Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers
We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in ± 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 the + K (– K ) valley can be described using a two-band model with a layer-pseudospin magnetic field Δ(r) that has the moiré period. We show that Δ(r) has a topologically nontrivial 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. As a result, 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.