Kramers-Kronig relation of graphene conductivity

TL;DR

This paper derives a Kramers-Kronig relation for graphene's conductivity using a Lorentz-covariant formulation, highlighting ambiguities in calculations and emphasizing the importance of non-perturbative effects for accurate electrical response analysis.

Contribution

It introduces a complete Lorentz-covariant framework for graphene conductivity and discusses the implications of ultraviolet ambiguities and non-perturbative contributions.

Findings

Derived a Kramers-Kronig relation for graphene conductivity.

Identified ambiguities in conductivity calculations at ultraviolet energies.

Highlighted the necessity of considering non-perturbative effects.

Abstract

Utilizing a complete Lorentz-covariant and local-gauge-invariant formulation, we discuss graphene response to arbitrary external electric field. The relation, which is called as Kramers-Kr(\ddot{o})nig relation in the paper, between imaginary part and real part of ac conductivity is given. We point out there exists an ambiguity in the conductivity computing, attributed to the wick behavior at ultraviolet vicinity. We argue that to study electrical response of graphene completely, non-perturbational contribution should be considered.