Connectivity of edge and surface states in topological insulators

Yongjin Jiang, Feng Lu, Feng Zhai, Tony Low, Jiangping Hu
2011 Physical Review B  
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
more » ... eorems 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.
doi:10.1103/physrevb.84.205324 fatcat:xyhhcyp7gjau5nixvpqnm4i3gi