54 research outputs found

### 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: $\sigma$-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

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