Spin Berry phase in anisotropic topological insulators

TL;DR

This paper demonstrates the existence and robustness of a spin Berry phase of pi in anisotropic topological insulators, regardless of cylindrical symmetry, through analytical and numerical methods.

Contribution

It explicitly shows the presence of a pi Berry phase in anisotropic topological insulators, even when cylindrical symmetry is broken, extending understanding of topological surface states.

Findings

Pi Berry phase exists in anisotropic topological insulators.

The Berry phase is robust against symmetry breaking.

Numerical simulations confirm analytical predictions.

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.