We study the surface resistivity of a three-dimensional topological insulator when the boundaries exhibit a non trivial curvature. We obtain an analytical solution for a spherical topological insulator, and we show that a non trivial quantum spin connection emerges from the three dimensional band structure. We analyze the effect of the spin connection on the scattering by a bump on a flat surface. Quantum effects induced by the geometry lead to resonances when the electron wavelength is comparable to the size of the bump.
@article{arxiv.1011.0565,
title = {Spin connection and boundary states in a topological insulator},
author = {V. Parente and P. Lucignano and P. Vitale and A. Tagliacozzo and F. Guinea},
journal= {arXiv preprint arXiv:1011.0565},
year = {2011}
}