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

Diamagnetic response of Aharonov-Bohm rings: Impurity backward scatterings

We report a theoretical calculation on the persistent currents of disordered normal-metal rings. It is shown that the diamagnetic responses of the rings in the vicinity of the zero magnetic field are attributed to multiple backward scatterings off the impurities. We observe the transition from the paramagnetic response to the diamagnetic one as the strength of disorder grows using both the analytic calculation and the numerical exact diagonalization.Comment: final versio

Differential identities for parametric correlation functions in disordered systems

Copyright © 2008 The American Physical Society.We derive a family of differential identities for parametric correlation functions in disordered systems by casting them as first- or second-order Ward identities of an associated matrix model. We show that this approach allows for a systematic classification of such identities, and provides a template for deriving higher-order results. We also reestablish and generalize some identities of this type which had been derived previously using a different method

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

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

Coulomb drag in quantum circuits

We study drag effect in a system of two electrically isolated quantum point contacts (QPC), coupled by Coulomb interactions. Drag current exhibits maxima as a function of QPC gate voltages when the latter are tuned to the transitions between quantized conductance plateaus. In the linear regime this behavior is due to enhanced electron-hole asymmetry near an opening of a new conductance channel. In the non-linear regime the drag current is proportional to the shot noise of the driving circuit, suggesting that the Coulomb drag experiments may be a convenient way to measure the quantum shot noise. Remarkably, the transition to the non-linear regime may occur at driving voltages substantially smaller than the temperature.Comment: 6 pages, 2 figure

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

Nonequilibrium electrons in tunnel structures under high-voltage injection

We investigate electronic distributions in nonequilibrium tunnel junctions subject to a high voltage bias $V$ under competing electron-electron and electron-phonon relaxation processes. We derive conditions for reaching quasi-equilibrium and show that, though the distribution can still be thermal for low energies where the rate of the electron-electron relaxation exceeds significantly the electron-phonon relaxation rate, it develops a power-law tail at energies of order of $eV$. In a general case of comparable electron-electron and electron-phonon relaxation rates, this tail leads to emission of high-energy phonons which carry away most of the energy pumped in by the injected current.Comment: Revised versio