Plasmon excitations in half-filled graphene: A Comparative study between Quantum Monte Carlo and Random Phase Approximation

Abstract

Transport properties of strongly correlated materials have contributions from quasiparticle excitations such as electrons and holes as well as emerging collective excitations such as plasmonic sound-like modes which are sustained by interactions. As was shown in Phys. Rev. B 106, 205127, the thermal excitation of the long-lived plasmons in graphene provides a substantial contribution to heat and momentum transport in the interaction-dominated regime. Detailed information on these excitations is therefore necessary for the quantitative understanding of hydrodynamic transport. On the other hand, dynamics of graphene plasmons is usually studied using Dirac perturbation theory, thus neglecting the effects of a finite Brillouin zone and higher-order perturbative corrections. Both these effects can be however significant for strong-interacting systems including free-standing graphene with the effective coupling constant of the order of alpha=2. In this paper, we studied the behavior of plasmons in half-filled free standing graphene using unbiased Quantum Monte Carlo calculations. We confirm the existence of well-defined resonance peaks for plasmons around the Gamma-point. Comparison with the Random-phase-approximation (RPA) calculation for the honeycomb lattice shows that RPA yields more stable plasmon modes, while QMC shows enhanced broadening due to non perturbative interaction effects. To account for this effect, we generalize the lattice RPA calculations by dressing the fermionic propagator by a constant lifetime. As a result, the plasmon frequencies are shifted towards higher energies and the spectrum is broadened, yielding a better agreement with QMC. Our findings highlight the need to account for both a finite Brillouin zone and strong interaction effects when developing theories of electronic transport in free-standing graphene.

11 pages, 14 figures, accepted for publication in Phys. Rev. B