Interaction corrections to the thermopower of the three-dimensional disordered electron gas.

Thermopower measures how efficiently charges move through a material when subject to an external temperature gradient. This type of charge transport requires particle-hole asymmetry in the system, meaning that particles and holes must behave differently. In a disordered electron gas, such asymmetry arises from differences in the diffusion coefficient (velocity) and the density of states for particles and holes. Consequently, the semi-classical Drude-Boltzmann result for the thermopower depends on the frequency-dependence of the diffusion coefficient $D$ and the density of states. In the diffusive regime, thermopower acquires interaction corrections to the semi-classical result. Previously, we investigated the interaction corrections to the thermopower of two-dimensional disordered electron gas systems, where the density of states can be assumed to be frequency-independent [1,2]. In this study, we extend the investigation of thermopower to three-dimensional systems such as thin films. In these systems, the diffusion modes are quantized in the direction perpendicular to the surface. However, the electronic degrees of freedom have a three-dimensional dispersion, which results in a frequency-dependent density of states.