U(1) x SU(2) gauge invariance leading to charge and spin conductivity of Dirac fermions in graphene

Gauge symmetries have been identified in graphene and associated with specific physical properties. For instance, the U(1) gauge group is related to electrodynamics in (1 + 2)-dimensional [(1 + 2) D] space-time and non-Abelian gauge groups can describe curvature and torsion. Here we demonstrate that the Dirac Lagrangian for massless electrons near the Dirac points is also invariant under the group SU(2) related to local spin rotations, leading to the correct spin-orbit interactions and a rigorous definition for the spin-current density. Furthermore, we computed the charge and spin conductivity within the framework of Kubo linear response theory, using the algebra of relativistic Dirac spinors in (1 + 2) D space-time. The minimal value of electrical conductivity is predicted to be pi q(2)/h, in agreement with typical experimental findings. DOI: 10.1103/PhysRevB.87.165416