Topological aspects of quantum spin Hall effect in graphene: Z2 topological order and spin Chern number
Abstract
For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z2 topological order and the spin Chern number proposed by Kane and Mele and by Sheng et al., respectively, in the quantum spin Hall effect. It turns out that a global gauge transformation connects different spin Chern numbers (even integers) modulo 4, which implies that the spin Chern number and the Z2 topological order yield the same classification. We present a method of computing spin Chern numbers and demonstrate it in single and double plane of graphene.
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