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

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 arising from non-Hermitian anomalous Berry connection. Moreover, it is a well-known fact that geometric structures of 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. In addition, we show the existence of a second-order nonlinear longitudinal conductivity induced by the non-Hermitian anomalous Berry connection, violating a well-known fact of the absence of a second-order nonlinear longitudinal conductivity in a Hermitian system with symmetric energy spectra. We illustrate these anomalous phenomena 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.