Moir\'{e} edge states in twisted bilayer graphene and their topological relation to quantum pumping

TL;DR

This paper investigates moiré edge states in twisted bilayer graphene, revealing their topological origin linked to sliding Chern numbers and demonstrating a bulk-edge correspondence through charge pumping during layer sliding.

Contribution

It uncovers the topological nature of moiré edge states in twisted bilayer graphene and connects their emergence to the sliding Chern number, a novel insight into topological charge pumping.

Findings

Edge states are associated with the moiré pattern.

Sliding one layer causes edge state transfer across the band gap.

Number of pumped edge states equals the sliding Chern number.

Abstract

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 moir\'{e} pattern, and the emergence of these moir\'{e} 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 the 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 moir\'{e} bilayer systems.