# Nonreciprocal thermal and thermoelectric transport of electrons in noncentrosymmetric crystals

## TL;DR

This paper investigates how inversion symmetry breaking in noncentrosymmetric crystals leads to nonreciprocal thermal and thermoelectric transport phenomena, deriving second-order conductivities and exploring their low-temperature behavior.

## Contribution

It derives second-order nonlinear conductivities for thermal and thermoelectric transport in noncentrosymmetric crystals using the Boltzmann equation, revealing their relation to linear conductivities and low-temperature effects.

## Key findings

- Non-vanishing thermal transport coefficients at zero temperature.
- Second-order conductivities described by two functions and their derivatives.
- Estimated nonlinear conductivities in MoS2 monolayer and BiTeX semiconductors.

## Abstract

Nonreciprocal transport phenomena indicate that the forward and backward flows differ, and are attributed to broken inversion symmetry. In this paper, we study the nonreciprocity of a thermal and thermoelectric transport of electronic systems resulting from inversion-symmetry-broken crystal structures. The nonlinear electric, thermoelectric, and thermal conductivities are derived up to the second order in an electric field and a temperature gradient by using the Boltzmann equation with the relaxation time approximation. All the second-order conductivities appearing in this paper are described by two functions and their derivatives, and these are related to each other in the same way that linear conductivities are e.g. via the Wiedemann-Franz law. We found that non-vanishing thermal-transport coefficients in the zero-temperature limit appear in nonlinear conductivities, which dominate the thermal transport at a sufficiently low temperature. The nonlinear conductivities and possible observable quantities are estimated in a $1H$ monolayer of the transition metal dichalcogenides MoS$_2$ and a polar semiconductor BiTeX(X=I,Br).