Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems

TL;DR

This paper explores how non-Hermitian anomalous Berry connection influences transport phenomena, revealing novel oscillations and conductivities in non-Hermitian systems through theoretical analysis and practical proposals.

Contribution

It uncovers new anomalous transport effects caused by non-Hermitian Berry connection, including oscillations and unconventional conductivities, expanding understanding beyond Hermitian systems.

Findings

Anomalous oscillations driven by electric fields due to non-Hermitian Berry connection.

Non-Hermitian anomalous Berry connection induces a longitudinal conductivity independent of scattering time.

Emergence of second-order nonlinear longitudinal conductivity violating Hermitian system constraints.

Abstract

Non-Hermitian materials can not only exhibit exotic energy band structures but also an anomalous velocity induced by non-Hermitian anomalous Berry connection as predicted by the semiclassical equations of motion for Bloch electrons. However, it is not clear how the modified semiclassical dynamics modifies transport phenomena. Here, we theoretically demonstrate the emergence of anomalous oscillations driven by either an external dc or ac electric field, which arise from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of electric wave functions can only affect the Hall conductivity. However, we are surprised to find a non-Hermitian anomalous Berry connection induced anomalous linear longitudinal conductivity independent of the scattering time. We also show the emergence of a second-order nonlinear longitudinal conductivity induced by non-Hermitian anomalous Berry connection, violating a well-known fact of its absence in a Hermitian system with symmetric energy spectra. These anomalous phenomena are illustrated in a pseudo-Hermitian system with large non-Hermitian anomalous Berry connection. Finally, we propose a practical scheme to realize the anomalous oscillations in an optical system.