The effect of fluctuations on the nuclear magnetic resonance (NMR) relaxation rate, $W$, is studied in a complete phase diagram of a 2D superconductor above the upper critical field line $H_{c2}(T)$ . In the region of relatively high temperatures and
low magnetic fields, the relaxation rate $W$ is determined by two competing effects. The first one is its decrease in result of suppression of quasi-particle density of states (DOS) due to formation of fluctuation Cooper pairs (FCP). The second one is a specific, purely quantum, relaxation process of the Maki-Thompson (MT) type, which for low field leads to an increase of the relaxation rate. The latter describes particular fluctuation processes involving self-pairing of a single electron on self-intersecting trajectories of a size up to phase-breaking length $l_{phi }$ which becomes possible due to an electron spin-flip scattering event at a nucleus. As a result, different scenarios with either growth or decrease of the NMR relaxation rate are possible upon approaching the normal metal - type-II superconductor transition. The character of fluctuations changes along the line $H_{c2}$ from the thermal long-wavelength type in weak magnetic fields to the clusters of rotating FCP in fields comparable to $H_{c2}$. We find that below the well-defined temperature $T^*_0approx 0.6T_{c0}$, the MT process becomes ineffective even in absence of intrinsic pair-breaking. The small scale of FCP rotations ($xi_{xy}$) in so high fields impedes formation of long (<$l_{phi }$) self-intersecting trajectories, causing the corresponding relaxation mechanism to lose its efficiency. This reduces the effect of superconducting fluctuations in the domain of high fields and low temperatures to just the suppression of quasi-particle DOS, analogously to the Abrikosov vortex phase below the $H_{c2}$ line.
Electron tunneling spectroscopy pioneered by Esaki and Giaever offered a powerful tool for studying electronic spectra and density of states (DOS) in superconductors. This led to important discoveries that revealed, in particular, the pseudogap in th
e tunneling spectrum of superconductors above their critical temperatures. However, the phenomenological approach is insufficient for describing the does not resolve the fine structure of low-bias behavior carrying significant information about electron scattering, interactions, and decoherence effects. Here we construct a complete microscopic theory of electron tunneling into a superconductor in the fluctuation regime. We reveal a non-trivial low-energy anomaly in tunneling conductivity due to Andreev-like reflection of injected electrons from superconducting fluctuations. Our findings enable real-time observation of fluctuating Cooper pairs dynamics by time-resolved scanning tunneling microscopy measurements and open new horizons for quantitative analysis of the fluctuation electronic spectra of superconductors.
We study the tunneling transport through a nanojunction in the far-from-equilibrium regime at relatively low temperatures. We show that the current-voltage characteristics is significantly modified as compared to the usual quasi-equilibrium result by
lifting the suppression due to the Coulomb blockade. These effects are important in realistic nanojunctions. We study the high-impedance case in detail to explain the underlying physics and construct a more realistic theoretical model for the case of a metallic junction taking into account dynamic Coulomb interaction. This dynamic screening further reduces the effect of the Coulomb blockade.
We propose a first-principles model for self-assembled magnetic surface structures on the water-air interface reported in earlier experiments cite{snezhko2,snezhko4}. The model is based on the Navier-Stokes equation for liquids in shallow water appro
ximation coupled to Newton equations for interacting magnetic particles suspended on the water-air interface. The model reproduces most of the observed phenomenology, including spontaneous formation of magnetic snake-like structures, generation of large-scale vortex flows, complex ferromagnetic-antiferromagnetic ordering of the snake, and self-propulsion of bead-snake hybrids. The model provides valuable insights into self-organization phenomena in a broad range of non-equilibrium magnetic and electrostatic systems with competing interactions.
