# Bulk-edge correspondence in topological transport and pumping

## TL;DR

This paper explores the bulk-edge correspondence in topological systems, demonstrating that quantized charge transport persists even with disorder, and clarifies the relation between bulk properties and edge states in topological pumps.

## Contribution

It establishes that topological pumping maintains quantized charge transport despite non-adiabatic edge effects and disorder, extending the understanding of bulk-edge correspondence in realistic conditions.

## Key findings

- Quantized pumped charge persists with disorder.
- Edge non-adiabatic effects do not break charge quantization.
- Bulk-edge compensation guarantees quantization in topological pumps.

## Abstract

The bulk-edge correspondence (BEC) refers to a one-to-one relation between the bulk and edge properties ubiquitous in topologically nontrivial systems. Depending on the setup, BEC manifests in different forms and govern the spectral and transport properties of topological insulators and semimetals. Although the topological pump is theoretically old, BEC in the pump has been established just recently [1] motivated by the state-of-the-art experiments using cold atoms [2,3]. The center of mass (CM) of a system with boundaries shows a sequence of quantized jumps in the adiabatic limit associated with the edge states. Although the bulk is adiabatic, the edge is inevitably non-adiabatic in the experimental setup or in any numerical simulations. Still the pumped charge is quantized and carried by the bulk. Its quantization is guaranteed by a compensation between the bulk and edges. We show that in the presence of disorder the pumped charge continues to be quantized despite the appearance of non-quantized jumps.