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

Original 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.