Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities

TL;DR

This paper explores thermoelectric properties of mixed-dimensional QED models, revealing duality-based relations and behaviors at self-dual points, bridging strongly and weakly interacting regimes.

Contribution

It derives thermoelectric relations using particle-vortex duality in mixed-dimensional QEDs, highlighting new duality-based insights into transport phenomena.

Findings

Wiedemann-Franz law and Mott's relation are derived for these models.

Thermal and electrical conductivities are related through duality at self-dual points.

Seebeck tensor behavior varies with the dynamic regime and Hall angle.

Abstract

We consider the thermoelectric properties of the mixed-dimensional quantum electrodynamics of the relativistic Dirac fermion and Wilson-Fisher boson. These models are self-dual, and can form non-trivial many-body phases depending on the values of chemical potential, background magnetic field and the electromagnetic fine-structure constant. Using particle-vortex duality, we derive a variety of thermoelectric relations for strongly-interacting phases with classic paradigms such as the Wiedemann-Franz law and the Mott's relation in the dual weakly interacting regimes. Besides, at the self-dual point, for the fermionic theory we find the ratio of thermal conductivity of electrical conductivity depends on the determinant of the Seebeck tensor and the phenomenological parameter Hall angle $\theta_H$. As for the bosonic theory, the dual fermion description explains how its Seebeck tensor varies depending on the dynamic regime characterized by $\theta_H$.