Helical Luttinger liquid in topological insulator nanowires

Abstract

We derive and analyze the effective low-energy theory for interacting electrons in a cylindrical nanowire made of a strong topological insulator. Three different approaches provide a consistent picture for the band structure, where surface states forming inside the bulk gap correspond to one-dimensional bands indexed by total angular momentum. When a half-integer magnetic flux pierces the nanowire, we find a strongly correlated helical Luttinger liquid topologically protected against weak disorder. We describe how transport experiments can detect this state.

4+ pages, 3 figures

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• Transport in a thin topological insulator with potential and magnetic barriers
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• Numerical analysis of surface and edge states in slabs, stripes, rods and surface steps of topological insulators
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