Connectivity of edge and surface states in topological insulators

Abstract

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.

References in corpus (10)

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Cited by in corpus (6)

• Junction between surfaces of two topological insulators
• D-Algebra Structure of Topological Insulators
• Anisotropic transport of normal metal-barrier-normal metal junctions in monolayer phosphorene
• Power law decay of local density of states oscillations near a line defect in a system with semi-Dirac points
• Edge states, spin transport and impurity induced local density of states in spin-orbit coupled graphene
• Transport and STM studies of hyperbolic surface states of topological insulators