47 research outputs found

### 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

### Mesoscopic conductance fluctuations and noise in disordered Majorana wires

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 $L$ 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 $L$ from
the Ohmic limit of short wires to the regime of a broad conductance
distribution when $L$ exceeds the correlation length of the system. In
addition, we calculate the average shot noise power and variance of the
topological index for arbitrary $L$. 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