Spin connection and boundary states in a topological insulator

TL;DR

This paper investigates how boundary curvature affects surface resistivity in 3D topological insulators, revealing a quantum spin connection and its impact on electron scattering and resonances.

Contribution

It introduces an analytical solution for spherical topological insulators and demonstrates the emergence of a quantum spin connection from the band structure.

Findings

Quantum spin connection arises from the band structure.

Boundary curvature influences surface resistivity.

Resonances occur when electron wavelength matches bump size.

Abstract

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.