Gapped out-of-phase plasmon modes in alternating-twist multilayer graphene

TL;DR

This paper theoretically analyzes plasmon modes in alternating-twist multilayer graphene, revealing unique out-of-phase modes with gaps, their dependence on twist angle, and tunability via electric fields, advancing understanding of moiré plasmonics.

Contribution

It introduces a novel theoretical framework for analyzing out-of-phase plasmon modes in moiré graphene systems, including their gaps, damping conditions, and tunability.

Findings

Out-of-phase modes have plasmon gaps from interband transitions.

Out-of-phase modes are undamped above a critical twist angle.

Plasmon modes can be tuned by an external electric field.

Abstract

We theoretically investigate the plasmon modes of alternating-twist multilayer graphene. In multilayer systems, interlayer coupling gives rise to distinctive plasmon modes, but calculations in moir\'e systems remain challenging due to their complex tunneling structures. Using the Kac-Murdock-Szeg\H{o} Toeplitz formalism, we derive that the in-phase mode exhibits the conventional $\sqrt{q}$ behavior, while the out-of-phase modes acquire plasmon gaps determined by specific interband transitions between Dirac cones with different velocities in the long-wavelength limit. We demonstrate that these out-of-phase modes remain undamped in the weak Coulomb-interaction limit when the twist angle exceeds a critical value ($\theta \gtrsim 2.75^\circ$ for the alternating-twist trilayer case), regardless of the carrier density as long as the low-energy effective Dirac Hamiltonian remains valid. Furthermore, we consider the effect of a perpendicular electric field, and demonstrate how plasmon modes can be tuned by a gate voltage.