Thermoelectric Relations in the Conformal Limit in Dirac and Weyl Semimetals

Vicente Arjona,María A H Vozmediano,Juan Borge

doi:10.3390/sym12050814

Abstract

Dirac and Weyl semimetals are three-dimensional electronic systems with the Fermi level at or near a band crossing. Their low energy quasi-particles are described by a relativistic Dirac Hamiltonian with zero effective mass, challenging the standard Fermi liquid (FL) description of metals. In FL systems, electrical and thermo–electric transport coefficient are linked by very robust relations. The Mott relation links the thermoelectric and conductivity transport coefficients. In a previous publication, the thermoelectric coefficient was found to have an anomalous behavior originating in the quantum breakdown of the conformal anomaly by electromagnetic interactions. We analyze the fate of the Mott relation in the system. We compute the Hall conductivity of a Dirac metal as a function of the temperature and chemical potential and show that the Mott relation is not fulfilled in the conformal limit.

Highlights

IntroductionDirac semimetals are three-dimensional (3D) crystals with band crossings near the Fermi level
Dirac semimetals are three-dimensional (3D) crystals with band crossings near the Fermi level.In a low energy continuum description their quasi particles obey the massless Dirac equation and the interacting system is identical to massless quantum electrodynamics (QED)
The main conclusion of this work is the violation of the Mott relation at the conformal point of

Summary

Introduction

Dirac semimetals are three-dimensional (3D) crystals with band crossings near the Fermi level. In a recent publication [29], it was shown that the conformal anomaly [30], related to metric deformations, gives rise to a special contribution to the Nernst signal which remains finite at zero temperature and chemical potential, a very unusual property This result was later confirmed with a more standard Kubo calculation in [31]. Extending the calculation to include a finite temperature and chemical potential, we see that the Mott relation is recovered at finite temperature and chemical potential This result implies the singularity of the conformal point and the fact that, as it was well known in graphene, its physics can not be reached by taking the μ → 0 limit of a doped system

Thermoelectric Relations

The Hall Conductivity

The Mott Relation

Discussion