Onset of superconductivity in a voltage-biased NSN microbridge

We study the stability of the normal state in a mesoscopic NSN junction biased by a constant voltage V with respect to the formation of the superconducting order. Using the linearized time-dependent Ginzburg-Landau equation, we obtain the temperature dependence of the instability line, V_{inst}(T), where nucleation of superconductivity takes place. For sufficiently low biases, a stationary symmetric superconducting state emerges below the instability line. For higher biases, the normal phase is destroyed by the formation of a non-stationary bimodal state with two superconducting nuclei localized near the opposite terminals. The low-temperature and large-voltage behavior of the instability line is highly sensitive to the details of the inelastic relaxation mechanism in the wire. Therefore, experimental studies of V_{inst}(T) in NSN junctions may be used as an effective tool to access parameters of the inelastic relaxation in the normal state.Comment: 5 pages, 2 figure

Energy relaxation rate and its mesoscopic fluctuations in quantum dots

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 $\varepsilon$ on top of the thermal state with the temperature $T$, fluctuations of its energy width become large and the Fermi-golden-rule description breaks down at $\max\{\varepsilon,T\}\sim\Delta\sqrt{g}$, where $\Delta$ is the mean level spacing in the quantum dot, and $g$ is its dimensionless conductance.Comment: 33 pages, 9 figure

Electron-phonon relaxation in periodic granular films

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

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 $\xi$ becomes comparable to the distance between neighboring grains $l$. Minigap magnitude $E_g$ grows from zero at $\xi \approx 1.4 l$ to third of superconducting gap $\Delta_0$ at $\xi \approx 0.5 l$. 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

Resonances in a single-lead reflection from a disordered medium: σ\sigma-model approach

We develop a general non-perturbative characterisation of universal features of the density $\rho(\Gamma)$ of $S$-matrix poles (resonances) $E_n-i\Gamma_n$ describing waves incident and reflected from a disordered medium via a single $M$-channel waveguide/lead. Explicit expressions for $\rho(\Gamma)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $\rho(\Gamma)\sim 1/\Gamma$ for narrow resonances reflecting exponential localization and $\rho(\Gamma)\sim 1/\Gamma^2$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode wires with $M\gg 1$, intermediate asymptotics $\rho(\Gamma)\sim 1/\Gamma^{3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts.Comment: Article+Supplemental Materia