arXiv subjects
Publications and source records attributed to K. E. Nagaev.
We show that electron--electron scattering gives a positive contribution to the resistivity of ballistic multimode wires whose width is much smaller than their length. This contribution is not exponentially small at low temperatures and therefore may be experimentally observable. It scales with temperature as $T^2$ for three-dimensional channels and as $T^{5/2}$ for two-dimensional ones.
We consider wide ballistic microcontacts with electron-electron scattering in the leads and calculate electric noise and nonlinear conductance in them. Due to a restricted geometry the collisions of electrons result in a shot noise even though they conserve the total momentum of electrons. We obtain the noise and the conductivity for arbitrary relations between voltage V and temperature T. The positive inelastic correction to the Sharvin conductance is proportional to T at low voltages eV << T, and to |V| at high voltages. At low voltages the noise is defined by the Nyquist relation and at high voltages the noise is related with the inelastic correction to the current by the Shottky formula S_{in} = 2eI_{in}.
We calculate the magnetic-field dependent nonlinear conductance and noise in a macroscopic inhomogeneous system. If the system does not possess a specific symmetry, the magnetic field induces a nonzero third cumulant of the current even at equilibrium. This cumulant is related to the first and second voltage derivatives of the spectral density and average current in the same way as for mesoscopic quantum-coherent systems. The system provides a robust test of a non-equilibrium fluctuation relation.
We calculate the AC linear response of a superconductor in a nonequilibrium electronic state. The nonequilibrium state is produced by injecting quasiparticles into the superconductor from normal leads through asymmetric tunnel contacts. The dissipative part of the response is drastically increased by the injected quasiparticles and is proportional to their total number regardless of the imbalance between the numbers of electron-like and hole-like excitations.
Using a semiclassical Boltzmann equation, we calculate corrections to the Sharvin conductance of a wide 2DEG ballistic contact that result from an electron--electron scattering in the leads. These corrections are dominated by collisions of electrons with nearly opposite momenta that come from different reservoirs. They are positive, increase with temperature, and are strongly suppressed by a magnetic field. We argue that this suppression may be responsible for an anomalous positive magnetoresistance observed in a recent experiment.
We calculate the corrections to the Sharvin conductance of ballistic multimode microcontacts that result from electron--electron scattering in the leads. Using a semiclassical Boltzmann equation, we obtain that these corrections are {\it positive} and scale with temperature as $T^2\ln(E_F/T)$ for three-dimensional contacts and as $T$ for two-dimensional ones. These results are relevant to recent experiments on 2DEG contacts.
In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem, in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero frequency, as a function of the voltage across the resistor. We also consider time dependent heating, an issue relevant for experiments in which current pulses are used, for instance in time-resolved calorimetry experiments.
We analyze the frequency dependence of shot noise in a spin filter consisting of a normal grain and ferromagnetic electrodes separated by tunnel barriers. The source of frequency-dependent noise is random spin-flip electron scattering that results from spin-orbit interaction and magnetic impurities. Though the latter mechanism does not contribute to the average current, it contributes to the noise and leads to its dispersion at frequencies of the order of the Korringa relaxation rate. Under nonequilibrium conditions, this rate is proportional to the applied bias $V$, but parametrically smaller than $eV/\hbar$.
We calculate the frequency dispersion of the third cumulant of current in diffusive-metal contacts. The cumulant exhibits a dispersion at the inverse time of diffusion across the contact, which is typically much smaller than the inverse $RC$ time. This dispersion is much more pronounced in the case of strong electron-electron scattering than in the case of purely elastic scattering because of a different symmetry of the relevant second-order correlation functions.
We calculate the third cumulant of current in a chaotic cavity with contacts of arbitrary transparency as a function of frequency. Its frequency dependence drastically differs from that of the conventional noise. In addition to a dispersion at the inverse RC time characteristic of charge relaxation, it has a low-frequency dispersion at the inverse dwell time of electrons in the cavity. This effect is suppressed if both contacts have either large or small transparencies.
The third and fourth cumulants of voltage in a current-biased diffusive metal contact of resistance $R$ are calculated for arbitrary temperatures and voltages using the semiclassical cascade approach. The third cumulant equals $e^2R^3I/3$ at high temperatures and $4e^2R^3I/15$ at low temperatures, whereas the fourth cumulant equals $2e^2R^3T/3$ at high temperatures and $(34/105)e^3R^4I$ at low temperatures.
The Boltzmann - Langevin approach is extended to calculations of third and fourth cumulants of current in diffusive-metal contacts. These cumulants result from indirect correlations between current fluctuations, which may be considered as "noise of noise". The calculated third cumulant coincides exactly with its quantum-mechanical value. The fourth cumulant tends to its quantum-mechanical value $-e^3I/105$ at high voltages and to a positive value $2e^2T/3R$ at V=0 changing its sign at $eV \sim 20T$.
We propose a simple semiclassical method for calculating higher-order cumulants of current in multichannel mesoscopic conductors. To demonstrate its efficiency, we calculate the third and fourth cumulants of current for a chaotic cavity with multichannel leads of arbitrary transparency and compare the results with ensemble-averaged quantum-mechanical quantities. We also explain the discrepancy between the quantum-mechanical results and previous semiclassical calculations.
It is often argued that a small non-degenerate quantum system coupled to a bath has a fixed energy in its ground state since a fluctuation in energy would require an energy supply from the bath. We consider a simple model of a harmonic oscillator (the system) coupled to a linear string and determine the mean squared energy fluctuations. We also analyze the two time correlator of the energy and discuss its behavior for a finite string.
Metal microbridges with a high impurity content and shorter than the energy relaxation length are considered. Their conductance is calculated with allowance made for the Coulomb electron-electron interaction. It is shown that nonequilibrium electrons in the microbridges gives rise to a nonlinear current-voltage characteristic (published in Physics Letters A, 1994).
A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage $eV < Δ$ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electron-electron scattering at sufficiently high voltages.
The shot noise in long diffusive SNS contacts is calculated using the semiclassical approach. At low frequencies and for purely elastic scattering, the voltage dependence of the noise is of the form S_I = (4Δ+ 2eV)/3R. The electron-electron scattering suppresses the noise at small voltages resulting in vanishing noise yet infinite dS_I/dV at V = 0. The distribution function of electrons consists of a series of steps, and the frequency dependence of noise exhibits peculiarities at ω= neV, ω= neV - 2Δ, and ω= 2Δ- neV for integer n.
We present a semiclassical theory of shot noise in diffusive superconductor - normal metal contacts. At subgap voltages, we reproduce the doubling of shot noise with respect to conventional normal-metal contacts, which is interpreted in terms of an energy balance of electrons. Above the gap, the voltage dependence of the noise crosses over to the standard one with a voltage-independent excess noise. The semiclassical description of noise leads to correlations between currents at different electrodes of multiterminal SN contacts which are always of fermionic type, i.e. negative. Using a quantum extension of the Boltzmann - Langevin method, we reproduce the peculiarity of noise at the Josephson frequency and obtain an analytical frequency dependence of noise at above-gap voltages.