Restricted Wiedemann-Franz law and vanishing thermoelectric power in one-dimensional conductors

TL;DR

This paper investigates thermal and electrical transport in one-dimensional Dirac conductors, revealing a restricted Wiedemann-Franz law with branch-specific temperatures and zero thermoelectric power due to electron-hole symmetry.

Contribution

It demonstrates that in 1D Dirac systems, the Wiedemann-Franz law applies separately to each branch with distinct temperatures, and shows thermoelectric power vanishes, supported by experimental validation.

Findings

Wiedemann-Franz law is restricted to each branch with its specific temperature.

Thermoelectric power vanishes due to electron-hole symmetry.

Experimental validation confirms theoretical predictions.

Abstract

In one-dimensional (1D) conductors with linear E-k dispersion (Dirac systems) intrabranch thermalization is favored by elastic electron-electron interaction in contrast to electron systems with a nonlinear (parabolic) dispersion. We show that under external electric fields or thermal gradients the carrier populations of different branches, treated as Fermi gases, have different temperatures as a consequence of self-consistent carrier-heat transport. Specifically, in the presence of elastic phonon scattering, the Wiedemann-Franz law is restricted to each branch with its specific temperature and is characterized by twice the Lorenz number. In addition thermoelectric power vanishes due to electron-hole symmetry, which is validated by experiment.