Coherent resistance of a disordered 1D wire: Expressions for all moments and evidence for non-Gaussian distribution

We model the effect of phase-breaking collisions on the coherent electron transport in a disordered one-dimensional single-channel wire. In our model the phase-breaking collisions break the wire into segments, where each segment is an independent series resistor with coherent electronic resistance and the segmentation is a stochastic process with Poisson distribution of phase-breaking scattering times. The wire resistance as a function of the wire length $L$, coherence length...

Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from numerical studies or analytical approximations. Here, we provide an exact, analytical solution to the problem of uniform phase disorder in a system of identical scatterers arranged with varying separations along a line. Relying on a relationship wi...

It is believed, that a disordered one-dimensional (1D) wire with coherent electronic conduction is an insulator with the mean resistance <\rho> \simeq e^{2L/\xi} and resistance dispersion \Delta_{\rho} \simeq e^{L/\xi}, where L is the wire length and \xi is the electron localisation length. Here we show that this 1D insulator undergoes at full coherence the crossover to a 1D "metal", caused by thermal smearing and resonant tunnelling. As a result, \Delta_{\rho} is smaller tha...

We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a universal current-voltage-characteristics. The relevance of our calculation for existing experiments is discussed as well as the connection with alternative theoretical approaches.

We show that the distribution P(g) of conductances g of a quasi one dimensional wire has non-analytic behavior in the insulating region, leading to a discontinuous derivative in the distribution near g=1. We give analytic expressions for the full distribution and extract an approximate scaling behavior valid for different strengths of disorder close to g=1.

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically for the first time the full distribution of conductance P(g) for a quasi one dimensional wire in the absence of electron-electron interaction. We show that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by an essentially `one sided' log-normal distribution. For larger disorder, the tail of the log-normal distribution for g >...

We calculate the distribution of the conductance G in a one-dimensional disordered wire at finite temperature T and bias voltage V in a independent-electron picture and assuming full coherent transport. At high enough temperature and bias voltage, where several resonances of the system contribute to the conductance, the distribution P(G(T,V)) can be represented with good accuracy by autoconvolutions of the distribution of the conductance at zero temperature and zero bias volt...

We determine analytically the distribution of conductances of quasi one-dimensional disordered electron systems, neglecting electron-electron interaction, for all strengths of disorder. We find that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by ``one-sided'' log-normal distribution. For larger disorder, the tail of the log-normal distribution is cut-off for g > 1 by a Gaussian.

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of conductances P(g) for a quasi one dimensional wire within the model of non-interacting fermions. The method has been used in [1-3] to predict sharp features in P(g) near g=1 and the existence of non-analyticity in the conductance distribution in the insulating and crossover regimes, as well as to show how P(g) changes from Gaussian to log-normal behavior...

We consider the problem of electron transport across a quasi-one-dimensional disordered multiply-scattering medium, and study the statistical properties of the electron density inside the system. In the physical setup that we contemplate, electrons of a given energy feed the disordered conductor from one end. The physical quantity that is mainly considered is the logarithm of the electron density, $\ln {\cal W}(x)$, since its statistical properties exhibit a self-averaging be...