Linear response function in the presence of elastic scattering: plasmons in graphene and the two-dimensional electron gas

TL;DR

This paper derives a linear response function accounting for elastic scattering effects, analyzing plasmon behavior in graphene and 2DEG beyond long-wavelength limits, revealing critical scattering thresholds for plasmon existence.

Contribution

It introduces a response function that incorporates elastic scattering effects beyond the long-wavelength approximation, applied to plasmons in graphene and 2DEG within RPA.

Findings

Below a critical scattering strength, plasmons are suppressed.

Critical scattering strength varies for intraband and interband plasmons in graphene.

Scattering strength decreases rapidly with frequency at low ω, more slowly at high ω.

Abstract

Within linear-response theory we derive a response function that thoroughly takes into account the influence of elastic scattering and is valid beyond the long-wavelength limit. We apply the theo-ry to plasmons in graphene and the two-dimensional electron gas (2DEG), in the random-phase ap-proximation, and for the former take into account intraband and interband excitations. The scatte-ring-modified dispersion relation shows that below a critical scattering strength $\gamma_c$, simply related to the plasmon frequency $\omega$, no plasmons are allowed. The critical strengths $\gamma_c$ and the allowed $(\omega, q)$ plasmon spectra for intraband and interband transitions in graphene are different. In both graphene and the 2DEG the strength $\gamma_c$ falls rapidly for small $\omega$ but much more slowly for large $\omega$.