It is known that the lowest propagating mode in a narrow ballistic ribbon of graphene may lack the twofold valley degeneracy of higher modes. Depending on the crystallographic orientation of the ribbon axis, the lowest mode mixes both valleys or lies predominantly in a single valley (chosen by the direction of propagation). We show, using a tight-binding model calculation, that a nonequilibrium valley polarization can be realized in a sheet of graphene, upon injection of current through a ballistic point contact with zigzag edges. The polarity can be inverted by local application of a gate voltage to the point contact region. Two valley filters in series may function as an electrostatically controlled ``valley valve'', representing a zero-magnetic-field counterpart to the familiar spin valve.Comment: RevTeX, 4 pages, 5 figure

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e 2 =h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1=3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.

We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic corrections proportional to p2 sigma(z) to the Dirac Hamiltonian that can drive an ordinary band insulator into a topological insulator (having an inverted band gap). We calculate the location of the phase boundary at weak disorder and show that it corresponds to the crossing of a band edge rather than a mobility edge. Our mechanism for the formation of a topological Anderson insulator is generic, and would apply as well to three-dimensional semiconductors with strong spin-orbit coupling.

We numerically calculate the conductivity σ of an undoped graphene sheet (size L) in the limit of vanishingly small lattice constant. We demonstrate one-parameter scaling for random impurity scattering and determine the scaling function β(σ) = d ln σ/d ln L. Contrary to a recent prediction, the scaling flow has no fixed point (β > 0) for conductivities up to and beyond the symplectic metalinsulator transition. Instead, the data supports an alternative scaling flow for which the conductivity at the Dirac point increases logarithmically with sample size in the absence of intervalley scattering -without reaching a scale-invariant limit.PACS numbers: 73.20.Fz, 73.20.Jc, 73.63.Nm Graphene provides a new regime for two-dimensional quantum transport [1,2,3], governed by the absence of backscattering of Dirac fermions [4]. A counterintuitive consequence is that adding disorder to a sheet of undoped graphene initially increases its conductivity [5,6]. Intervalley scattering at stronger disorder strengths enables backscattering [7], eventually leading to localization and to a vanishing conductivity in the thermodynamic limit [8,9]. Intervalley scattering becomes less and less important if the disorder is more and more smooth on the scale of the lattice constant a. The fundamental question of the new quantum transport regime is how the conductivity σ scales with increasing system size L if intervalley scattering is suppressed.In usual disordered electronic systems, the hypothesis of one-parameter scaling plays a central role in our conceptual understanding of the metal-insulator transition [10,11]. According to this hypothesis, the logarithmic derivative d ln σ/d ln L = β(σ) is a function only of σ itself [12] -irrespective of the sample size or degree of disorder. A positive β-function means that the system scales towards a metal with increasing system size, while a negative β-function means that it scales towards an insulator. The metal-insulator transition is at β = 0, β ′ > 0. In a two-dimensional system with symplectic symmetry, such as graphene, one would expect a monotonically increasing β-function with a metal-insulator transition at [13] σ S ≈ 1.4 (see Fig.