End states in a one-dimensional topological Kondo insulator in large-Nlimit

Abstract

To gain further insight into the properties of interacting topological insulators, we study a one-dimensional model of topological Kondo insulators which can be regarded as the strongly interacting limit of the Tamm-Shockley model. Treating the model in a large-$N$ expansion, we find a number of competing ground-state solutions, including topological insulating and valence bond ground states. One of the effects to emerge in our treatment is a reconstruction of the Kondo screening process near the boundary of the material (``Kondo band-bending''). Near the boundary for localization into a valence bond state, we find that the conduction character of the edge state grows substantially, leading to states that extend deeply into the bulk. We speculate that such states are the one-dimensional analog of the light $f$-electron surface states which appear to develop in the putative topological Kondo insulator, ${\mathrm{SmB}}_{6}$.