Chern pump: a bridge between integer quantum Hall effect and quantum spin Hall effect

TL;DR

This paper introduces the Chern pump as a mechanism linking the integer quantum Hall effect and quantum spin Hall effect, providing a unified framework for understanding topological insulators and their edge states.

Contribution

It proposes the Chern pump concept to explain IQHE and QSHE, establishing a bulk-edge correspondence in 2D topological insulators and predicting measurable QSHE in isolated devices.

Findings

Chern pump explains IQHE in Chern insulators.

Bulk-edge correspondence established in 2D topological insulators.

QSHE can be directly measured in isolated devices.

Abstract

We propose a electron-pumping mechanism called Chern pump to explain the integer quantum Hall effect(IQHE) in the Chern insulator. By using the parallel transport gauge in the hybrid Wannier representation we establish the bulk and edge states correspondence in the Chern insulator. The same correspondence can also be established in two dimensional(2D) topological insulator(TI). So we can consider 2D TI as two time reversal(TR) related CIs put together. The quantum spin Hall effect(QSHE) can be viewed as two TR related Chern pumps pumping electrons to opposite directions. Compared with the Z2 spin pump, the two Chern pumps explanation of QSHE is inherently 2D and predict that the QSHE can be detected in isolated device, thus make the QSHE directly measurable.