Relaxation terms for anomalous hydrodynamic transport in Weyl semimetals from kinetic theory

TL;DR

This paper models Weyl semimetal thermoelectric transport using a relativistic fluid with chiral anomaly, analyzing relaxation effects and deriving new DC conductivity results consistent with kinetic theory.

Contribution

It introduces all possible relaxation mechanisms compatible with fundamental constraints and derives their impact on transport properties using kinetic theory.

Findings

Relaxations that respect charge conservation and Onsager reciprocity violate the second law.

Derived DC conductivities differ from previous literature.

Established a kinetic theory framework for relaxation effects in Weyl semimetals.

Abstract

We consider as a model of Weyl semimetal thermoelectric transport a $(3+1)$-dimensional charged, relativistic and relaxed fluid with a $U(1)_{V} \times U(1)_{A}$ chiral anomaly. We take into account all possible mixed energy, momentum, electric and chiral charge relaxations, and discover which are compatible with electric charge conservation, Onsager reciprocity and a finite DC conductivity. We find that all relaxations respecting these constraints necessarily render the system open and violate the second law of thermodynamics. We then demonstrate how the relaxations we have found arise from kinetic theory and a modified relaxation time approximation. Our results lead to DC conductivities that differ from those found in the literature opening the path to experimental verification.