Weak momentum scattering and the conductivity of graphene

Electrical transport in graphene offers a fascinating parallel to spin transport in semiconductors including the spin-Hall effect. In the weak momentum scattering regime the steady-state density matrix contains two contributions: one is linear in the carrier number density n and characteristic scattering time tau, and the other is independent of either. In this paper we take the Liouville equation as our starting point and demonstrate that these two contributions can be identified with pseudospin conservation and nonconservation, respectively, and are connected in a nontrivial manner by scattering processes. The scattering term has a distinct form, which is peculiar to graphene and has important consequences in transport. The contribution linear in tau is analogous to the part of the spin-density matrix which yields a steady-state spin density, while the contribution independent of tau is analogous to the part of the spin-density matrix which yields a steady-state spin current. Unlike in systems with spin-orbit interactions, the n- and tau-independent part of the conductivity is reinforced in the weak momentum scattering regime by scattering between the conserved and nonconserved pseudospin distributions.