Dynamical density response and collective modes of topological insulator ultra-thin films

TL;DR

This paper analytically studies the density response and collective excitations in ultra-thin topological insulator films, revealing unique mode behaviors influenced by tunneling effects, with potential tunability of mode velocities.

Contribution

It provides the first analytical calculation of intra- and inter-surface dynamical responses in topological insulator films considering finite tunneling, highlighting differences from conventional bilayer systems.

Findings

Out-of-phase mode remains linear at long wavelengths despite tunneling.

Mode velocity can be tuned relative to the Fermi velocity.

Finite tunneling lowers the energy of collective modes.

Abstract

We analytically calculate the intra- and inter-surface dynamical density-density linear responses of ultra-thin topological insulator films with finite tunneling between their top and bottom surfaces in both metallic and insulating regimes. Employing the random phase approximation we investigate the dispersions of in-phase and out-of-phase collective density modes of this system in the metallic regime. We find that in contrast to the bilayers of the conventional two-dimensional electron gas, where finite tunneling gaps out the out-of-phase mode, in topological insulator thin films, this mode remains linear at long wavelengths. Depending on different system parameters, the velocity of out-of-phase mode can be tuned to be larger or substantially smaller than the Fermi velocity of electrons on the isolated surfaces of the topological insulator. Finite tunneling generally reduces the energy of collective modes, making them more confined in space.