Polarization tensor in spacetime of three dimensions and quantum field theoretical description of the nonequilibrium Casimir force in graphene systems

TL;DR

This paper presents a simplified, unified expression for the polarization tensor in graphene, enabling more efficient analysis of nonequilibrium Casimir forces and other physical phenomena in graphene-based systems.

Contribution

The authors derive a compact, real-frequency formalism for the polarization tensor in graphene, applicable to on- and off-shell electromagnetic waves, facilitating diverse physical investigations.

Findings

Unified expressions for polarization tensor components applicable in various regimes.

Demonstrated the formalism on nonequilibrium Casimir force between graphene-coated plates.

Analyzed the effects of temperature, energy gap, and chemical potential on Casimir forces.

Abstract

The polarization tensor of graphene derived in the framework of the Dirac model using the methods of thermal quantum field theory in (2+1) dimensions is recast in a mathematically equivalent but more compact and convenient in computations form along the real frequency axis. The obtained unified expressions for the components of the polarization tensor are equally applicable in the regions of the on- and off-the-mass-shell electromagnetic waves. The advantages of the presented formalism are demonstrated on the example of nonequilibrium Casimir force in the configuration of two parallel graphene-coated dielectric plates one of which is either hotter or colder than the environment. This force is investigated as a function of temperature, the energy gap, and chemical potential of graphene coatings with account of the effects of spatial dispersion. Besides the thermodynamically nonequilibrium Casimir and Casimir-Polder forces, the obtained form of the polarization tensor can be useful for investigation of many diverse physical phenomena in graphene systems, such as surface plasmons, reflectances, electrical conductivity, radiation heat transfer, etc.