Quantum theory of nonlinear electromagnetic response

TL;DR

This paper develops a comprehensive quantum theory for nonlinear electromagnetic responses to both electric and magnetic fields, using Matsubara Green's functions, and applies it to phenomena like nonlinear Hall effects.

Contribution

It introduces a systematic quantum framework for nonlinear responses to electric and magnetic fields, including diagrammatic methods and analysis of quantum geometric effects.

Findings

Derived nonlinear Hall and magneto-nonlinear Hall effects.

Revealed the role of quantum geometric quantities.

Analyzed Zeeman interaction contributions.

Abstract

In recent years, the investigation of nonlinear electromagnetic responses has received significant attention due to its potential for elucidating the quantum properties of matter. Although remarkable progress has been achieved in developing quantum theories of nonlinear responses to electric field, a comprehensive quantum theory framework that systematically addresses nonlinear responses to both electric and magnetic fields has yet to be thoroughly discussed. Here, we present a systematic quantum theory of nonlinear electromagnetic response using the Matsubara Green's function approach, which explicitly incorporates the wave vector dependence of external electromagnetic fields. We provide diagrammatic representation and reveal the general properties of transport coefficients. We apply our theory to second-order responses, deriving the nonlinear Hall effects and magneto-nonlinear Hall effects in both time-reversal symmetric and time-reversal breaking systems. These effects stem from diverse quantum geometric quantities. Additionally, we analyze the contributions arising from the Zeeman interaction. Our work presents a unified quantum theory of nonlinear electromagnetic response, paving the way for further exploration of novel phenomena in this field.