Protection of the surface states in topological insulators: Berry phase perspective

TL;DR

This paper explores how the topologically protected surface states of topological insulators are influenced by geometry, demonstrating protection on hyperbolic surfaces through Berry phase effects and induced vector potentials.

Contribution

It introduces the concept that surface states in topological insulators are inherently protected by their Berry phase, extending protection to complex geometries like hyperbolic surfaces.

Findings

Surface states induce effective vector potentials on curved surfaces.

Protection of surface states extends beyond simple geometries.

Berry phase plays a key role in topological protection.

Abstract

The metallic surface state of a topological insulator (TI) is not only topologically protected, but exhibits a remarkable property of inducing an effective vector potential on curved surfaces. For an electron in the surface state of a spherical or a cylindrical TI (TI nanoparticle or nanowire) a pseudo-magnetic monopole or a fictitious solenoid is effectively induced, encoding the geometry of the system. Here, by taking an example of a hyperbolic surface we demonstrate that as a consequence of this property stemming from its active spin degree of freedom, the surface state is by itself topologically protected.