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

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.Comment: 16 pages, 13 figure

Shear Viscosity expression for Graphene system in Relaxation time approximation

We have gone through the detailed microscopic calculation of the shear viscosity of a 2-dimensional graphene system in the relaxation time approximation-based kinetic theory framework. After getting its final expressions, we compared it with the shear viscosity expressions of other possible 2-dimensional as well as 3-dimensional non-relativistic and ultra-relativistic fluid systems. The aim of the comparison is to reveal -- how their different one-body dispersion relations affect their many-body fluid properties like shear viscosity and viscosity to entropy density ratio. It is also aimed to reveal the 3-dimension to the 2-dimension transformation of their mathematical structures. We have numerically explored the differences in their order of magnitude and dependence on thermodynamical parameters -- temperature and chemical potential. Marking two thermodynamical domains -- Dirac fluid and Fermi liquid for a 2-dimensional graphene system, we have noticed that shear viscosity, entropy density as well as their ratios decrease towards saturated values when one goes from Fermi liquid to Dirac fluid domain. When one shifts from mili-electron Volt scales of temperature and chemical potential in condensed matter physics location to their Mega-electron Volt scales in high energy physics location, then the same results may be expected for hot quark matter case, where the transition from the neutron star to early universe domains may be considered as Fermi liquid to Dirac fluid transition.Comment: 14 pages, 7 figure