We have studied non-equilibrium phase transitions in the vortex lattice in superconducting MgB2, where metastable states are observed in connection with an intrinsically continuous rotation transition. Using small-angle neutron scattering and a stop-motion technique, we investigated the manner in which the metastable vortex lattice returns to the equilibrium state under the influence of an ac magnetic field. This shows a qualitative difference between the supercooled case which undergoes a discontinuous transition, and the superheated case where the transition to the equilibrium state is continuous. In both cases the transition may be described by an an activated process, with an activation barrier that increases as the metastable state is suppressed, as previously reported for the supercooled vortex lattice [E. R. Louden et al., Phys. Rev. B 99, 060502(R) (2019)]. Separate preparations of superheated metastable vortex lattices with different domain populations showed an identical transition towards the equilibrium state. This provides further evidence that the vortex lattice metastability, and the kinetics associated with the transition to the equilibrium state, is governed by nucleation and growth of domains and the associated domain boundaries.
The vortex lattice in MgB2 is characterized by the presence of long-lived metastable states, which arise from cooling or heating across the equilibrium phase boundaries. A return to the equilibrium configuration can be achieved by inducing vortex motion. Here we report on small-angle neutron scattering studies of MgB2, focusing on the structural properties of the vortex lattice as it is gradually driven from metastable to equilibrium states by an AC magnetic field. Measurements were performed using initial metastable states obtained either by cooling or heating across the equilibrium phase tra…
We study the relaxation dynamics of flux lines in dirty high-temperature superconductors using numerical simulations of a London-Langevin model of the interacting vortex lines. By analysing the equilibrium dynamics in the vortex liquid phase we find a dynamic crossover to a glassy non-equilibrium regime. We then focus on the out-of-equilibrium dynamics of the vortex glass phase using tools that are common in the study of other glassy systems. By monitoring the two-times roughness and dynamic wandering we identify and characterize finite-size effects that are similar, though more complex, than …
Small-angle neutron scattering on high quality single crystalline Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ reveals the transition from a low--field vortex solid phase with orientational order to a vortex polycrystal at high magnetic field. The vortex order-disorder transition is correlated with the second-peak feature in isothermal hysteresis loops, and is interpreted in terms of the generation of supplementary vortex solid dislocations. The sharp drop of the structure factor above the second peak field is explained by the dynamics of freezing of the vortex ensemble in the high field phase.
We report a crucial experimental test of the present models of the peak effect in weakly disordered type-II superconductors. Our results favor the scenario in which the peak effect arises from a crossover between the Larkin pinning length and a rapidly falling elastic length in a vortex phase populated with thermally excited topological defects. A thickness dependence study of the onset of the peak effect at varying driving currents suggests that both screw and edge dislocations are involved in the vortex lattice disordering. The driven dynamics in 3D samples are drastically different from tho…
We analyze the rhombic to square vortex lattice phase transition in anisotropic superconductors using a variant of Ginzburg-Landau (GL) theory. The mean-field phase diagram is determined to second order in the anisotropy parameter, and shows a reorientation transition of the square vortex lattice with respect to the crystal lattice. We then derive the long-wavelength elastic moduli of the lattices, and use them to show that thermal fluctuations produce a reentrant rhombic to square lattice transition line, similar to recent studies which used a nonlocal London model.
A numerical scheme to study the mixed states in a mesoscopic type-II superconducting cylinder is described. Steady-state configurations and transient behavior of the magnetic vortices for various values of the applied magnetic field H are presented. Transitions between different multi-vortex states as H is changed is demonstrated by contour plots and jumps in the B vs H plot. Evolving a uniformly-superconducting initial state using the simplest set of relaxation equations shows that the system passes through nearly metastable intermediate configurations, while seeking the final minimum-energy,…
Recent developments of the Josephson plasma resonance and transport c-axis measurements in layered high T$_{c}$ superconductors allow to probe Josephson coupling in a wide range of the vortex phase diagram. We derive a relation between the field dependent Josephson coupling energy and the density correlation function of the vortex liquid. This relation provides a unique opportunity to extract the density correlation function of pancake vortices from the dependence of the plasma resonance on the $ab$-component of the magnetic field at a fixed $c$-axis component.
The rhombic-to-square transition field $H_{\Box}(T)$ for cubic and tetragonal materials in fields along [001] is evaluated using the nonlocal London theory with account of thermal vortex fluctuations. Unlike extended Ginzburg-Landau models, our approach shows that the line $H_{\Box}(T)$ and the upper critical field $H_{c2}(T)$ do not cross due to strong fluctuations near $H_{c2}(T)$ which suppress the square anisotropy induced by the nonlocality. In increasing fields, this causes re-entrance of the rhombic structure in agreement with recent neutron scattering data on borocarbides.
Using small-angle neutron scattering, we investigated the behavior of a metastable vortex lattice state in MgB2 as it is driven towards equilibrium by an AC magnetic field. This shows an activated behavior, where the AC field amplitude and cycle count are equivalent to, respectively, an effective "temperature" and "time". The activation barrier increases as the metastable state is suppressed, corresponding to an aging of the vortex lattice. Furthermore, we find a cross-over from a partial to a complete suppression of metastable domains depending on the AC field amplitude, which may empirically…
Vortex-line equilibrium configurations and critical currents for type-II superconducting films at zero-temperature are studied theoretically. The films are assumed to be of thickness less than or equal to the penetration depth, free of pinning by imperfections, and to be subjected to a magnetic field parallel to the film surfaces and to a transport current perpendicular to the field. By numerical minimization of the exact London theory energy expression, using simulated annealing techniques, the equilibrium configurations are determined with great accuracy over a wide range of fields and curre…
We study the relaxational dynamics of flux lines in high-temperature superconductors with random pinning using Langevin dynamics. At high temperatures the dynamics is stationary and the fluctuation dissipation theorem (FDT) holds. At low temperatures the system does not equilibrate with its thermal bath: a simple multiplicative aging is found, the FDT is violated and we found that an effective temperature characterizes the slow modes of the system. The generic features of the evolution -- scaling laws -- are dictated by the ones of the single elastic line in a random environment.
Like orbitals in atoms and molecules, persistent currents may appear in larger aggregates. Though classically, equilibrium magnetic moment of non-rotating objects is forbidden, it is known that equilibrium quantum circulating currents are allowed. Such currents were predicted to be periodic with the external magnetic field. It is shown that in general, whenever a periodic component is found, there must be a large aperiodic component forcing aperiodic contribution to the equilibrium magnetic moment as a function of the external field.
We investigated magnetic vortices in two stoichiometric LiFeAs samples by means of scanning tunneling microscopy and spectroscopy. The vortices were revealed by measuring the local electronic density of states (LDOS) at zero bias conductance of samples in magnetic fields between 0.5 and 12 T. From single vortex spectroscopy we extract the Ginzburg-Landau coherence length of both samples as $4.4\pm0.5$ nm and $4.1\pm0.5$ nm, in accordance with previous findings. However, in contrast to previous reports, our study reveals that the reported hexagonal to square-like vortex lattice transition is ab…
In this communication we argue that the Vortex Lattice Melting scenario fails to explain several key experimental results published in the literature. From a careful analysis of these results we conclude that the Flux Line Lattice (FLL) does not melt along a material- and sample-dependent boundary $H_j(T)$ but the opposite, it de-couples from the superconducting matrix becoming more ordered. When the FLL depinning is sharp, the difference between the equilibrium magnetization $M_{eq}(T,H)$ of the pinned and unpinned FLL leads to the observed step-like change $ΔM_{eq}(T,H)$. We demonstrate that…
We report a clear anomaly in the rf response of a tunnel-diode resonator measured in borocarbide crystals in dc fields along the $c-$axis. We associate the anomaly in the dynamic magnetic susceptibility, $χ$, with a structural transition in the vortex lattice. $χ$ is sensitive to the Campbell penetration depth $λ_{C}$ of the rf perturbation into the mixed state. $λ_{C}$ depends on the vortex lattice elastic moduli, which in turn depend on the vortex lattice structure. The high-field transition line is clearly mapped and shown to behave in agreement with theory.
Externally driven glassy systems may undergo non-equilibrium phase transitions (NEPTs). In particular, ac-driven systems display special features, like those observed in the vortex matter of $\mathrm{NbSe_2}$, where oscillatory drives reorganize the system into partially ordered vortex lattices. We provide experimental evidence for this dynamic reorganization and we show an unambiguous signature of its connection with an NEPT driven by ac forces. We perform a scaling analysis and we estimate critical exponents for this transition. Our results share similarities with some glass-to-viscous-liqui…
The peak effect in critical current density J_c is investigated by studying the flux dynamics in V_3Si using bulk magnetometry, small-angle neutron scattering, and transport measurements on clean single-crystal samples from the same ingot. For a field-cooled history, well-defined structure in the vortex lattice was found for fields and temperatures (H,T) below the peak-effect line H_P(T); above this line, the structure disappeared. History-dependent, metastable disorder is found only for (H,T) below H_P(T) but the vortex system is reproducibly re-ordered either by field-cooling or a low-freque…
We introduce a model of vortices in type-II superconductors with a four-fold anisotropy in the vortex-vortex interaction potential. Using numerical simulations we show that the vortex lattice undergoes structural transitions as the anisotropy is increased, with a triangular lattice at low anisotropy, a rhombic intermediate state, and a square lattice for high anisotropy. In some cases we observe a multi-$q$ state consisting of an Archimedean tiling that combines square and triangular local ordering. At very high anisotropy, domains of vortex chain states appear. We discuss how this model can b…
Systems of nearly parallel, slender vortex filaments in which angular momentum is conserved are an important simplification of the Navier-Stokes equations where turbulence can be studied in statistical equilibrium. We study the canonical Gibbs distribution based on the Klein-Majda-Damodaran (KMD) model and find a divergence in the mean square vortex position from that of the point vortex model of Onsager at high temperature. We subsequently develop a free energy equation based on the non-interacting case, with a spherical constraint, which we approximate using the method of Kac-Berlin, adding …
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 non-equilibrium 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 quantitative estimate for the location of these t…
The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local \emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking'. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid …
Nernst and electrical resistivity measurements in superconducting YBCO and BSCCO with and without columnar defects show a distinctive thermodynamics of the respective liquid vortex matter. At a field dependent high temperature region in the phase diagram the Nernst signal is independent of structural defects in both materials. At lower temperatures, in YBCO, defects contribute only to the vortex mobility and the transport entropy is that of a system of vortex lines. The transition to lower temperatures in BSCCO has a different origin, the maximum in the Nernst signal when decreasing temperatur…
We discuss the use of Langevin molecular dynamics in the investigation of the non-equilibrium properties of disordered vortex matter. Our special focus is set on values of system parameters that are realistic for disordered high-$T_c$ superconductors such as YBCO. Using a discretized elastic line model, we study different aspects of vortices far from thermal equilibrium. On the one hand we investigate steady-state properties of driven magnetic flux lines in a disordered environment, namely the current-voltage characteristics, the gyration radius, and the pinning time statistics. On the other h…
The continuum theory of domain structures in ferromagnetic/superconducting bilayers fails when the equilibrium domain size becomes comparable with effective penetration depth $Λ$. Instead, a lattice of discrete vortices must be considered. Here, we report our results on the discrete vortex lattices in stripe domain structures of ferromagnetic/superconducting bilayers. The vortices are assumed to be situated periodically on chains in stripe domains. We study the configurations containing up to three chains per domain, and calculate their equilibrium energies, equilibrium domain size and vortex …
With increasing applied current we show that the moving vortex lattice changes its structure from a triangular one to a set of parallel vortex rows in a pinning free superconductor. This effect originates from the change of the shape of the vortex core due to non-equilibrium effects (similar to the mechanism of vortex motion instability in the Larkin-Ovchinnikov theory). The moving vortex creates a deficit of quasiparticles in front of its motion and an excess of quasiparticles behind the core of the moving vortex. This results in the appearance of a wake (region with suppressed order paramete…
Effects of the paramagnetic depairing on structural transitions between vortex lattices of a quasi two dimensional d-wave superconductor are examined. It is found that, in systems with Maki parameter $α_{\rm M}$ of order unity, a square lattice induced by a d-wave pairing is destabilized with {\it increasing} fields, and that a reentrant rhombic lattice occurs in higher fields. Further, a weak Fermi surface anisotropy competitive with the pairing symmetry induces another structural transition near $H_{c2}$. These results are consistent with the structure changes of the vortex lattice in CeCoIn…
This paper studies the striking correlation between nanosized structural patterns in YBCO films and macroscopic transport current. A nanosized network of parallel Josephson junctions laced by insulating dislocations is almost mimicking the grain boundary structural network. It contributes to the macroscopic properties and accounts for the strong intergranular pinning across the film in the intermediate temperature range. The correlation between the two networks enables to find out an outstanding scaling law in the (Jc,B) plane and to determine meaningful parameters concerning the matching betw…
Within the non-linear Ginzburg-Landau (GL) theory, we investigate the vortex structure in a superconducting thin film with a ferromagnetic disk on top of it. Antivortices are stabilized in shells around a central core of vortices (or a giant-vortex) with size-magnetization controlled ``magic numbers''. An equilibrium vortex phase diagram is constructed. The transition between the different vortex phases occurs through the creation of a vortex-antivortex pair under the magnetic disk edge.
Of the many different kinds of glassy states found in nature, spin glasses and structural glasses (e.g. normal window glass) have probably received the most attention. One of the central questions concerning the glassy state is whether the "glass" is a distinct thermodynamic phase from the "liquid" phase. It is believed that this may actually be the case for spin glasses, whereas the glass transition in structural glasses appears to be mostly kinetic in nature. Supercooled structural liquids, however, exhibit a wide range of behaviors, which can be classified using the "strong-fragile" scheme …
We present a detailed study of the dynamic interactions between Josephson vortices and stacks of pancake vortices in a Bi2Sr2CaCu2O8 single crystal, obtained by measuring the effect of applied inplane magnetic field pulses on the c-axis magnetisation. The predominant interaction is to relax the system towards equilibrium. However, using a highly sensitive AC technique we are able to measure also the forces acting to drive the system away from equilibrium, consistent with the existence of dragging interactions between the Josephson and pancake systems. Such forces were discussed recently as the…
We study the non-equilibrium dynamical regimes of a moving vortex lattice in the periodic pinning of a Josephson junction array (JJA) for {\it finite temperatures} in the case of a fractional or submatching field. We obtain a phase diagram for the current driven JJA as a function of the driving current I and temperature T. We find that when the vortex lattice is driven by a current, the depinning transition at $T_p(I)$ and the melting transition at $T_M(I)$ become separated even for a field for which they coincide in equilibrium. We also distinguish between the depinning of the vortex lattice …
Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state.
The pre-melting of high vortex density planes observed recently in layered superconductors in tilted magnetic field is explained theoretically. Based on the structural information of the crossing lattices of pancake and Josephson vortices the effective vortex cage potential at different lattice sites is determined numerically. Melting takes place when the thermal energy allows proliferation of vacancy-interstitial pairs. It is found that the increased density of pancake vortex stacks in the planes containing Josephson vortices, rather than their incommensurate structure, is the main cause for …
We study the phase diagram of the superconducting vortex system in layered high-temperature superconductors in the presence of a magnetic field perpendicular to the layers and of random atomic scale point pinning centers. We consider the highly anisotropic limit where the pancake vortices on different layer are coupled only by their electromagnetic interaction. The free energy of the vortex system is then represented as a Ramakrishnan-Yussouff free energy functional of the time averaged vortex density. We numerically minimize this functional and examine the properties of the resulting phases. …
We have investigated the magnetic phase diagram of a fully oxygenated detwinned YBa2Cu3O7 single crystal by means of magneto-caloric and magnetization measurements, and found thermodynamic evidence for a temperature dependent first-order phase-transition line deep within the vortex-solid region. The associated discontinuities in the entropy are apparently proportional to the magnetic flux density, which may hint at a structural transition of the vortex lattice.
We formulate the time-dependent Ginzburg-Landau theory, with the assumption of local equilibrium made in the reference frame floating with normal electrons. This theory with floating nucleation kernel is applied to the far infrared (FIR) conductivity in the Abrikosov vortex lattice. It yields better agreement with recent experimental data [PRB {\bf 79}, 174525 (2009)] than the customary time-dependent Ginzburg-Landau theory.
Inverse melting, in which a crystal reversibly transforms into a liquid or amorphous phase upon decreasing the temperature, is considered to be very rare in nature. The search for such an unusual equilibrium phenomenon is often hampered by the formation of nonequilibrium states which conceal the thermodynamic phase transition, or by intermediate phases, as was recently shown in a polymeric system. Here we report a first-order inverse melting of the magnetic flux line lattice in Bi2Sr2CaCu2O8 superconductor. At low temperatures, the material disorder causes significant pinning of the vortices, …
We present a systematic study of the topology of the vortex solid phase in superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ samples with low doses of columnar defects. A new state of vortex matter imposed by the presence of geometrical contours associated with the random distribution of columns is found. The results show that the first order liquid-solid transition in this vortex matter does not require a structural symmetry change.
We study the melting of a moving vortex lattice through numerical simulations with the current driven 3D XY model with disorder. We find that there is a first-order phase transition even for large disorder when the corresponding equilibrium transition is continuous. The low temperature phase is an anisotropic moving glass.
We study numerically correlation and response functions in non-equilibrium driven vortex lattices with random pinning. From a generalized fluctuation-dissipation relation we calculate an effective transverse temperature in the fluid moving phase. We find that the effective temperature decreases with increasing driving force and becomes equal to the equilibrium melting temperature when the dynamic transverse freezing occurs. We also discuss how the effective temperature can be measured experimentally from a generalized Kubo formula.
We report structural evidence of dynamic reorganization in vortex matter in clean NbSe$_2$ by joint small angle neutron scattering and ac-susceptibility measurements. The application of oscillatory forces in a transitional region near the order-disorder transition results in robust bulk vortex lattice configurations with an intermediate degree of disorder. These dynamically-originated configurations correlate with intermediate pinning responses previously observed, resolving a long standing debate regarding the origin of such responses.
The melting transition of the vortex lattice in highly anisotropic, layered superconductors with commensurate, periodic columnar pins is studied in a geometry where magnetic field and columnar pins are normal to the layers. Thermodynamic properties and equilibrium density distributions are obtained from numerical minimizations of an appropriate free-energy functional. We find a line of first-order transitions that ends at a critical point as the pin concentration is increased. A simple Landau theory providing a semi-quantitative explanation of the numerical results is proposed.
The discrete vortex lattices in a ferromagnet/superconductor bilayer are studied when the ferromagnet has periodic stripe domains with an out-of-plane magnetization. The vortices are assumed to be situated periodically on chains in the stripe domains. Only up to two vortex chains per domain configurations are considered. When the domain period is fixed, the threshold magnetization is calculated at which the transition from the Meissner state to the mixed state occurs. When the domain period is not fixed, the equilibrium domain size and vortex positions are calculated, depending on the domain's…
We investigate the vortex lattice and vortex bound states in CsFe$_2$As$_2$ single crystals by scanning tunneling microscopy/spectroscopy (STM/STS) under various magnetic fields. A possible structural transition or crossover of vortex lattice is observed with the increase of magnetic field, i.e., the vortex lattice changes from a distorted hexagonal lattice to a distorted tetragonal one at the magnetic field near 0.5 T. It is found that a mixture of stripelike hexagonal and square vortex lattices emerges in the crossover region. The vortex bound state is also observed in the vortex center. The…
Measurements of the $^{17}$O nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in HgBa$_{2}$CuO$_{4+δ}$ were performed over a range of magnetic fields from 6.4 to 30\,T in the superconducting state. Oxygen isotope exchanged single crystals were investigated with doping corresponding to superconducting transition temperatures from 74\,K underdoped, to 78\,K overdoped. The apical oxygen site was chosen since its NMR spectrum has narrow quadrupolar satellites that are well separated from any other resonance. Non-vortex contributions to the spectra can be deconvolved in the ti…
Nowadays superconductors serve in numerous applications, from high-field magnets to ultra-sensitive detectors of radiation. Mesoscopic superconducting devices, i.e. those with nanoscale dimensions, are in a special position as they are easily driven out of equilibrium under typical operating conditions. The out-of-equilibrium superconductors are characterized by non-equilibrium quasiparticles. These extra excitations can compromise the performance of mesoscopic devices by introducing, e.g., leakage currents or decreased coherence times in quantum devices. By applying an external magnetic field…
A perturbed system relaxes towards an equilibrium given by a minimum in the potential energy landscape. This often occurs by thermally activated jumps over metastable states. The corresponding dynamics is named creep and follows Arrhenius' law. Here we consider the situation where the equilibrium position depends on temperature. We show that this effect occurs in the vortex lattice of the anisotropic superconductor $2\mathrm{H}$-$\mathrm{Nb}\mathrm{Se}_{2}$ when the magnetic field is tilted away from the principal axes, and that it leads to the peculiar appearance of creep when cooling the sam…
We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II su- perconductors, magnetic materials and aspects of cosmology. We characterise the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very hig…
The problem of vortex structure in a single Josephson junction in an external magnetic field, in the absence of transport currents, is reconsidered from a new mathematical point of view. In particular, we derive a complete set of exact analytical solutions representing all the stationary points (minima and saddle-points) of the relevant Gibbs free-energy functional. The type of these solutions is determined by explicit evaluation of the second variation of the Gibbs free-energy functional. The stable (physical) solutions minimizing the Gibbs free-energy functional form an infinite set and are …
We present numerical studies of the dynamics of vortices in the Ginzburg Landau model using equations derived from the gradient flow of the free energy. These equations have previously been proposed to describe the dynamics of n-vortices away from equilibrium. We are able to model the dynamics of multiple n-vortex configurations starting far from equilibrium. We find generically that there are two time scales for equilibration: a short time scale related to the formation time for a single n-vortex, and a longer time scale that characterizes vortex-vortex interactions.
At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster-crystal. In the present work we explore the out-of-equilibrium dynamics for a two-dimensional realization, which is relevant to superconducting materials with multi-scale intervortex forces. We find that for small temperatures following a quench, the suppression of the thermally-activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in term…
The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly pinned Co0.0075NbSe2 single crystal, we show that at low temperatures, the vortex lattice in a 3-dimensional superconductor disorders in two steps across the peak effect. At the onset of the peak effect, the equilibrium Bragg glass transforms into an orientational glass through the proliferation of dislocations. At a higher field, the dislocations dissociate …
We develop a theory for dislocation-mediated structural transitions in the vortex lattice which allows for a unified description of phase transitions between the three phases, the elastic vortex glass, the amorphous vortex glass, and the vortex liquid, in terms of a free energy functional for the dislocation density. The origin of a critical endpoint of the melting line at high magnetic fields, which has been recently observed experimentally, is explained.
Langevin dynamics simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced point defects as a smoothened distribution of a random potential. Both the electromagnetic and Josephson interactions among pancake vortices were included. A special shaking and annealing process was introduced to let the system approach the equilibrium configuration. We are able to see the inverse melting transition from the Bragg-glass to the amorphous vortex glass state, in agreement with recent experiments.
We examine energy relaxation of non-equilibrium quasiparticles in different vortex configurations in ``dirty'' $s$-wave superconductors. The heat flow from the electronic subsystem to phonons in a mesoscopic superconducting disk with a radius of the order of several coherence lengths is calculated both in the Meissner and giant vortex states using the Usadel approach. The recombination process is shown to be strongly affected by interplay of the subgap states, located in the vortex core and in the region at the sample edge where the spectral gap $E_{\rm g}$ is reduced by the Meissner currents.…
Vortex structures in mesoscopic cylinder placed in external magnetic field are studied under the general de Gennes boundary condition for the order parameter corresponding to the suppression of surface superconductivity. The Ginzburg-Landau equations are solved based on trial functions for the order parameter for vortex-free, single-vortex, multivortex, and giant vortex phases. The equilibrium vortex diagrams in the plane of external field and cylinder radius and magnetization curves are calculated at different values of de Gennes "extrapolation length" characterizing the boundary condition fo…
We present a study of the behaviour of metastable vortex states in mesoscopic superconductors. Our analysis relies on the London limit within which it is possible to derive closed analytical expressions for the magnetic field and the Gibbs free energy. We consider in particular the situation where the vortices are symmetrically distributed along a closed ring. There, we obtain expressions for the confining Bean-Livingston barrier and for the magnetization which turns out to be paramagnetic away from thermodynamic equilibrium. At low temperature, the barrier is high enough for this regime to be…
A many-particle system must posses long-range interactions in order to be hyperuniform at thermal equilibrium. Hydrodynamic arguments and numerical simulations show, nevertheless, that a three-dimensional elastic-line array with short-ranged repulsive interactions, such as vortex matter in a type-II superconductor, forms at equilibrium a class-II hyperuniform two-dimensional point pattern for any constant-$z$ cross section. In this case, density fluctuations vanish isotropically as $\sim q^α$ at small wave-vectors $q$, with $α=1$. This prediction includes the solid and liquid vortex phases in …
