Magnetoplasmons in N-layer structures

We provide a systematic framework to investigate magnetoplasmons in multilayer two-dimensional electron systems using the the Kac-Murdock-Szegő (KMS) Toeplitz matrix to describe 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 large layer separation and weak magnetic-field limit. When interlayer tunneling is present, we clarify the magnetoplasmon dispersion, both qualitatively and quantitatively, by identifying the magnetoplasmon mode associated with each interband transition, including tunneling magnetoplasmons arising from interband transitions with the same Landau level index. Our study reveals the symmetry-governed hybridization between the identified modes, 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.