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We consider intrinsic contributions to the spin Hall and spin Nernst effectsin a bilayer graphene. The relevant electronic spectrum is obtained from thetight binding Hamiltonian, which also includes the intrinsic spin-orbitinteraction. The corresponding spin Hall and spin Nernst conductivities arecompared with those obtained from effective Hamiltonians appropriate for statesin the vicinity of the Fermi level of a neutral bilayer graphene. Bothconductivities are determined within the linear response theory and Greenfunction formalism. The influence of an external voltage between the two atomicsheets is also included. We found transition from the topological spin Hallinsulator phase at low voltages to conventional insulator phase at largervoltages.

Topological spin Hall and spin Nernst effects in a bilayer graphene