Graphene is neither Relativistic nor Non-Relativistic case: Thermodynamics Aspects

TL;DR

This paper investigates the unique thermodynamic behavior of electrons in graphene, revealing that they do not conform strictly to relativistic or non-relativistic models, and explores the implications for understanding electron fluids and related phenomena.

Contribution

It provides a systematic microscopic analysis of thermodynamic quantities in graphene's electron fluid and compares them with non-relativistic and relativistic cases, highlighting a transition in thermodynamic behavior.

Findings

Identifies the transition between Dirac fluid and Fermi liquid regimes in graphene.

Derives a general expression for specific heat across the transition.

Connects thermodynamic transitions to Wiedemann-Franz Law violations in graphene.

Abstract

Discovery of electron hydrodynamics in graphene system has opened a new scope of analytic calculations in condensed matter physics, which was traditionally well cultivated in science and engineering as a non-relativistic hydrodynamics and in high energy nuclear and astro physics as relativistic hydrodynamics. Electrons in graphene follow neither non-relativistic nor relativistic hydrodynamics and thermodynamics. Present article has gone through systematic microscopic calculations of thermodynamical quantities like pressure, energy density, etc. of electron-fluid in graphene and compared with corresponding estimations for non-relativistic and ultra-relativistic cases. Identifying the Dirac fluid and Fermi liquid domains, we have sketched the transition of temperature and Fermi energy dependency of electron thermodynamics for graphene and other cases. An equivalent transition for quark matter is also discussed. The most exciting part is the general expression of specific heat, whose Fermi to Dirac fluid domain transition can be realized as a transition from a solid-based to a fluid-based picture. This understanding may be connected to the experimentally observed Wiedemann-Franz Law violation in the Dirac fluid domain of graphene system.