Magnetoplasmons in $N$-layer structures

TL;DR

This paper develops a systematic framework using the Kac--Murdock--Szeg\

Contribution

It introduces a novel analytic formalism for understanding magnetoplasmons in multilayer 2D electron systems, accounting for interlayer Coulomb interactions and tunneling effects.

Findings

Single-layer magnetoplasmon splits into N modes in multilayer systems.

Derived asymptotic behaviors for long-wavelength, large separation, and strong magnetic fields.

Identified hybridization and enhanced gaps in magnetoplasmon modes.

Abstract

We provide a systematic framework to investigate the magnetoplasmons of multilayer two-dimensional electron systems by using the Kac--Murdock--Szeg\H{o} (KMS) Toeplitz matrix to consider interlayer Coulomb interactions. In the absence of interlayer tunneling, we show that the single-layer magnetoplasmon branch splits into $N$ collective modes -- one in-phase mode and $N-1$ out-of-phase modes -- and derive their asymptotic behaviors in the long-wavelength limit, as well as in the limit of large layer separation and strong magnetic fields. When interlayer tunneling is present, we clarify the magnetoplasmon dispersion, both qualitatively and quantitatively, by identifying the magnetoplasmon mode associated with each interband transition, as well as tunneling magnetoplasmons arising from interband transitions with the same Landau level index. Our study presents the hybridization between the modes governed by underlying symmetries, along with an enhanced tunneling magnetoplasmon gap exceeding the associated interband gap. The KMS-based analytic formalism thus provides a comprehensive physical understanding of magnetoplasmons in multilayer structures.