Graphene is neither relativistic nor non-relativistic: thermodynamics aspects

Abstract

Discovery of electron hydrodynamics in graphene systems has opened a new scope of theoretical research in condensed matter physics, which was traditionally well cultivated in science and engineering as a non-relativistic hydrodynamics and in high energy nuclear and astrophysics as relativistic hydrodynamics. Electrons in graphene follow neither non-relativistic nor relativistic hydrodynamics. Similar to other hydrodynamical descriptions, the energy–momentum tensor of graphene also has an ideal component and a dissipating component, but in an unconventional way, so popularly, it is sometimes called as unconventional hydrodynamics. The unconventional part of the dissipating component for the energy–momentum tensor is recently addressed in Phys. Rev. B 108, 235172 (2023) but its ideal component, which is connected with the thermodynamics of graphene, has not been zoomed in a very systematic way. This article has gone through systematic microscopic calculations of thermodynamical quantities like pressure, energy density, etc., of electron-fluid in graphene and compared with the corresponding estimations for non-relativistic and ultra-relativistic cases. We have sketched the temperature and Fermi energy dependency of electron thermodynamics for graphene and other cases where the transition from Fermi liquid to Dirac fluid domain is explored. An equivalent transition for quark matter is also discussed. Interestingly, an enhancement of specific heat within the low-temperature and Fermi energy region is found, which may be connected to the recently observed Wiedemann–Franz law violation.