Valerii M. Vinokur

Superinsulator and quantum synchronization.

Synchronized oscillators are ubiquitous in nature, and synchronization plays a key part in various classical and quantum phenomena. Several experiments have shown that in thin superconducting films, disorder enforces the droplet-like electronic texture—superconducting islands immersed into a normal matrix—and that tuning disorder drives the system from superconducting to insulating behaviour. In the vicinity of the transition, a distinct state forms: a Cooper-pair insulator, with thermally activated conductivity. It results from synchronization of the phase of the superconducting order parameter at the islands across the whole system. Here we show that at a certain finite temperature, a Cooper-pair insulator undergoes a transition to a superinsulating state with infinite resistance. We present experimental evidence of this transition in titanium nitride films and show that the superinsulating state is dual to the superconducting state: it is destroyed by a sufficiently strong critical magnetic field, and breaks down at some critical voltage that is analogous to the critical current in superconductors.

Dendritic flux avalanches and nonlocal electrodynamics in thin superconducting films.

We report a mechanism of nonisothermal dendritic flux penetration in superconducting films. Our numerical and analytical analysis of coupled nonlinear Maxwell and thermal diffusion equations shows that dendritic flux pattern formation results from spontaneous branching of propagating flux filaments due to nonlocal magnetic flux diffusion and positive feedback between flux motion and Joule heating. The branching is triggered by a thermomagnetic edge instability, which causes stratification of the critical state. The resulting distribution of thermomagnetic microavalanches is not universal, because it depends on a spatial distribution of defects. Our results are in good agreement with experiments on Nb films.

Dislocations and the critical endpoint of the melting line of vortex line lattices

line merge. 14 In this paper we present an explanation for the existence of a critical endpoint of the first-order melting line in the presence of point disorder. Our argumentation is based on a unified description of the vortex lattice phases. We demonstrate that all phase transitions between vortex lattice phases can be described as dislocation mediatedby deriving the free energy for an ensemble of directed dislocations as a function of the dislocation density in the presence of thermal and disorder. Each of the experimentally observed phases is characterized by its inherent dislocation density or, equivalently, by the characteristic dislocation spacing RD . The elastic VG is dislocation-free and has RD5‘. The VL can be viewed as a vortex array saturated with dislocations such that RD;a, and in the amorphous VG, R D ;R a , where R a is the socalled positional correlation length on which typical vortex displacements are of the order of the lattice spacing a. 2 Within our approach each phase corresponds to one of the local minima in the dislocation ensemble free energy, and dislocation densities in these minima represent the equilibrium dislocation densities in the corresponding phases. The global minimum corresponds to the thermodynamically stable phase under the given conditions, phase transitions occur when two local minima exchange their role as global minimum. This mechanism for the transitions enables us to derive Lindemann-criteria both for the locations of the thermal melting line and for the disorder-induced instability line of the BrG. Furthermore, the characteristic scale set by the mean distance between free dislocations offers a natural explanation of the critical endpoint of the first-order melting line: While at low magnetic fieldsRa@a and the amorphous VG appears to contain significantly less dislocations than the VL, at higher field where R a 5a the two phases become thermodynamically equivalent and the first-order melting line has to terminate.

Vortex Avalanches and Magnetic Flux Fragmentation in Superconductors

We report the results of numerical simulations of nonisothermal dendritic flux penetration in type-II superconductors. We propose a generic mechanism of dynamic branching of a propagating hot spot of a flux flow/normal state triggered by a local heat pulse. The branching occurs when the flux hot spot reflects from inhomogeneities or the boundary on which magnetization currents either vanish, or change direction. The hot spot then undergoes a cascade of successive splittings, giving rise to a dissipative dendritic-type flux structure. This dynamic state eventually cools down, turning into a frozen multifilamentary pattern of magnetization currents.

Mesoscopic superconductor as a ballistic quantum switch

Several key experiments have revealed a rich variety of vortex structures in mesoscopic superconductors in which only a few quanta of magnetic flux are trapped: these structures are polygon-like vortex ‘molecules’ and multi-quanta giant vortices. Ginzburg–Landau calculations confirmed second-order phase transitions between the giant vortex states and stable molecule-like configurations. Here we study theoretically the electronic structure and the related phase-coherent transport properties of such mesoscopic superconductor systems. The quasiparticle excitations in the vortices form coherent quantum-mechanical states that offer the possibility of controlling the phase-coherent transport through the sample by changing the number of trapped flux quanta and their configuration. The sample conductance measured in the direction of the applied magnetic field is determined by the transparency of multi-vortex configurations, which form a set of quantum channels. The transmission coefficient for each channel is controlled by multiple Andreev reflections within the vortex cores and at the sample edge. These interference phenomena result in a stepwise behaviour of the conductance as a function of the applied magnetic field, and we propose to exploit this effect to realize a vortex-based quantum switch where the magnetic field plays the role of the gate voltage.

Driven dynamics of periodic elastic media in disorder.

We analyze the large-scale dynamics of vortex lattices and charge-density waves driven in a disordered potential. Using a perturbative coarse-graining procedure, we present an explicit derivation of nonequilibrium terms in the renormalized equation of motion, in particular Kardar-Parisi-Zhang nonlinearities and dynamic strain terms. We demonstrate the absence of glassy features such as diverging linear friction coefficients and transverse critical currents in the drifting state. We discuss the structure of the dynamical phase diagram containing different elastic phases at very small and very large drives, and plastic phases at intermediate velocity.

Glassy Motion of Elastic Manifolds.

We discuss the low-temperature dynamics of an elastic manifold driven through a random medium. For driving forces well below the {ital T}=0 depinning force, the medium advances via thermally activated hops over the energy barriers separating favorable metastable states. We show that the distribution of waiting times for these hopping processes scales as a power law. This power-law distribution naturally yields a nonlinear glassy response for the driven medium, {ital v}{approximately}exp({minus}const{times}{ital F}{sup {minus}{mu}}). {copyright} {ital 1996 The American Physical Society.}

Superinsulator-Superconductor Duality in Two Dimensions

Abstract For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii–Kosterlitz–Thouless (BKT) transition in the vortex–antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor–insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity–superinsulation duality.

Elastic string in a random potential.

We have studied numerically the dynamics of a directed elastic string in a twodimensional array of quenched random impurities. The string is driven by a constant transverse force and thermal fluctuations are neglected. There is a transition from pinned to unpinned behavior at a critical value F T of the driving force. At the transition the average string velocity scales with the driving force. The scaling is equally well described by a power law υ d ∼(F-F T ) ζ , with ζ=0.24±0.1, or by a logarithm, υ d ∼1/ln(F-F T )

Dynamic melting and decoupling of the vortex lattice in layered superconductors

The dynamic phase diagram of vortex lattices driven in disorder is calculated in two and three dimensions. A modified Lindemann criterion for the fluctuations of the distance of neighboring vortices is used, which unifies previous analytic approaches to the equilibrium and nonequilibrium phase transitions. The temperature shifts of the dynamic melting and decoupling transitions are found to scale inversely proportional to large driving currents. A comparison with two-dimensional simulations shows that this phenomenological approach can provide a quantitative estimate for the location of these transitions.