On the Wiedemann–Franz law violation in graphene and quark–gluon plasma systems

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 have been performed. We observe that the enthalpy per net charge carrier 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 carrier 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 such as Compressed Baryonic Matter and Nuclotron-based Ion Collider fAcility experiments.