Moire edge states in twisted bilayer graphene and their topological relation to quantum pumping

摘要

We study the edge states of twisted bilayer graphene and their topological origin. We show that the twisted bilayer graphene has special edge states associated with the moire pattern, and the emergence of these moire edge states is linked with the sliding Chern number, which describes topological charge pumping caused by relative interlayer sliding. When one layer of the twisted bilayer is relatively slid with respect to the other layer, the edge states are transferred from a single band to another across the band gap, and the number of edge states pumped in a sliding cycle is shown to be equal to the sliding Chern number of the band gap. The relationship can be viewed as a manifestation of the bulk-edge correspondence inherent in moire bilayer systems.