Topological phases of topological insulator thin films

Abstract

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi${}_2$Se${}_3$ and Bi${}_2$Te${}_3$. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi${}_2$Se${}_3$, making Bi${}_2$Te${}_3$, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators.

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Cited by in corpus (12)

• Finite-size Topology
• Electron-Hole Asymmetry of Surface States in Topological Insulator Sb2Te3 Thin Films Revealed by Magneto-Infrared Spectroscopy
• Gapped Dirac cones and spin texture in thin film topological insulator
• Spectroscopic signature of surface states and bunching of bulk subbands in topological insulator (Bi${}_{0.4}$Sb${}_{0.6}$)${}_2$Te${}_3$ thin films
• Transport in a thin topological insulator with potential and magnetic barriers
• Surface step states and Majorana end states in profiled topological insulator thin films
• Observation of the surface hybridization gap in the electrical transport properties of the ultrathin topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$
• Particle-hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films
• Artificial oxide heterostructures with non-trivial topology
• Photo-induced Multiply Quantized Vortex States in Dirac-like Materials
• Emergent topology in thin films of nodal line semimetals
• Dynamical density response and collective modes of topological insulator ultra-thin films