here $\kappa$, ${\kappa }^{\prime }$, and $\mu$ label the two inequivalent corners and the intermediate point between them of the superlattice Brillouin zone as indicated in (c).