Single-Electron Spectra and Plasmonic Excitations in Chern Insulators

Collective excitations in topological insulators have drawn increasing attention in recent years. On the fundamental science level, these systems incorporate an interplay between topology and interactions. Technologically, it is promising to make functional plasmonic and magnonic devices by exploiting the topological feature of the underlying structures. We have investigated plasmons in one-dimensional (1D) and two-dimensional (2D) Su-Schrieffer-Heeger (SSH) models in previous studies [1-3] where some topological features are reflected and observed in collective excitations. In this work, we focus on plasmonic excitations in Chern insulators. The model being considered is the Qi-Wu-Zhang (QWZ) model, which is a 2D square lattice with two internal degrees of freedom on each site. By fixing the nearest-neighbor hopping and varying the on-site energy, we can tune the model into different topological sectors with Chern numbers C=-1, 0 or 1. We study the QWZ model in various forms: 2D periodic case (torus), ribbon (cylinder) and 2D open case (finite-sized). In the 2D periodic model, the plasmon dispersion in momentum space has different characteristic shapes in the different topological sectors. Generally, plasmons in topologically nontrivial phases (C=1,-1) show enhanced dispersion spectra compared to the trivial phase (C=0). On the open edges of the ribbon structure and on the open boundaries of finite-sized samples, plasmonic edge states are observed in the topologically non-trivial phases. These results assume that the Coulomb interaction does not specifically depend on the internal degrees of freedom. We discuss how to extend this method to cases when the Coulomb interaction takes different forms in the internal subspace.