Interaction correction to the conductance of a ballistic conductor

In disordered metals, electron-electron interactions are the origin of a small correction to the conductivity, the "Altshuler-Aronov correction". Here we investigate the Altshuler-Aronov correction of a conductor in which the electron motion is ballistic and chaotic. We consider the case of a double quantum dot, which is the simplest example of a ballistic conductor in which the Altshuler-Aronov correction is nonzero. The fact that the electron motion is ballistic leads to an exponential suppression of the correction if the Ehrenfest time is larger than the mean dwell time or the inverse temperature.Comment: 4 pages, 2 figure

Tunneling Density of States of the Interacting Two-Dimensional Electron Gas

We investigate the influence of electron--electron interactions on the density of states of a ballistic two--dimensional electron gas. The density of states is determined nonperturbatively by means of path integral techniques allowing for reliable results near the Fermi surface, where perturbation theory breaks down. We find that the density of states is suppressed at the Fermi level to a finite value. This suppression factor grows with decreasing electron density and is weakened by the presence of gates.Comment: 4 pages, 2 figures; slightly shortened version published in PR

The Scaling Behavior of Classical Wave Transport in Mesoscopic Media at the Localization Transition

The propagation of classical wave in disordered media at the Anderson localization transition is studied. Our results show that the classical waves may follow a different scaling behavior from that for electrons. For electrons, the effect of weak localization due to interference of recurrent scattering paths is limited within a spherical volume because of electron-electron or electron-phonon scattering, while for classical waves, it is the sample geometry that determine the amount of recurrent scattering paths that contribute. It is found that the weak localization effect is weaker in both cubic and slab geometry than in spherical geometry. As a result, the averaged static diffusion constant D(L) scales like ln(L)/L in cubic or slab geometry and the corresponding transmission follows ~ln L/L^2. This is in contrast to the behavior of D(L)~1/L and ~1/L^2 obtained previously for electrons or spherical samples. For wave dynamics, we solve the Bethe-Salpeter equation in a disordered slab with the recurrent scattering incorporated in a self-consistent manner. All of the static and dynamic transport quantities studied are found to follow the scaling behavior of D(L). We have also considered position-dependent weak localization effects by using a plausible form of position-dependent diffusion constant D(z). The same scaling behavior is found, i.e., ~ln L/L^2.Comment: 11 pages, 12 figures. Submitted to Phys. Rev. B on 3 May 200

Crossover from diffusive to strongly localized regime in two-dimensional systems

We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean conductance, g, in agreement with the strong version of the single-parameter scaling hypothesis. The distribution seems to change drastically at a critical value very close to one. For conductances larger than this critical value, the distribution is roughly Gaussian while for smaller values it resembles a log-normal distribution. The two distributions match at the critical point with an often appreciable change in behavior. This matching implies a jump in the first derivative of the distribution which does not seem to disappear as system size increases. We have also studied 1/g corrections to the skewness to quantify the deviation of the distribution from a Gaussian function in the diffusive regime.Comment: 4 pages, 4 figure

Logarithmic temperature dependence of conductivity at half-integer filling factors: Evidence for interaction between composite fermions

We have studied the temperature dependence of diagonal conductivity in high-mobility two-dimensional samples at filling factors $\nu=1/2$ and 3/2 at low temperatures. We observe a logarithmic dependence on temperature, from our lowest temperature of 13 mK up to 400 mK. We attribute the logarithmic correction to the effects of interaction between composite fermions, analogous to the Altshuler-Aronov type correction for electrons at zero magnetic field. The paper is accepted for publication in Physical Review B, Rapid Communications.Comment: uses revtex macro

Doped Mott insulators are insulators: hole localization in the cuprates

We demonstrate that a Mott insulator lightly doped with holes is still an insulator at low temperature even without disorder. Hole localization obtains because the chemical potential lies in a pseudogap which has a vanishing density of states at zero temperature. The energy scale for the pseudogap is set by the nearest-neighbour singlet-triplet splitting. As this energy scale vanishes if transitions, virtual or otherwise, to the upper Hubbard band are not permitted, the fundamental length scale in the pseudogap regime is the average distance between doubly occupied sites. Consequently, the pseudogap is tied to the non-commutativity of the two limits $U\to\infty$ ($U$ the on-site Coulomb repulsion) and $L\to\infty$ (the system size).Comment: 4 pages, 3 .eps file

Scaling and interaction-assisted transport in graphene with one-dimensional defects

We analyze the scattering from one-dimensional defects in intrinsic graphene. The Coulomb repulsion between electrons is found to be able to induce singularities of such scattering at zero temperature as in one-dimensional conductors. In striking contrast to electrons in one space dimension, however, repulsive interactions here can enhance transport. We present explicit calculations for the scattering from vector potentials that appear when strips of the material are under strain. There the predicted effects are exponentially large for strong scatterers.Comment: 4 pages, 2 figure

Universal Conductance Fluctuations in Mesoscopic Systems with Superconducting Leads: Beyond the Andreev Approximation

We report our investigation of the sample to sample fluctuation in transport properties of phase coherent normal metal-superconductor hybrid systems. Extensive numerical simulations were carried out for quasi-one dimensional and two dimensional systems in both square lattice (Fermi electron) as well as honeycomb lattice (Dirac electron). Our results show that when the Fermi energy is within the superconducting energy gap $\Delta$, the Andreev conductance fluctuation exhibits a universal value (UCF) which is approximately two times larger than that in the normal systems. According to the random matrix theory, the electron-hole degeneracy (ehD) in the Andreev reflections (AR) plays an important role in classifying UCF. Our results confirm this. We found that in the diffusive regime there are two UCF plateaus, one corresponds to the complete electron-hole symmetry (with ehD) class and the other to conventional electron-hole conversion (ehD broken). In addition, we have studied the Andreev conductance distribution and found that for the fixed average conductance $,G>$ the Andreev conductance distribution is a universal function that depends only on the ehD. In the localized regime, our results show that ehD continues to serve as an indicator for different universal classes. Finally, if normal transport is present, i.e., Fermi energy is beyond energy gap $\Delta$, the AR is suppressed drastically in the localized regime by the disorder and the ehD becomes irrelevant. As a result, the conductance distribution is that same as that of normal systems