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.
@article{arxiv.1211.2088,
title = {Protection of the surface states in topological insulators: Berry phase perspective},
author = {Ken-Ichiro Imura and Yositake Takane},
journal= {arXiv preprint arXiv:1211.2088},
year = {2013}
}