Melting of heterogeneous vortex matter: The vortex ‘nanoliquid’

Disorder and porosity are parameters that strongly influence the physical behavior of materials, including their mechanical, electrical, magnetic and optical properties. Vortices in superconductors can provide important insight into the effects of disorder because their size is comparable to characteristic sizes of nanofabricated structures. Here we present experimental evidence for a novel form of vortex matter that consists of inter-connected nanodroplets of vortex liquid caged in the pores of a solid vortex structure, like a liquid permeated into a nanoporous solid skeleton. Our nanoporous skeleton is formed by vortices pinned by correlated disorder created by high-energy heavy ion irradiation. By sweeping the applied magnetic field, the number of vortices in the nanodroplets is varied continuously from a few to several hundred. Upon cooling, the caged nanodroplets freeze into ordered nanocrystals through either a first-order or a continuous transition, whereas at high temperatures a uniform liquid phase is formed upon delocalization-induced melting of the solid skeleton. This new vortex nanoliquid displays unique properties and symmetries that are distinct from both solid and liquid phases.     

Melting of the nanocrystalline vortex matter in highly anisotropic high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly anisotropic high-temperature superconductor Bi2Sr2CaCu2O8 were performed. We introduced low concentration of columnar defects satisfying Bphi < or = B. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid, and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.     

Phases of atom-molecule vortex matter

We study ground state vortex configurations in a rotating atom-molecule Bose-Einstein condensate. It is found that the coherent coupling between the atomic and molecular condensates can render a pairing of atomic and molecular vortices into a composite structure that resembles a carbon dioxide molecule. Structural phase transitions of vortex lattices are also explored through different physical parameters including the rotational frequency of the system.     

Dynamic melting of confined vortex matter

We study dynamic melting of confined vortex matter moving in disordered, mesoscopic channels by mode-locking experiments. The dynamic melting transition, characterized by a collapse of the mode-locking effect, strongly depends on the frequency, i.e., on the average velocity of the vortices. The associated dynamic ordering velocity diverges upon approaching the equilibrium melting line T(m,e)(B) as v(c) approximately (T(m,e)-T)(-1). The data provide the first direct evidence for velocity dependent melting and show that the phenomenon also takes place in a system under disordered confinement.     

Peak effect in polycrystalline vortex matter

We report a study of the peak-effect phase diagram of a strongly disordered type-II superconductor V-21 at. %Ti using ac magnetic susceptibility and small-angle neutron scattering (SANS). In this system, the peak effect appears only at fields higher than 3.4 T. The sample is characterized by strong atomic disorder. Vortex states with field-cooled thermal histories show that both deep in the mixed state, as well as close to the peak effect, there exist no long-range orientationally ordered vortex lattices. The SANS scattering radial widths reveal vortex states ordered in the sub-mum scale. We conjecture that the peak effect in this system is a remnant of the Bragg glass disordering transition, but occurs on submicron length scales due to the presence of strong atomic disorder on larger length scales.     

Scanning Hall probe microscopy of vortex matter

Scanning Hall probe microscopy (SHPM) is a novel scanned probe magnetic imaging technique whereby the stray fields at the surface of a sample are mapped with a sub-micron semiconductor heterostructure Hall probe. In addition an integrated scanning tunnelling microscope (STM) or atomic force microscope (AFM) tip allows the simultaneous measurement of the sample topography, which can then be correlated with magnetic images. SHPM has several advantages over alternative methods; it is almost completely non-invasive, can be used over a very wide range of temperatures (0.3–300 K) and magnetic fields (0–7 T) and yields quantitative maps of the z-component of magnetic induction. The approach is particularly well suited to low temperature imaging of vortices in type II superconductors with very high signal:noise ratios and relatively high spatial resolution (>100 nm). This paper will introduce the design principles of SHPM including the choice of semiconductor heterostructure for different measurement conditions as well as surface tracking and scanning mechanisms. The full potential of the technique will be illustrated with results of vortex imaging studies of three distinct superconducting systems: (i) vortex chains in the “crossing lattices” regime of highly anisotropic cuprate superconductors, (ii) vortex–antivortex pairs spontaneously nucleated in ferromagnetic-superconductor hybrid structures, and (iii) vortices in the exotic p-wave superconductor Sr₂RuO₄ at milliKelvin temperatures.     

Melting pattern of diquark condensates in quark matter

Thermal color superconducting phase transitions in high density three-flavor quark matter are investigated in the Ginzburg-Landau approach. The effects of nonzero strange quark mass, electric and color charge neutrality, and direct instantons are considered. Weak coupling calculations show that an interplay between the mass and electric neutrality effects near the critical temperature gives rise to three successive second-order phase transitions as the temperature increases: a modified color-flavor locked (mCFL) phase (ud, ds, and us pairings) --> a d-quark superconducting (dSC) phase (ud and ds pairings) --> an isoscalar pairing phase (ud pairing) --> a normal phase (no pairing). The dSC phase is novel in the sense that while all eight gluons are Meissner screened as in the mCFL phase, three out of nine quark quasiparticles are always gapless.     

Supercooling across first-order phase transitions in vortex matter

Hysteresis in cycling through first-order phase transitions in vortex matter, akin to the well-studied phenomenon of supercooling of water, has been discussed in literature. Hysteresis can be seen while varying either temperature T or magnetic field H (and thus the density of vortices). Our recent work on phase transitions with two control variables shows that the observable region of metastability of the supercooled phase would depend on the path followed in H-T space, and will be larger when T is lowered at constant H compared to the case when H is lowered at constant T. We discuss the effect of isothermal field variations on metastable supercooled states produced by field-cooling. This path dependence is not a priori applicable to metastability caused by reduced diffusivity or hindered kinetics.     

Thermal fluctuations of vortex matter in trapped bose-einstein condensates

We perform Monte Carlo studies of vortices in three dimensions in a cylindrical confinement, with uniform and nonuniform density. The former is relevant to rotating 4He; the latter is relevant to a rotating trapped Bose-Einstein condensate. In the former case, we find dominant angular thermal vortex fluctuations close to the cylinder wall. For the latter case, a novel effect is that at low temperatures the vortex solid close to the center of the trap crosses directly over to a tensionless vortex tangle near the edge of the trap. At higher temperatures an intermediate tensionful vortex liquid located between the vortex solid and the vortex tangle may exist.     

Mode locking of vortex matter driven through mesoscopic channels

We investigated the driven dynamics of vortices confined to mesoscopic flow channels by means of a dc-rf interference technique. The observed mode-locking steps in the IV curves provide detailed information on how both the number of vortex rows and the lattice structure in each flow channel change with magnetic field. Minima in flow stress occur when an integer number of rows is moving coherently, while maxima appear when the incoherent motion of mixed n and n+/-1 row configurations is predominant. Simulations show that the enhanced pinning at mismatch originates from quasistatic fault zones with misoriented edge dislocations induced by disorder in the channel edges.     

Temperature-dependent vortex matter in a superconducting mesoscopic circular sector

Nonlinear time-dependent Ginzburg–Landau (TDGL) equations were solved in the present work using the link variables method. Vortex configurations were investigated in a superconducting circular sector immersed in an external magnetic field applied perpendicular to its plane. Magnetization and free energy were calculated as a function of the applied magnetic field at several temperatures. This paper illustrates how the vortices moved around at the transition fields before they become accommodated into an equilibrium configuration. A linear dependence of the magnetization dependence on temperature has been found for a certain magnetic field.     

Nonequilibrium phase transitions of vortex matter in three-dimensional layered superconductors

Large-scale simulations on the three-dimensional (3D) frustrated anisotropic XY model have been performed to study the nonequilibrium phase transitions of vortex matter in weak random pinning potential in layered superconductors. The first-order phase transition from the moving Bragg glass to the moving smectic is clarified, based on thermodynamic quantities. A washboard noise is observed in the moving Bragg glass in 3D simulations for the first time. It is found that the activation of the vortex loops plays the dominant role in the dynamical melting at high drive.     

Theory of the vortex matter transformations in high-Tc superconductor YBCO

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transition line. The line, however, makes a wiggle near the experimentally claimed critical point at 12 T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy, and the specific heat discontinuities at melting compare well with experiments.     

Lattice orientations of driven vortex matter in amorphous MoGe films

We have investigated the lattice orientation of driven vortex matter in amorphous MoGe films. Mode locking experiments in the flux flow state reveal that in addition to the theoretically predicted lattice orientation parallel to the flow direction also the perpendicular orientation occurs. Mapping out the orientations in a phase diagram, the perpendicular orientation is found to dominate the phase diagram covering a wide field and temperature range. Scanning tunneling microscopy images of the vortex lattice frozen from the flux flow state confirm the switching between parallel and perpendicular orientations in the phase diagram. The effect is possibly caused by the influence of the sample edge.     

Spatial structure of a vortex in low density neutron matter

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.     

Structural phase transitions of vortex matter in an optical lattice

We consider the vortex structure of a rapidly rotating trapped atomic Bose-Einstein condensate in the presence of a corotating periodic optical lattice potential. We observe a rich variety of structural phases which reflect the interplay of the vortex-vortex and vortex-lattice interactions. The lattice structure is very sensitive to the ratio of vortices to pinning sites and we observe structural phase transitions and domain formation as this ratio is varied.     

Instabilities in the vortex matter and the peak effect phenomenon

In single crystals of 2H-NbSe2, we identify for the first time a crossover from a weak collective to a strong pinning regime in the vortex state which is not associated with the peak effect phenomenon. Instead, we find the crossover is associated with an anomalous history dependent magnetization response. In the dc magnetic field (Bdc)-temperature (T) vortex matter phase diagram we demarcate this pinning crossover boundary. We also delineate another boundary which separates the strong pinning region from a thermal fluctuation dominated regime, and find that a peak effect appears on this boundary.     

Quantitative theory of thermal fluctuations and disorder in the vortex matter

A metastable supercooled homogeneous vortex liquid state exists down to zero fluctuation temperature in systems of mutually repelling objects. The zero temperature liquid state therefore serves as a (pseudo) ‘fixed point’ controlling the properties of vortex liquid below and even around the melting point. Based on this picture, a quantitative theory of vortex melting and glass transition in Type II superconductors in the framework of Ginzburg-Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps are calculated. The point-like disorder shifts the line downwards and joins the order-disorder transition line. On the other hand, the disorder induces irreversible effects via replica symmetry breaking. The irreversibility line can be calculated within the Gaussian variational method. Therefore, the generic phase diagram contains four phases divided by the irreversibility line and melting line: liquid, solid, vortex glass and Bragg glass. We compare various experimental results with the theoretical formula.