Quantum Theory and Unusual Dielectric Functions of Graphene

TL;DR

This paper derives the spatially nonlocal dielectric functions of graphene from first principles using quantum field theory, analyzing their properties across frequencies and discussing implications for the Casimir effect.

Contribution

It introduces a first-principles derivation of graphene's dielectric functions considering spatial nonlocality and explores their unique features at various frequencies.

Findings

Identification of a double pole at zero frequency in the transverse dielectric function.

Analysis of the real and imaginary parts of dielectric functions at different frequency regimes.

Discussion of implications for resolving experimental-theoretical discrepancies in the Casimir effect.

Abstract

We address the spatially nonlocal dielectric functions of graphene at any frequency derived starting fromthe first principles of thermal quantum field theory using the formalism of the polarization tensor. After a brief review of this formalism, the longitudinal and transverse dielectric functions are considered at any relationship between the frequency and the wave vector. The analytic properties of their real and imaginary parts are investigated at low and high frequencies. Emphasis is given to the double pole at zero frequency which arises in the transverse dielectric function. The role of this unusual property for solving the problem of disagreement between experiment and theory in the Casimir effect is discussed. We guess that a more complete dielectric response of ordinary metals should also be spatially nonlocal and its transverse part may possess the double pole in the region of evanescent waves.