Charge response function and a novel plasmon mode in graphene

TL;DR

This paper investigates the polarizability of 2D Dirac electrons in graphene, revealing the importance of ladder-type vertex corrections near the electron-hole excitation threshold and discovering a new plasmon mode due to excitonic effects.

Contribution

It analytically sums ladder diagrams to account for excitonic effects, showing their crucial role in the screening process and plasmon resonance formation in graphene.

Findings

Ladder corrections become significant near the excitation threshold.

A strong, narrow plasmon resonance emerges due to excitonic effects.

The real part of the polarization operator becomes positive beyond the threshold.

Abstract

Polarizability of non-interacting 2D Dirac electrons has a 1/\sqrt{qv-\omega} singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N -> infinity, where N is the ``color'' degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the n-th order ladder term to the same order RPA contribution is (\ln|qv-\omega|)^n/N^n$. We perform analytical summation of the infinite series of ladder diagrams which describe excitonic effect. Beyond the threshold, qv>\omega, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.