Ballistic transport in disordered graphene

An analytic theory of electron transport in disordered graphene in a ballistic geometry is developed. We consider a sample of a large width W and analyze the evolution of the conductance, the shot noise, and the full statistics of the charge transfer with increasing length L, both at the Dirac point and at a finite gate voltage. The transfer matrix approach combined with the disorder perturbation theory and the renormalization group is used. We also discuss the crossover to the diffusive regime and construct a ``phase diagram'' of various transport regimes in graphene.Comment: 23 pages, 10 figure

Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length $L_\varphi$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time $\tau_\varphi$ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.Comment: 35 pages, revtex4, 25 figures (34 pdf files

A model of a transition neutral pion formfactor measured in annihilation and scattering channels

We consider an alternative explanation of newly found growth of neutral pion transition form factor with virtuality of one of photon. It is based on Sudakov suppression of quark-photon vertex. Some applications to scattering and annihilation channels are considered including the relevant experiments with lepton-proton scattering.Comment: 5 pages, 4 figur

Instanton Corrections to Quark Form Factor at Large Momentum Transfer

Within the Wilson integral formalism, we discuss the structure of nonperturbative corrections to the quark form factor at large momentum transfer analyzing the infrared renormalon and instanton effects. We show that the nonperturbative effects determine the initial value for the perturbative evolution of the quark form factor and attribute their general structure to the renormalon ambiguities of the perturbative series. It is demonstrated that the instanton contributions result in the finite renormalization of the next-to-leading perturbative result and numerically are characterized by a small factor reflecting the diluteness of the QCD vacuum within the instanton liquid model.Comment: Version coincident with the journal publication, 9 pages; REVTe

Two-scale localization in disordered wires in a magnetic field

Calculating the density-density correlation function for disordered wires, we study localization properties of wave functions in a magnetic field. The supersymmetry technique combined with the transfer matrix method is used. It is demonstrated that at arbitrarily weak magnetic field the far tail of the wave functions decays with the length $L_{{\rm cu}}=2L_{{\rm co}}$, where $L_{{\rm co}}$ and $L_{{\rm cu}}$ are the localization lengths in the absence of a magnetic field and in a strong magnetic field, respectively. At shorter distances, the decay of the wave functions is characterized by the length $L_{{\rm co}}$. Increasing the magnetic field broadens the region of the decay with the length $L_{{\rm cu}}$, leading finally to the decay with $L_{{\rm cu}}$ at all distances. In other words, the crossover between the orthogonal and unitary ensembles in disordered wires is characterized by two localization lengths. This peculiar behavior must result in two different temperature regimes in the hopping conductivity with the boundary between them depending on the magnetic field.Comment: 4 page

Phase dependent current statistics in short-arm Andreev interferometer

We calculate analytically the current statistics for a short diffusive wire between the normal reservoir and a short superconductor-normal metal-superconductor (SNS) junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference $\phi$ across the junction, approaching the normal-state value at $\phi=\pi$. At T=0 and at the applied voltage much smaller than the proximity gap $\Delta_\phi$, the current noise $P_I$ doubles and the third current cumulant $C_3$ is 4 times larger with respect to their values in the normal state; at $eV \gg \Delta_\phi$ they acquire large excess components. At the gap edge, $eV = \Delta_\phi$, the effective transferred charge defined through $dP_I/dI$ and $dP_I/dV$ approaches $0e$ and $3e$, respectively, which makes doubtful the interpretation of these quantities as physical elementary transferred charge. At $T \neq 0$, $C_3$ shows a non-monotonous voltage dependence with a dip near $eV = \Delta_\phi$.Comment: 13 pages, to be published in Proc. NATO ARW "Quantum Transport in Metallic and Hybrid Nanostructures", StPetersburg, 200

Symmetry Dependence of Localization in Quasi- 1- dimensional Disordered Wires

The crossover in energy level statistics of a quasi-1-dimensional disordered wire as a function of its length L is used, in order to derive its averaged localization length, without magnetic field, in a magnetic field and for moderate spin orbit scattering strength. An analytical function of the magnetic field for the local level spacing is obtained, and found to be in excellent agreement with the magnetic field dependent activation energy, recently measured in low-mobility quasi-one-dimensional wires\cite{khavin}. This formula can be used to extract directly and accurately the localization length from magnetoresistance experiments. In general, the local level spacing is shown to be proportional to the excitation gap of a virtual particle, moving on a compact symmetric space.Comment: 4 pages, 2 Eqs. added, Eperimental Data included in Fig.

Universal Statistics of Transport in Disordered Conductors

In low temperature limit, we study electron counting statistics of a disordered conductor. We derive an expression for the distribution of charge transmitted over a finite time interval by using a result from the random matrix theory of quasi one dimensional disordered conductors. In the metallic regime, we find that the peak of the distribution is Gaussian and shows negligible sample to sample variations. We also find that the tails of the distribution are neither Gaussian nor Poisson and exhibit strong sample to sample variations.Comment: 11 pages, REVTEX3.0, MIT-CMT-HL940

Semiclassical theory of shot-noise suppression

The Boltzmann-Langevin equation is used to relate the shot-noise power of a mesoscopic conductor to classical transmission probabilities at the Fermi level. This semiclassical theory is applied to tunneling through n barriers in series. For n -> infinity the shot noise approaches one third of the Poisson noise, independent of the transparency of the barriers. This confirms that the one-third suppression known to occur in diffusive conductors does not require phase coherence.Comment: pages, RevTeX, 1 figur

Magnetolocalization in disordered quantum wires

The magnetic field dependent localization in a disordered quantum wire is considered nonperturbatively. An increase of an averaged localization length with the magnetic field is found, saturating at twice its value without magnetic field. The crossover behavior is shown to be governed both in the weak and strong localization regime by the magnetic diffusion length L_B. This function is derived analytically in closed form as a function of the ratio of the mean free path l, the wire thickness W, and the magnetic length l_B for a two-dimensional wire with specular boundary conditions, as well as for a parabolic wire. The applicability of the analytical formulas to resistance measurements in the strong localization regime is discussed. A comparison with recent experimental results on magnetolocalization is included.Comment: 22 pages, RevTe