On the separation of Hall and Ohmic nonlinear responses

TL;DR

This paper extends the analysis of Hall and Ohmic responses beyond linear order, providing a general method to distinguish them at any order and revealing symmetry-dependent properties of quadratic conductivity.

Contribution

It introduces a universal decomposition method for separating Hall and Ohmic responses at all orders, beyond linear response, based on symmetry and basic physical requirements.

Findings

The Hall vs Ohmic decomposition is unique under certain conditions.

In five magnetic point groups, quadratic dc conductivity is purely Ohmic and time-reversal even.

Quadratic responses can be classified based on symmetry and disorder mediation.

Abstract

The symmetric and antisymmetric parts of the linear conductivity describe the dissipative (Ohmic) and nondissipative (Hall) parts of the current. The Hall current is always transverse to the applied electric field regardless of its orientation; the Ohmic current is purely longitudinal in cubic crystals, but in lower-symmetry crystals it has a transverse component whenever the field is not aligned with a principal axis. In this work, we extend that analysis beyond the linear regime. We consider all possible ways of partitioning the current at any order in the electric field without taking symmetry into account, and find that the Hall vs Ohmic decomposition is the only one that satisfies certain basic requirements. A general prescription is given for achieving that decomposition, and the case of the quadratic conductivity is analyzed in detail. By performing a symmetry analysis we find that in five of the 122 magnetic point groups the quadratic dc conductivity is purely Ohmic and even under time reversal, a type of response that is entirely disorder mediated.