Distribution function of persistent current

We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the presence of local interactions as well. Breakdown of the Gaussian statistics is predicted for the tails of the distribution function at large deviations

Mesoscopic oscillations of the conductance of disordered metallic samples as a function of temperature

We show theoretically and experimentally that the conductance of small disordered samples exhibits random oscillations as a function of temperature. The amplitude of the oscillations decays as a power law of temperature, and their characteristic period is of the order of the temperature itself

Influence of trigonal warping on interference effects in bilayer graphene

Bilayer graphene (two coupled graphitic monolayers arranged according to Bernal stacking) is a two-dimensional gapless semiconductor with a peculiar electronic spectrum different from the Dirac spectrum in the monolayer material. In particular, the electronic Fermi line in each of its valleys has a strong p -> -p asymmetry due to trigonal warping, which suppresses the weak localization effect. We show that weak localization in bilayer graphene may be present only in devices with pronounced intervalley scattering, and we evaluate the corresponding magnetoresistance

Conductance fluctuations in quasi-two-dimensional systems: a practical view

The universal conductance fluctuations of quasi-two-dimensional systems are analyzed with experimental considerations in mind. The traditional statistical metrics of these fluctuations (such as variance) are shown to have large statistical errors in such systems. An alternative characteristic is identified, the inflection point of the correlation function in magnetic field, which is shown to be significantly more useful as an experimental metric and to give a more robust measure of phase coherence.Comment: 9 pages, 7 figure

Observation of mesoscopic conductance fluctuations in YBaCuO grain boundary Josephson Junctions

Magneto-fluctuations of the normal resistance R_N have been reproducibly observed in high critical temp erature superconductor (HTS) grain boundary junctions, at low temperatures. We attribute them to mesoscopic transport in narrow channels across the grain boundary line. The Thouless energy appears to be the relevant energy scale. Our findings have significant implications on quasiparticle relaxation and coherent transport in HTS grain boundaries.Comment: Revised version, minor changes. 4 pages, 4 figure

Magnetoconductivity of low-dimensional disordered conductors at the onset of the superconducting transition

Magnetoconductivity of the disordered two- and three-dimensional superconductors is addressed at the onset of superconducting transition. In this regime transport is dominated by the fluctuation effects and we account for the interaction corrections coming from the Cooper channel. In contrast to many previous studies we consider strong magnetic fields and various temperature regimes, which allow to resolve the existing discrepancies with the experiments. Specifically, we find saturation of the fluctuations induced magneto-conductivity for both two- and three-dimensional superconductors at already moderate magnetic fields and discuss possible dimensional crossover at the immediate vicinity of the critical temperature. The surprising observation is that closer to the transition temperature weaker magnetic field provides the saturation. It is remarkable also that interaction correction to magnetoconductivity coming from the Cooper channel, and specifically the so called Maki-Thompson contribution, remains to be important even away from the critical region.Comment: 4 pages, 1 figur

Ferromagnetism of Weakly-Interacting Electrons in Disordered Systems

It was realized two decades ago that the two-dimensional diffusive Fermi liquid phase is unstable against arbitrarily weak electron-electron interactions. Recently, using the nonlinear sigma model developed by Finkelstein, several authors have shown that the instability leads to a ferromagnetic state. In this paper, we consider diffusing electrons interacting through a ferromagnetic exchange interaction. Using the Hartree-Fock approximation to directly calculate the electron self energy, we find that the total energy is minimized by a finite ferromagnetic moment for arbitrarily weak interactions in two dimensions and for interaction strengths exceeding a critical proportional to the conductivity in three dimensions. We discuss the relation between our results and previous ones

Coulomb drag at zero temperature

We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is inversely proportional to the third power of the dimensionless sheet conductance. The effect is therefore the strongest in low mobility samples. This behavior should be contrasted with the conventional (second order) prediction that the transresistance scales as a certain power of temperature and is almost mobility-independent. The result demonstrates that the zero-temperature drag is not an unambiguous signature of a strongly-coupled state in double-layer systems.Comment: 4 pages, 2 figure

Nonequilibrium mesoscopic conductance fluctuations

We investigate the amplitude of mesoscopic fluctuations of the differential conductance of a metallic wire at arbitrary bias voltage V. For non-interacting electrons, the variance increases with V. The asymptotic large-V behavior is \sim V/V_c (where eV_c=D/L^2 is the Thouless energy), in agreement with the earlier prediction by Larkin and Khmelnitskii. We find, however, that this asymptotics has a very small numerical prefactor and sets in at very large V/V_c only, which strongly complicates its experimental observation. This high-voltage behavior is preceded by a crossover regime, V/V_c \lesssim 30, where the conductance variance increases by a factor \sim 3 as compared to its value in the regime of universal conductance fluctuations (i.e., at V->0). We further analyze the effect of dephasing due to the electron-electron scattering on at high voltages. With the Coulomb interaction taken into account, the amplitude of conductance fluctuations becomes a non-monotonic function of V. Specifically, drops as 1/V for voltages V >> gV_c, where g is the dimensionless conductance. In this regime, the conductance fluctuations are dominated by quantum-coherent regions of the wire adjacent to the reservoirs.Comment: 14 pages, 4 figures. Fig.2 and one more appendix added, accepted for publication in PR