Conductivity of graphene in the framework of Dirac model: Interplay between nonzero mass gap and chemical potential

TL;DR

This paper develops a comprehensive theory for graphene's electrical conductivity considering mass gap and chemical potential, providing analytical expressions and numerical results that enhance understanding of its electromagnetic response.

Contribution

It introduces a complete analytical framework for graphene conductivity incorporating mass gap and chemical potential, refining previous models and enabling detailed comparison with experiments.

Findings

Analytical expressions for graphene's conductivity at various temperatures.

Interplay between mass gap and chemical potential affects conductivity.

Numerical results illustrating the conductivity behavior under different parameters.

Abstract

The complete theory of electrical conductivity of graphene at arbitrary temperature is developed with taken into account mass-gap parameter and chemical potential. Both the in-plane and out-of-plane conductivities of graphene are expressed via the components of the polarization tensor in (2+1)-dimensional space-time analytically continued to the real frequency axis. Simple analytic expressions for both the real and imaginary parts of the conductivity of graphene are obtained at zero and nonzero temperature. They demonstrate an interesting interplay depending on the values of mass gap and chemical potential. In the local limit, several results obtained earlier using various approximate and phenomenological approaches are reproduced, refined and generalized. The numerical computations of both the real and imaginary parts of the conductivity of graphene are performed to illustrate the obtained results. The analytic expressions for the conductivity of graphene obtained in this paper can serve as a guide in the comparison between different theoretical approaches and between experiment and theory.