On the Wiedemann-Franz law violation in Graphene and quark-gluon plasma systems

TL;DR

This paper compares the thermodynamic and transport properties of quark-gluon plasma and graphene, revealing that the Wiedemann-Franz law is violated in fluidic regimes but obeyed at higher carrier densities, indicating a fluid to non-fluid transition.

Contribution

It demonstrates the violation of the Wiedemann-Franz law in fluidic regimes of graphene and quark-gluon plasma, linking this to enthalpy per charge carriers and carrier density.

Findings

Lorenz ratio deviates from unity in fluidic regimes.

Graphene obeys the Wiedemann-Franz law at high carrier density.

Quark-gluon plasma likely violates the law at high density, pending future experiments.

Abstract

A comparative study of the thermodynamic and transport properties of the ultra-relativistic quark-gluon plasma produced in heavy ion collisions with the "quasi-relativistic" massless electron-hole plasma in graphene sample has been performed. We observe that the enthalpy per net charge carriers emerges as a useful physical quantity determining the transport variables in hydrodynamic domain. Lorenz ratio is defined as thermal to electrical conductivity ratio, normalized by temperature and Lorenz number $L_{0}=\frac{\pi^{2}}{3}\left(\frac{k_{B}}{e}\right)^{2}$. The validity of the Wiedemann-Franz law can be checked by evaluating the Lorenz ratio, which is expected to be unity. We investigate the validity of the Wiedemann-Franz law by examining whether the Lorenz ratio equals unity or deviates from it. Our findings indicate that, within the fluid-based framework, the Lorenz ratio consistently leads to a violation of the Wiedemann-Franz law. This is attributed to the proportional relation between Lorenz ratio and enthalpy per net charge carriers in the fluid. Based on the experimental observation, graphene and quark-gluon plasma, both systems at a low net carrier density, violate the Wiedemann-Franz law due to their fluidic nature. However, graphene at a relatively high net carrier density obeys the Wiedemann-Franz law, followed by metals with high Fermi energy or electron density. It indicates a fluid to the non-fluid transition of the graphene system from low to high carrier density. In this regard, the fluid or non-fluid aspect of quark-gluon plasma at high density is yet to be explored by future facilities like Compressed Baryonic Matter and Nuclotron-based Ion Collider fAcility experiments.