Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers

We show that moire 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 MoTe2. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe2 at the +K (-K) valley can be described using a two-band model with a layer-pseudospin magnetic field Delta(r) that has the moire period. We show that Delta(r) has a topologically nontrivial skyrmion lattice texture in real space, and that the topmost moire 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 moire cell.