Non-local quantum effects in plasmons of graphene superlattices

TL;DR

This paper investigates quantum non-local effects on graphene plasmons in a superlattice, revealing anisotropic dispersion at low energies and isotropic behavior at higher energies, challenging semiclassical models.

Contribution

It introduces a full quantum mechanical response framework for graphene superlattices, highlighting non-local effects and anisotropic plasmon behavior at low energies.

Findings

Plasmons propagate perpendicularly to the superlattice at low energies.

Electronic transitions damp plasmons along the superlattice direction.

At high energies, plasmon dispersion becomes isotropic and Drude-like.

Abstract

By using a non-local, quantum mechanical response function we study graphene plasmons in a one-dimensional superlattice (SL) potential $V_0 \cos G_0x$. The SL introduces a quantum energy scale $E_G \sim \hbar v_F G_0$ associated to electronic sub-band transitions. At energies lower than $E_G$, the plasmon dispersion is highly anisotropic; plasmons propagate perpendicularly to the SL axis, but become damped by electronic transitions along the SL direction. These results question the validity of semiclassical approximations for describing low energy plasmons in periodic structures. At higher energies, the dispersion becomes isotropic and Drude-like with effective Drude weights related to the average of the absolute value of the local chemical potential. Full quantum mechanical treatment of the kinetic energy thus introduces non-local effects that delocalize the plasmons in the SL, making the system behave as a meta-material even near singular points where the charge density vanishes.