Journal
PHYSICAL REVIEW LETTERS
Volume 101, Issue 1, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.101.016804
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We report theoretical investigations of the quantized spin-Hall conductance fluctuation of graphene in the presence of disorder. Two graphene models that exhibit the quantized spin-Hall effect (QSHE) are analyzed. Model I is with unitary symmetry under an external magnetic field B not equal 0 but with a zero spin-orbit interaction, t(SO)=0. Model II is with symplectic symmetry where B=0 but t(SO)not equal 0. The two models give exactly the same universal QSHE conductance fluctuation value 0.285 +/- 0.005e/4 pi regardless of symmetry. We also examined a third model that exhibits QSHE but with quadratic dispersion and obtained the same results. Finally, all three models of QSHE have a one-sided log-normal distribution for spin-Hall conductance. Our results strongly suggest that the quantized spin-Hall conductance fluctuation belongs to a new universality class.
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