We derive the transport equations for two-dimensional electron systems with Rashba spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations, we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation and spin current in a finite-size sample for an arbitrary ratio between spin-orbit energy splitting Delta and elastic scattering rate tau(-1). We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.

We demonstrate that in a wide range of temperatures Coulomb drag between two weakly coupled quantum wires is dominated by processes with a small interwire momentum transfer. Such processes, not accounted for in the conventional Luttinger liquid theory, cause drag only because the electron dispersion relation is not linear. The corresponding contribution to the drag resistance scales with temperature as T2 if the wires are identical, and as T5 if the wires are different.

Minimal conductivity of a single undoped graphene layer is known to be of the order of the conductance quantum, independent of the electron velocity. We show that this universality does not survive electron-electron interaction which results in the non-trivial frequency dependence. We begin with analyzing the perturbation theory in the interaction parameter g for the electron selfenergy and observe the failure of the random-phase approximation. The optical conductivity is then derived from the quantum kinetic equation and the exact result is obtained in the limit when g ≪ 1 ≪ g| ln ω|.PACS numbers: 73.23.-b, 72.30.+q Introduction. Recent experiments on transport in graphene layers [1,2,3] have validated extensive theoretical efforts directed at understanding of various properties of two-dimensional Dirac fermions. A lot of these efforts are devoted to the zero temperature dc conductivity which has a universal value of the order of the conductance quantum [4,5]. Such a value is not unexpected from the dimension analysis since the intrinsic (undoped) graphene lacks a characteristic momentum scale. Two different minimal conductivities are conventionally defined. The dc limit of an ac conductivity in a clean graphene (τ −1 = 0, ω → 0) was shown to be σ = e 2 /4h [6]. Another possible definition of a strict dc limit of impure graphene (ω = 0, τ −1 → 0) gives a different, but numerically close valueσ = 2e2 /π 2h [6]. Recent calculations have largely confirmed [7,8,9,10,11,12,13] the results of Ref. 6, while others obtained different values [14]. Conductivity in a bilayer graphene has also been a subject of close theoretical attention [17,18,19,20].It is noteworthy that the minimal conductivity σ is very much analogous to the optical conductivity of a twodimensional electron system with spin-orbit-split band structure, where it is due to the "chiral resonance", and the corresponding value e 2 /16h [15, 16] is exactly 4 times smaller than σ (which is the degree of spin-nodal degeneracy in graphene). This analogy is due to similarity in the chiral properties of the eigenstates in the two systems.In the present paper we demonstrate that the notable universality of the values of σ andσ does not hold in the presence of electron-electron interactions, which result in a strong frequency dependence of the conductivity. Here, we concentrate on the optical conductivity σ(ω) in the strict disorder-free graphene (τ −1 = 0) and show that the optical conductivity is actually suppressed by interactions in comparison with its "universal" value.Single intrinsic 2D graphene layer is described by the chiral Hamiltonian,

PACS 73.23.-b -Electronic transport in mesoscopic systems PACS 73.25.+i -Surface conductivity and carrier phenomenaAbstract. -Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be σ = σ0(1 + 0.01g), where g is the dimensionless ("fine structure") coupling constant. The calculations are performed using three different methods: i) electron polarization function, ii) Kubo formula for the conductivity, iii) quantum transport equation. Surprisingly, these methods yield different results unless a proper ultraviolet cut-off procedure is implemented, which requires that the interaction potential in the effective Dirac Hamiltonian is cut-off at small distances (large momenta).