Thermoelectric Transport Driven by Quantum Distance

TL;DR

This paper demonstrates that the thermoelectric performance of materials is fundamentally linked to the quantum geometric structure of Bloch wave functions, specifically the Hilbert-Schmidt quantum distance, which can significantly enhance device efficiency.

Contribution

It introduces a geometric framework using quantum distance to characterize thermoelectric transport, revealing how quantum geometry can double the power factor in certain materials.

Findings

Maximum quantum distance $d_{max}$ correlates with thermoelectric power factor.

When $d_{max}$ reaches one, the power factor doubles.

Quantum geometric effects are significant beyond Berry curvature in thermoelectric performance.

Abstract

The geometric characteristics of Bloch wave functions play a crucial role in electronic transport properties. We show that the thermoelectric performance of materials is governed by the geometric structure of Bloch wave functions within the framework of the Boltzmann equation. The essential geometric notion is the Hilbert-Schmidt quantum distance, measuring the resemblance between two quantum states. We establish a geometric characterization of the scattering rate by extending the concept of quantum distance between two states in momentum space at a distance.Employing isotropic quadratic band touching semimetals, where one can concentrate on the role of quantum geometric effects other than the Berry curvature, we find that the response functions for electrical quantum transport and, therefore, the thermoelectric power factor can be succinctly expressed in terms of the maximum quantum distance, $d_\mathrm{max}$. Specifically, when $d_\mathrm{max}$ reaches one, the power factor doubles compared to the case with trivial geometry ($d_\mathrm{max}=0$). Our finding highlights the significance of quantum geometry in improving the performance of thermoelectric devices.