Adiabatic charge transport through non-Bloch bands

TL;DR

This paper investigates non-Hermitian topological phases in an extended Su-Schrieffer-Heeger model, emphasizing non-Bloch bands and adiabatic charge transport, and establishes a unified framework for static and driven cases.

Contribution

It introduces a microscopic analysis of non-Bloch bands using non-Bloch momentum, linking bulk-boundary correspondence with adiabatic charge transport in non-Hermitian systems.

Findings

Non-Bloch momentum accurately predicts bulk-boundary correspondence.

Quantized charge flow is preserved when no gap-closing occurs during evolution.

Unified description of non-Bloch bands for static and driven non-Hermitian systems.

Abstract

We explore the non-reciprocal intracell hopping mediated non-Hermitian topological phases of an extended Su-Schrieffer-Heeger model hosting second-nearest-neighbour hopping. We microscopically analyze the phase boundaries using the non-Bloch momentum while the off-critical (critical) phases are directly associated with the gapped (gapless) nature of the non-Bloch bands that we derive from the characteristic equation using the gauge freedom. The non-Bloch momentum accurately reflects the bulk boundary correspondence (BBC) explaining the winding number profile under open boundary conditions. We examine the adiabatic dynamics to promote the concept of adiabatic charge transport in a non-Hermitian scenario justifying the BBC in spatio-temporal Bott index and non-Bloch Chern number. Once the non-Bloch bands experience no (a) gap-closing during the evolution of time, quantized flow of is preserved (broken). Our study systematically unifies the concept of non-Bloch bands for both static and driven situations.