Abstract
The original motivation of great interest to topological insulators was the
hope to observe the quantum spin Hall effect. Therefore if a material is in the
topological insulator state they frequently call it the quantum spin Hall
state. However, despite impressive experimental results confirming the
existence of the quantum spin Hall state, the quantum spin Hall effect has not
yet been detected. After a short overview of what was originally suggested as
the quantum spin Hall effect (quantum spin conductance determined by the
topological Chern number) the paper analyzes the crucial role of the boundary
condition on the observation of the effect and finally discusses whether and
how the quantum spin Hall effect could be observed.
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