Symmetry selection rules for the intrinsic nonlinear thermal Hall effect in altermagnets: Role of quantum metric and $C_{2}$ rotational symmetry

TL;DR

This paper derives symmetry-based rules for the intrinsic nonlinear thermal Hall effect in altermagnets, emphasizing the roles of quantum metric and specific symmetry breakings, and demonstrates these principles using tight-binding models.

Contribution

It establishes the symmetry conditions necessary for the nonlinear thermal Hall effect in altermagnets, highlighting the importance of quantum metric and symmetry breaking.

Findings

Nonvanishing nonlinear thermal Hall conductivity requires breaking mirror and $C_2$ symmetries.

$d$-wave altermagnets naturally break $C_2$, enabling the effect.

$g$-wave systems preserve $C_2$, suppressing the response.

Abstract

We establish symmetry-based selection rules for the intrinsic nonlinear thermal Hall effect driven by the quantum metric in altermagnets. We show that a nonvanishing nonlinear thermal Hall conductivity $\kappa_{xyy}$ requires three conditions: (i) a nontrivial quantum metric, (ii) breaking of mirror symmetry $M_{x}$, and (iii) breaking of twofold rotational symmetry $C_{2}$. Using tight-binding models on a square lattice, we demonstrate that $d$-wave altermagnets naturally break $C_{2}$ through parity-mixing orbital hybridizations, while $g$-wave systems preserve $C_{2}$, forcing the response to vanish identically. Step-by-step Taylor expansions and explicit unitary matrix proofs establish these results. Our framework provides predictive power for material selection and lays the groundwork for nonlinear spin-caloritronic devices.