47 research outputs found

    Energy relaxation rate and its mesoscopic fluctuations in quantum dots

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    We analyze the applicability of the Fermi-golden-rule description of quasiparticle relaxation in a closed diffusive quantum dot with electron-electron interaction. Assuming that single-particle levels are already resolved but the initial stage of quasiparticle disintegration can still be described by a simple exponential decay, we calculate the average inelastic energy relaxation rate of single-particle excitations and its mesoscopic fluctuations. The smallness of mesoscopic fluctuations can then be used as a criterion for the validity of the Fermi-golden-rule description. Technically, we implement the real-space Keldysh diagram technique, handling correlations in the quasi-discrete spectrum non-perturbatively by means of the non-linear supersymmetric sigma model. The unitary symmetry class is considered for simplicity. Our approach is complementary to the lattice-model analysis of Fock space: thought we are not able to describe many-body localization, we derive the exact lowest-order expression for mesoscopic fluctuations of the relaxation rate, making no assumptions on the matrix elements of the interaction. It is shown that for the quasiparticle with the energy ε\varepsilon on top of the thermal state with the temperature TT, fluctuations of its energy width become large and the Fermi-golden-rule description breaks down at max{ε,T}Δg\max\{\varepsilon,T\}\sim\Delta\sqrt{g}, where Δ\Delta is the mean level spacing in the quantum dot, and gg is its dimensionless conductance.Comment: 33 pages, 9 figure

    Electron-phonon relaxation in periodic granular films

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    We study the electron-phonon relaxation in the model of a granular metal film, where the grains are formed by regularly arranged potential barriers of arbitrary transparency. The relaxation rate of Debye acoustic phonons is calculated taking into account two mechanisms of electron-phonon scattering: the standard Frohlich interaction of the lattice deformation with the electron density and the interaction mediated by the displacement of grain boundaries dragged by the lattice vibration. At lowest temperatures, the electron-phonon cooling power follows the power-law temperature dependence typical for clean systems, but with the prefactor growing as the transparency of the grain boundaries decreases.Comment: 8 pages, 4 figure

    Gapful electrons in a vortex core in granular superconductors

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    We calculate the quasiparticle density of states (DoS) inside the vortex core in a granular superconductor, generalizing the classical solution applicable for dirty superconductors. A discrete version of the Usadel equation for a vortex is derived and solved numerically for a broad range of parameters. Electron DoS is found to be gapful when the vortex size ξ\xi becomes comparable to the distance between neighboring grains ll. Minigap magnitude EgE_g grows from zero at ξ1.4l\xi \approx 1.4 l to third of superconducting gap Δ0\Delta_0 at ξ0.5l\xi \approx 0.5 l. The absence of low-energy excitations is the main ingredient needed to understand strong suppression of microwave dissipation recently observed in a mixed state of granular Al

    Mesoscopic conductance fluctuations and noise in disordered Majorana wires

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    Superconducting wires with broken time-reversal and spin-rotational symmetries can exhibit two distinct topological gapped phases and host bound Majorana states at the phase boundaries. When the wire is tuned to the transition between these two phases and the gap is closed, Majorana states become delocalized leading to a peculiar critical state of the system. We study transport properties of this critical state as a function of the length LL of a disordered multichannel wire. Applying a non-linear supersymmetric sigma model of symmetry class D with two replicas, we identify the average conductance, its variance and the third cumulant in the whole range of LL from the Ohmic limit of short wires to the regime of a broad conductance distribution when LL exceeds the correlation length of the system. In addition, we calculate the average shot noise power and variance of the topological index for arbitrary LL. The general approach developed in the paper can also be applied to study combined effects of disorder and topology in wires of other symmetries.Comment: 21 pages, 7 figure