Nonlinear Ohmic electromagnetic response

TL;DR

This paper develops a quantum field-theoretic framework to analyze nonlinear Ohmic responses, revealing intrinsic contributions from band geometry and predicting observable effects in specific materials.

Contribution

It introduces a systematic approach to nonlinear Ohmic transport, highlighting a previously unrecognized intrinsic response linked to quantum geometry.

Findings

Intrinsic Ohmic conductivity from band geometry predicted in bilinear magnetoelectric effects.

Demonstrated observability of geometrically induced nonlinear response in Dirac materials.

Identified conditions such as high Fermi velocity and narrow band gaps for experimental detection.

Abstract

We systematically investigate nonlinear Ohmic responses in second-harmonic generation and bilinear magnetoelectric effects within the Matsubara Green's function formalism. The optical nonlinear Ohmic conductivity is shown to consist of a nonlinear Drude-like part and an intrinsic term determined by the fully symmetrized normalized quantum metric dipole. Notably, we predict a previously unrecognized intrinsic Ohmic conductivity arising from band geometry in the bilinear magnetoelectric response, which exhibits transverse behavior similar to its optical counterpart. Using a two-dimensional Dirac model, we demonstrate that this geometrically induced nonlinear Ohmic response is observable in materials with high Fermi velocity and narrow band gaps. Our work provides a systematic quantum field-theoretic framework for describing nonlinear Ohmic transport in condensed matter systems.