Nonlinear thermal and thermoelectric transport from quantum geometry

Quantum geometry may enable the development of quantum phases ranging from superconductivity to topological states. One powerful probe of quantum geometry is the spontaneous (nonlinear anomalous) Hall effect which detects Berry curvature dipole in systems with time-reversal invariance and broken inversion symmetry. With broken time-reversal symmetry, it is also associated with quantum metric dipole. Here we study the nonlinear thermal and thermoelectric responses, providing a wealth of new information about quantum geometry [1]. We uncover a web of connections between these quantities that parallel the standard Wiedemann-Franz and Mott relations. Our results motivate new probes of quantum metric and Berry curvature in multilayer graphene [2] and moiré TMD systems and, furthermore, suggest thermal and thermoelectric transport as a new means to elucidate the strongly correlated gapless topology of the Weyl-Kondo semimetals [3,4,5]. Further implications will be discussed.

[1] Y. Fang, et.al., arXiv:2505.16999.

[2] H. Zhou et al. Science 375, 774 (2022).

[3] H.-H. Lai, S. E. Grefe et al., PNAS 115, 93 (2018).

[4] S. Dzsaber et al., PNAS 118, e2013386118 (2021).

[5] S. Sur et al., arXiv:2411.16675.