Symmetry selection rules for the intrinsic nonlinear thermal Hall effect in altermagnets: Role of quantum metric and $C_2$ rotational symmetry

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.

arXiv comment5 pages, 4 figures