Interaction-Induced Bloch Geometry and Transverse Thermoelectric Transport

Abstract

Electron--electron interactions can reconstruct Bloch wave functions, changing their geometry and the associated thermoelectric response. We derive the linear thermoelectric response within the Hartree--Fock (HF) approximation using the thermal length-gauge density-matrix approach, resolving Drude, symmetric quantum-metric, and antisymmetric Berry-curvature contributions. In a noninteracting Bloch eigenbasis, we separate the reconstructed Berry connection into the noninteracting connection and an interaction connection. This gives bare, coherence, and interaction-connection contributions to the anomalous thermoelectric response. We determine the constraints imposed by spatial inversion, rotational, time-reversal, and combined symmetries on the three transport channels. In the relaxation-time approximation, the leading weak-broadening behavior is $\Gamma^{-1}$ for the Drude contribution, $\Gamma$ for the quantum-metric contribution, and $\Gamma^0$ for the Berry-curvature contribution. The interband scalings apply away from band degeneracies. Self-consistent calculations for the triangular-lattice extended Hubbard model illustrate how interactions generate Berry curvature and a quantum metric, change the symmetry of the system, and thereby contribute to transverse thermoelectric transport.