Intrinsic Spin Hall and Spin Nernst Effects in Single-Layer Graphene: Tight-Binding vs. Effective Model

We calculate topological contributions to the spin Hall and spin Nernst effects due to intrinsic spin-orbit interaction in a single-layer graphene. To describe electronic spectrum of the graphene we have assumed the k·p model as well as the full tight-binding Hamiltonian. The corresponding contributions to the spin Hall and spin Nernst effects have been determined using the linear response theory and Green function formalism.