Plasmons in multilayer structures

In multilayer structures, the coupling between layers gives rise to unique plasmon modes, but analytic solutions are typically available only for bilayers due to the increasing complexity as the number of layers increases. We investigate plasmons in multilayer structures, including the effects of interlayer tunneling. By introducing the Coulomb eigenvector basis for multilayer systems, which can be solved exactly using Kac-Murdock-Szegö Toeplitz matrices, we analytically derive the long-wavelength plasmon dispersions both with and without interlayer tunneling. In the N-layer systems, we find that, in the absence of interlayer tunneling, the out-of-phase acoustic or charge neutral plasmon modes with linear dispersions (ω_α ∝ q / (1 - cos((α - 1)π / N)) for α = 2, 3, ..., N) exist, while the in-phase classical plasmon mode exhibits its conventional dispersion (ω₁ ∝ √q). When isotropic interlayer tunneling is present, the out-of-phase modes develop plasmon gaps that are governed by specific interband transitions, whereas the classical mode remains unaffected. Furthermore, we apply our method to alternating-twist multilayer graphene (ATMG) and show that the gapped out-of-phase modes are generated by interband transitions between Dirac cones with different velocities. These modes remain undamped when the twist angle exceeds a critical value (θ ≥ 2.5° for the alternating-twist trilayer case), regardless of the carrier density. This work have been published in Phys. Rev. B 112, L041111 (2025); additional results are in preparation.