Dynamical current-current susceptibility of gapped graphene

TL;DR

This paper derives analytical formulas for the current-current correlation in gapped graphene, analyzing magnetic and oscillatory properties, and compares results with a traditional 2D electron gas, revealing unique magnetic behaviors due to band structure.

Contribution

It provides the first comprehensive analytical expressions for current-current susceptibility in gapped graphene across various parameters, including frequency, wave vector, doping, and band gap.

Findings

Orbital magnetic susceptibility is smeared out by the band gap.

Plasmon dispersion matches that of a 2DEG in the nonrelativistic limit.

Gapped graphene exhibits pseudospin paramagnetism due to its band structure.

Abstract

We present analytical expressions for the current-current correlation function in graphene for arbitrary frequency, wave vector, doping, and band gap induced by a mass term. In the static limit we analyze the Landau (orbital) and Pauli magnetization, as well as the Lindhard correction which describes Friedel and RKKY oscillations. In the nonrelativistic limit we compare our results with the situation of the usual two-dimensional electron gas (2DEG). We find that the orbital magnetic susceptibility (OMS) in gapped graphene is smeared out on an energy scale given by the inverse mass. The nonrelativistic limit of the plasmon dispersion and the Lindhard function reproduces the results of the 2DEG. The same conclusion is true for the Pauli part of the susceptibility. The peculiar band structure of gapped graphene leads to pseudospin paramagnetism and thus to a special form of the OMS.