Abstract Spin Hall and spin Nernst effects in graphene are studied based on Green's function formalism. We calculate intrinsic contributions to spin Hall and spin Nernst conductivities in Kane-Mele model with various structures. When both intrinsic and Rashba spin-orbit interactions are present, their interplay leads to some characteristics of the dependence of spin Hall and spin Nernst conductivities on the Fermi level. When Rashba spin-orbit interaction is smaller than intrinsic spin-orbit coupling, a weak kink in the conductance appears. The kink disappears and a divergence appears when the Rashba spin-orbit interaction enhances. When the Rashba spin-orbit interaction approaches and is stronger than intrinsic spin-orbit coupling, the divergence becomes more obvious.
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10934010), and the National Key Basic Research Special Foundation of China (Grant Nos. 2011CB921502 and 2012CB821305).
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