Surface plasmon on graphene at finite $T$

TL;DR

This paper investigates how finite temperature affects surface plasmons in graphene using the polarization tensor, revealing distinct dispersion characteristics for TE and TM modes at zero chemical potential.

Contribution

It introduces a finite temperature analysis of surface plasmons in graphene with a non-zero mass gap, extending previous zero-temperature studies.

Findings

TE plasmons have a bounded below momentum region for real dispersion

TM plasmons have a bounded above momentum region for real dispersion

Temperature influences the existence and dispersion of surface plasmons in graphene

Abstract

Using the recently developed polarization tensor in (2+1) dimensions for the electronic excitations of graphene, we investigate the influence of temperature on the surface plasmons on graphene. We consider non-zero mass gap, but zero chemical potential. Plasmons may exist for both polarizations, TE and TM, of the electromagnetic field. For TE, the momentum region, where the dispersion function is real, appears bounded from below, whereas for TM it is bounded from above. We discuss the similarities of these features with those found previously in the case with non-zero chemical potential, but zero temperature.