Thermoelectric Transport Driven by Quantum Distance

The geometric characteristics of Bloch wavefunctions play crucial roles in the properties of electronic transport. Within the Boltzmann equation framework we demonstrate that the thermoelectric performance of materials is significantly influenced by the Hilbert-Schmidt quantum distance of Bloch wavefunctions. The connection between the distribution of quantum distance on the Fermi surface and the electronic transport scattering rate is established in the presence of magnetic and nonmagnetic impurities. We apply our general formulation to isotropic quadratic band-touching semimetals, where one can concentrate on the role of quantum geometric effects other than the Berry curvature. We verify that 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 findings highlight the significance of quantum geometry in understanding and improving the performance of thermoelectric devices.