ductance is determined by quasiparticle tunneling, which is independent on the boundary conditions in y-direction if L ≪ W. (For illustrations we choose periodic boundary conditions with W/L = 7). We find that a single impurity placed in an ideal sheet of undoped graphene modifies the tunneling states and leads to the conductivity enhancement provided the impurity strength is close to one of the multiple resonant values. Away from the Dirac point the presence of an impurity causes a suppression of the conductance. In this study we restrict ourselves to the single-valley Dirac equation for graphene, −i¯hv σ · ∇Ψ + V Ψ = εΨ, (1) where Ψ is a spinor of wave amplitudes for two nonequivalent sites of the honeycomb lattice. The Fermienergy ε and the impurity potential V (x, y) in graphene sample (0 < x < L) are considered to be much smaller than the Fermi-energy EF in the ideal metallic leads (x < 0 and x> L). For zero doping the conductance is determined by the states at the Dirac point, ε = 0. Transport properties at finite energies determine the conductance of doped graphene. The Dirac equation in the leads has a trivial solution Ψ ∼ exp(±ikr) with the wave vector k = (kx, q) for the energy ε = ¯hv √ k 2 x + q 2 − EF. In order to make our notations more compact we let ¯hv = 1 in the rest of the paper. The units are reinstated in the final results and in the figures. For definiteness we choose periodic boundary conditions in y direction, hence the transversal momentum q is quantized as qn = 2πn/W, with n = 0, ±1, ±2, · · · ± M. The value of M is determined by the Fermi energy EF in the leads, M = Int [W/λF], where λF = 2π/EF, and the number of propagating channels is given by N = 2M + 1. For ε ≪ EF the conductance is dominated by modes with a small transversal momentum qn ≪ kF. The corresponding scattering state for a quasiparticle injected from the left lead is given b
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