Fundamental Distinction between Intrinsic and Extrinsic Nonlinear Thermal Hall Effects

TL;DR

This paper theoretically distinguishes intrinsic and extrinsic nonlinear thermal Hall effects, revealing their different temperature dependencies and providing a method to identify their contributions in tilted Dirac materials.

Contribution

It introduces a theoretical framework to differentiate intrinsic and extrinsic nonlinear thermal Hall effects based on temperature dependence and Fermi energy positioning.

Findings

Intrinsic contribution scales with temperature squared at low temperatures.

Extrinsic contributions are temperature independent.

Extrinsic effects can be two to three orders of magnitude larger than intrinsic ones.

Abstract

We theoretically investigated the fundamental distinction between intrinsic and extrinsic nonlinear thermal Hall effect in the presence of disorder at the second-order response to the temperature gradient in terms of the semi-classical Boltzmann equation. We found that, at low temperatures, the intrinsic contribution of the nonlinear thermal Hall conductivity is proportional to the square of temperature, whereas the extrinsic contributions (side-jump and skew-scattering) are independent of temperature. This distinct dependency on temperature provide a new approach to readily distinguish the intrinsic and extrinsic contributions. Specifically, we analysed the nonlinear thermal Hall effect for a tilted two-dimensional massive Dirac material. In particular, we showed that when the Fermi energy is located at the Dirac point, the signal is solely from the intrinsic mechanism; when the Fermi energy is higher, the extrinsic contributions are dominant, which are uncovered to be two to three orders of magnitude larger than the intrinsic contribution.