Connectivity of edge and surface states in topological insulators
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by
Yongjin Jiang, Feng Lu, Feng Zhai, Tony Low, Jiangping Hu
2011
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.
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