# Thermoelectric Hall conductivity and figure of merit in Dirac/Weyl materials

## TL;DR

This paper investigates the thermoelectric properties of three-dimensional Dirac and Weyl semimetals, revealing quantized Hall responses and significant enhancements in thermoelectric efficiency under magnetic fields.

## Contribution

It demonstrates that Dirac/Weyl materials exhibit a quantized thermoelectric Hall coefficient and substantial figure of merit improvements at accessible magnetic fields, unlike traditional systems.

## Key findings

- $ ext{α}_{xy}$ becomes quantized at high magnetic fields.
- Thermoelectric figure of merit can increase by over 100% at moderate fields.
- Significant thermopower enhancements are observed in Dirac/Weyl semimetals.

## Abstract

We calculate the thermoelectric response coefficients of three-dimensional Dirac or Weyl semimetals as a function of magnetic field, temperature, and Fermi energy. We focus in particular on the thermoelectric Hall coefficient $\alpha_{xy}$ and the Seebeck coefficient $S_{xx}$, which are well-defined even in the dissipationless limit. We contrast the behaviors of $\alpha_{xy}$ and $S_{xx}$ with those of traditional Schr\"{o}dinger particle systems, such as doped semiconductors. Strikingly, we find that for Dirac materials $\alpha_{xy}$ acquires a constant, quantized value at sufficiently large magnetic field, which is independent of the magnetic field or the Fermi energy, and this leads to unprecedented growth in the thermopower and the thermoelectric figure of merit. We further show that even relatively small fields, such that $\omega_c \tau \sim 1$ (where $\omega_c$ is the cyclotron frequency and $\tau$ is the scattering time), are sufficient to produce a more than $100\%$ increase in the figure of merit.