The edge states of a two-dimensional quantum spin Hall (QSH) insulator form a one-dimensional helical metal which is responsible for the transport property of the QSH insulator. Conceptually, such a one-dimensional helical metal can be attached to any scattering region as the usual metallic leads. We study the analytical property of the scattering matrix for such a conceptual multiterminal scattering problem in the presence of time reversal invariance. As a result, several theorems on the connectivity property of helical edge states in two-dimensional QSH systems as well as surface states of three-dimensional topological insulators are obtained. Without addressing real model details, these theorems, which are phenomenologically obtained, emphasize the general connectivity property of topological edge/surface states from the mere time reversal symmetry restriction.
@article{arxiv.1112.0597,
title = {Connectivity of edge and surface states in topological insulators},
author = {Yongjin Jiang and Feng Lu and Feng Zhai and Tony Low and Jiangping Hu},
journal= {arXiv preprint arXiv:1112.0597},
year = {2011}
}