Intrinsic anomalous thermal hall effect as a signature of quantum metric in d-wave altermagnets

TL;DR

This paper uncovers a third-order nonlinear anomalous thermal Hall effect in d-wave altermagnets driven by quantum geometry, with distinctive angular, temperature, and chemical potential dependencies, highlighting their potential for geometric transport studies.

Contribution

It introduces the concept of a nonlinear thermal Berry-connection polarizability and demonstrates its role in the intrinsic anomalous thermal Hall effect in altermagnets.

Findings

The first nonvanishing thermal Hall response appears at third order in temperature gradient.

The response depends on a newly defined quantum geometric quantity, the thermal Berry-connection polarizability.

Distinctive angular dependence of thermal Hall conductance is observed as the thermal gradient orientation varies.

Abstract

We investigate the intrinsic anomalous thermal Hall effect in d-wave altermagnets, where a transverse heat current is generated by a longitudinal temperature gradient in the absence of a magnetic field, with the leading response proportional to $(\nabla T)^3$. In these systems, the intrinsic Berry curvature-driven linear and thermal quantum-metric-driven second-order anomalous thermal Hall currents vanish as a consequence of crystalline symmetry. We show that the first nonvanishing contribution arises at third order in the temperature gradient and is governed by a nonlinear thermal Berry-connection polarizability, a quantity introduced in this work. Our analysis reveals a distinctive angular dependence of the anomalous thermal Hall conductance as the applied thermal gradient is rotated with respect to the crystal axes. We also find characteristic temperature and chemical-potential dependences that can be tested experimentally. These results identify unique quantum geometry-induced thermal responses and establish altermagnets as a promising platform for exploring intrinsic (i.e., scattering-time-independent) geometric transport phenomena.