Charge and Spin Hall Conductivity in Metallic Graphene

Graphene has an unusual low-energy band structure with four chiral bands and half-quantized and quantized Hall effects that have recently attracted theoretical and experimental attention. We study the Fermi energy and disorder dependence of its spin Hall conductivity ${\sigma }_{xy}^{\mathrm{SH}}$. In the metallic regime we find that vertex corrections enhance the intrinsic spin Hall conductivity and that skew scattering can lead to ${\sigma }_{xy}^{\mathrm{SH}}$ values that exceed the quantized ones expected when the chemical potential is inside the spin-orbit induced energy gap. We predict that large spin Hall conductivities will be observable in graphene even when the spin-orbit gap does not survive disorder.

Figure 1

Self-energy Feynman diagram.

Figure 2

Vertex correction Feynman diagram. Black dots represent the Pauli operator.