Reflectivity properties of graphene with nonzero mass-gap parameter

TL;DR

This paper analyzes how a nonzero mass-gap parameter affects graphene's reflectivity across frequencies and temperatures, providing explicit formulas and numerical results for potential optical device applications.

Contribution

It introduces a simplified explicit representation of the polarization tensor for gapped graphene and derives analytic expressions for reflectivity at various frequencies and temperatures.

Findings

Reflectivity of gapped graphene approaches zero at zero frequency and zero temperature.

At nonzero temperature, reflectivity at zero frequency equals unity.

Resonance behavior occurs at the gap border frequency, with reflectivity dropping near certain frequencies.

Abstract

The reflectivity properties of graphene with nonzero mass-gap parameter are investigated in the framework of Dirac model using the polarization tensor in (2+1)-dimensional space-time. For this purpose, a more simple explicit representation for the polarization tensor along the real frequency axis is found. The approximate analytic expressions for the polarization tensor and for the reflectivities of graphene are obtained in different frequency regions at any temperature. We show that the nonzero mass-gap parameter has a profound effect on the reflectivity of graphene. Specifically, at zero temperature the reflectivity of gapped graphene goes to zero with vanishing frequency. At nonzero temperature the same reflectivities are equal to unity at zero frequency. We also find the resonance behavior of the reflectivities of gapped graphene at both zero and nonzero temperature at the border frequency determined by the width of the gap. At nonzero temperature the reflectifities of graphene drop to zero in the vicinity of some frequency smaller than the border frequency. Our analytic results are accompanied with numerical computations performed over a wide frequency region. The developed formalism can be used in devising nanoscale optical detectors, optoelectronic switches and in other optical applications of graphene.