Topological insulators in twisted transition metal dichalcogenide homobilayers

Abstract

We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in $\pm K$ valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe${}_2$. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe${}_2$ at $+K$ ($-K$) valley can be described using a two-band model with a layer-pseudospin magnetic field $\mathbf{\Delta }(\mathbf{r})$ that has the moiré period. We show that $\mathbf{\Delta }(\mathbf{r})$ has a topologically non-trivial skyrmion lattice texture in real space, and that the topmost moiré valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moiré cell.

5+5 pages, 4+4 figures. Title has been modified. Accepted by Physical Review Letters on February 7, 2019