Bulk-edge correspondence in topological pumping

TL;DR

This paper revisits topological pumping through the lens of bulk-edge correspondence, demonstrating how edge states ensure quantized charge transfer and proposing a gauge-invariant formulation of pumped charge.

Contribution

It explicitly links the quantization of topological pumping to edge state dynamics and introduces a gauge-invariant expression for the pumped charge.

Findings

Pumped charge is related to Berry connection in time.

Edge states cause singular CM motion ensuring quantization.

A gauge-invariant form of pumped charge is proposed.

Abstract

The topological pumping [1-3] is revisited from a view point of the bulk-edge correspondence. Shift of the center of mass (CM) as a pumped charge is explicitly given by the Berry connection in time direction. We show that observed pumping is due to the bulk, but its quantization is guaranteed by singular motion of the CM caused by edge states. This is the bulk-edge correspondence in the topological pumping. A gauge invariant form of the pumped charge is proposed by the temporal gauge and is used to establish this bulk-edge correspondence.