We study the edge spectrum of twisted sheets of single layer and bilayer graphene in cases where the continuum model predicts a valley Chern insulator - an insulating state in which the occupied moiré mini-bands from each valley have a net Chern number, but both valleys together have no net Chern number, as required by time-reversal symmetry. In a simple picture, such a state might be expected to have chiral valley polarized counterpropagating edge states. We present results from exact diagonalization of the tight-binding model of commensurate structures in the ribbon geometry. We find that for both the single-layer and bilayer moiré ribbons robust edge modes are generically absent. We attribute this lack of edge modes to the fact that the edge induces valley mixing.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics