Comparative study of plasmons in half-filled graphene via Quantum Monte Carlo and Random Phase Approximation

TL;DR

The study addresses plasmons in half-filled graphene, a regime where hydrodynamic transport is strongly influenced by collective excitations. It employs unbiased lattice Quantum Monte Carlo (QMC) on the honeycomb lattice with full long-range Coulomb interactions to characterize plasmon dispersion and spectral weight, and compares the results to Random Phase Approximation (RPA) predictions based on Dirac theory. The key findings are that well-defined plasmon resonances exist near the Γ point with a square-root dispersion in the long-wavelength limit and a plasmon residue scaling as $|k|^{3/2}$, but the prefactor deviates from RPA due to finite Brillouin zone and short-range screening effects; when screening is enhanced (Coulomb > NNN), the dispersion can become linear or intermediate, and higher-order inelastic processes further shorten plasmon lifetimes. The work underscores the necessity of lattice-aware theories that incorporate short-range screening and higher-order scattering to accurately describe graphene plasmons and their impact on transport in the interaction-dominated regime.

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 sounds and plasmons which are sustained by interactions. It was previously shown in [Phys. Rev. B 106, 205127] that 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 understanding of hydrodynamic transport with quantitative precision. On the other hand, dynamics of graphene plasmons is usually studied using the perturbation theory within the Dirac-cone approximation, 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 where the effective coupling constant can reach values up to two. Therefore, in this paper, we studied the behavior of plasmons in half-filled free standing graphene using unbiased Quantum Monte Carlo (QMC) calculations. We confirm the existence of well-defined resonance peaks for plasmons around the $Γ$ point, report their dispersion and the dependence of their quasiparticle residue on momentum. Comparison with the Random-phase-approximation (RPA) calculation for the Dirac theory shows that strong interactions and finite Brillouin zone effects, automatically taken into account in QMC calculations substantially alter the results. Our findings highlight the need to account for these effects analytically when developing theories of electronic transport in free-standing graphene.

Figures (8)

• Figure 1: Coulomb potential of different setups used in our QMC simulations
• Figure 2: Single-electron spectral functions for the "Full Coulomb" setup from section \ref{['sec:model']}. (a) $T=0.1$ and large interaction $\alpha=1.15$; (b) $T=0.1$ and small interaction $\alpha=0.14375$; (c) $T=0.25$ and large interaction $\alpha=1.15$; (d) $T=0.25$ and small interaction $\alpha=0.14375$.
• Figure 3: Spectral functions for AFM spin waves for the "Full Coulomb" setup from section \ref{['sec:model']}. (a) $T=0.1$ and large interaction $\alpha=1.15$; (b) $T=0.1$ and small interaction $\alpha=0.14375$; (c) $T=0.25$ and small interaction $\alpha1.15$; (d) $T=0.25$ and small interaction $\alpha=0.14375$.
• Figure 4: Spectral functions for CDW excitations for the "Full Coulomb" setup from section \ref{['sec:model']}. (a) $T=0.1$ and large interaction $\alpha=1.15$; (b) $T=0.1$ and small interaction $\alpha=0.14375$; (c) $T=0.25$ and small interaction $\alpha1.15$; (d) $T=0.25$ and small interaction $\alpha=0.14375$.
• Figure 5: Spectral functions for plasmons for the "Full Coulomb" setup from section \ref{['sec:model']}. (a) $T=0.1$ and large interaction $\alpha=1.15$; (b) $T=0.1$ and small interaction $\alpha=0.14375$; (c) $T=0.25$ and large interaction $\alpha=1.15$; (d) $T=0.25$ and small interaction $\alpha=0.14375$.