Spin Berry phase in anisotropic topological insulators

Abstract

Three-dimensional topological insulators are characterized by the presence of protected gapless spin helical surface states. In realistic samples these surface states are extended from one surface to another, covering the entire sample. Generally, on a curved surface of a topological insulator an electron in a surface state acquires a spin Berry phase as an expression of the constraint that the effective surface spin must follow the tangential surface of real space geometry. Such a Berry phase adds up to pi when the electron encircles, e.g., once around a cylinder. Realistic topological insulators compounds are also often layered, i.e., are anisotropic. We demonstrate explicitly the existence of such a pi Berry phase in the presence and absence (due to crystal anisotropy) of cylindrical symmetry, that is, regardless of fulfilling the spin-to-surface locking condition. The robustness of the spin Berry phase pi against cylindrical symmetry breaking is confirmed numerically using a tight-binding model implementation of a topological insulator nanowire penetrated by a pi-flux tube.

9 pages, 4 figures (6 panels)

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• Delocalization of surface Dirac electrons in disordered weak topological insulators
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• Dephasing-Induced Stabilization of a Perfectly Conducting Channel in Disordered Graphene Nanoribbons with Zigzag Edges
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• Finite-size scaling analysis of the conductivity of Dirac electrons on a surface of disordered topological insulators
• Dirac plasmon polaritons and magnetic modes in topological-insulator nanoparticles
• Electromagnetic response of the surface states of a topological insulator nanowire embedded within a resonator
• Equatorial magnetoplasma waves