Two-dimensional Abrikosov-vortex microclusters: Shell structure and melting

Melting of two-dimensional Abrikosov-vortex microclusters in a type-II superconductor island with thickness less than the coherence length has been studied. Equilibrium configurations corresponding to local and global minima of potential energy for clusters with N=1–50 particles are calculated. The temperature dependences of the structure and of mean-square radial and angular vortex displacements are investigated. It is shown that vortex microclusters melt in two stages: first the frozen-out phase transfers to a state corresponding to rotational reorientation of crystalline shells with respect to one another, followed by a transition to a state with no radial order at a substantially higher temperature. The reason for this is that the barrier to shell rotation is significantly lower than that to radial breakdown of shells. Fiz. Tverd. Tela (St. Petersburg) 39, 1005–1010 (June 1997)     

Pinning-induced formation of vortex clusters and giant vortices in mesoscopic superconducting disks

Merged, or giant, multiquanta vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualize vortices in small Nb disks with varying degrees of disorder, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.     

Two-dimensional microclusters of vortices: Shell structure and melting

The melting of two-dimensional microclusters of “particles” which repel one another according to a logarithmic law and are confined by an external quadratic potential is investigated. The model describes Abrikosov vortices in a superconducting island of vortices in a rotating superfluid liquid and electrons in a semiconductor nanostructure surrounded by a low-permittivity medium. The structure of clusters and its dependence on temperature and melting are investigated. The melting of microclusters of vortices proceeds in two stages: 1. A transition from a frozen phase into a state corresponding to rotational reorientation of crystal shells relative to one another. 2. At a higher temperature, the radial order vanishes. This is connected with the fact that the barrier for rotation of the shells is much lower than the barrier for radial breakup of the shells. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 268–273 (10 February 1997)     

Critical fluctuations in a mesoscopic superconducting ring

The nonlocal magnetoconductivity fluctuations in a superconducting submicron ring, with radius comparable to the Ginzburg-Landau coherence length, are studied. The order parameter mode separation yields to the solution of the time-dependent Ginzburg-Landau equation and the paraconductivity Fourier components are calculated in the vicinity of the critical temperature, including the critical fluctuation region. The homogeneous component has a logarithmic singularity at T(c) while the other components are found to be not singular.     

Quantum melting of mesoscopic clusters

The phase diagram of a two-dimensional mesoscopic system of charges or dipoles, whose realizations could be electrons in a semiconductor quantum dot or indirect excitons in a system of two vertically coupled quantum dots, is investigated. Quantum calculations using ab initio Monte Carlo integration along trajectories determine the properties of such objects in the temperature-quantum de-Boer-parameter plane. At zero (sufficiently low) temperature, as the quantum fluctuations of the particles increase, two types of quantum disordering phenomena occur with increasing quantum de Boer parameter q: first, for q∼10⁻⁵ the systems transform into a radially ordered but orientationally disordered state wherein various shells of the “atom” rotate relative to one another. For much larger q∼0.1, a transition occurs to a disordered state (a superfluid in the case of a system of bosons). Fiz. Tverd. Tela (St. Petersburg) 41, 1856–1862 (October 1999)     

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.     

A single Abrikosov vortex trapped in a mesoscopic superconducting cylindrical surface

We investigate the behaviour of a single Abrikosov vortex trapped in a mesoscopic superconducting cylindrical surface with a magnetic field applied transverse to its axis. In the framework of the time-dependent Ginzburg-Landau formalism we show that, provided the transport current and the magnetic field are not large, the vortex behaves as an overdamped quasi-particle in a tilted washboard potential. The cylindrical thin strip with the trapped vortex exhibits E(J) curves and time-dependent electric fields very similar to the ones exhibited by a resistively shunted Josephson weak link.     

Experimental evidence for giant vortex states in a mesoscopic superconducting disk

The response of a mesoscopic superconducting disk to perpendicular magnetic fields is studied by using the multiple-small-tunnel-junction method, in which transport properties of several small tunnel junctions attached to the disk are measured simultaneously. This allows us to make the first experimental distinction between the giant vortex states and multivortex states. Moreover, we experimentally find a magnetic-field induced rearrangement and combination of vortices. The experimental results are well reproduced in numerical results based on the nonlinear Ginzburg-Landau theory.     

Two-dimensional mesoscopic dusty plasma clusters: Structure and phase transitions

A two-dimensional mesoscopic cluster of “dusty plasma” particles, which can be interpreted as a system of microparticles in an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors are found for clusters of N=22–40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as first-order or second-order phase transitions with respect to the parameter R. The disorder (“melting”) of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed. Zh. éksp. Teor. Fiz. 116, 1300–1312 (October 1999)     

Unconventional dynamics of vortex shells in mesoscopic superconducting corbino disks

The dynamics of vortex matter in mesoscopic superconducting Corbino disk is strongly influenced by the discrete vortex structure arranged in shells. While in previous works the vortex dynamics has been studied in large (macroscopic) and in very small mesoscopic disks (containing only few shells), in the intermediate-size regime it is much more complex and unusual, due to: (i) the competition between the vortex–vortex interaction and confinement and (ii) (in)commensurability among the vortex shells. We found that the interplay between these effects can result in a very unusual vortex dynamical behavior: (i) unconventional angular melting (i.e., propagating from the boundary, where the shear stress is minimum, towards the center) and (ii) unconventional dynamics of shells (i.e., the inversion of shell velocities with respect to the gradient driving force). This unusual behavior is found for different number of shells.     

Experimental distinction between giant vortex and multivortex states in mesoscopic superconducting squares

We study the distinction between giant vortex states and multivortex states in a thin mesoscopic superconducting square by using the temperature dependence of the vortex expulsion fields. We find that the results agree well with those obtained from the multiple-small-tunnel-junction method, indicating that the distinction by the temperature dependence of the vortex expulsion fields is applicable to superconducting squares.     

Direct observation of vortex shells and magic numbers in mesoscopic superconducting disks

We have studied vortex configurations in mesoscopic superconducting disks using the Bitter decoration technique. For a broad range of vorticities L the circular geometry is found to lead to the formation of concentric shells of vortices. From images obtained on disks of different sizes in a range of magnetic fields we traced the evolution of vortex states and identified stable and metastable configurations of interacting vortices. Furthermore, the analysis of shell filling with increasing L allowed us to identify magic numbers corresponding to the appearance of consecutive new shells.     

A new vortex state with non-uniform vorticity in superconducting mesoscopic rings

A study is presented of the superconducting states in mesoscopic rings. On the basis of self-consistent solution of the Ginzburg-Landau equations, a new kind of vortex states with non-uniform vorticity is found for some cases to be thermodynamically more stable, than the solution with unique winding number for the whole ring. There are indications that the solution with non-uniform vorticity concerns a metastable state of a superconducting mesoscopic ring.     

Calculation of the vortex structure in a superconducting alloy

We calculate properties of an isolated vortex in a dirty BCS superconductor at zero temperature by numerical integration of a diffusion equation. This is supplemented by a self-consistency equation for the order parameter, and we show that a simple trial form gives quite a good solution of it. The electronic density of states and low temperature specific heat are also calculated for extreme type II material. The difference between the density of states at frequencies ω and 0 is proportional to ω² for small ω, and the specific heat is similar to that predicted by previous approximate theory.     

Characteristic features of the melting of two-dimensional mesoscopic Wigner clusters

Two-dimensional Wigner microclusters in a semiconductor dot are studied. Their melting is investigated in detail and it is shown that, for typical mesoscopic clusters possessing a shell structure, melting occurs in two stages: orientational melting (rotation of the shells relative to one another) and total melting, where the shells start to overlap with one another and exchange particles. An example of a “magic” microstructure which has a triangular structure and melts in a single stage is presented. For this, the temperature dependences of various quantities characterizing cluster structure are investigated. The change in the distribution of cluster configurations over local minima of the potential energy with increasing temperature is investigated. At temperatures below the temperature of total melting, a cluster is always located near the configuration of a global minimum and, at temperatures above the temperature of complete melting, a cluster can be located with finite probability near configurations corresponding to various local minima of the potential energy. Fiz. Tverd. Tela (St. Petersburg) 41, 1499–1504 (August 1999)     

双能隙介观超导体的涡旋结构模拟

本文运用了含时Ginzburg-Landau理论研究了双能带结构的介观超导体在外磁场作用下涡旋随时间的演化. 给出了实际温度在s波和d波的临界温度之间s波、d波以及磁场的分布, 从 理论上模拟得到涡旋进入和退出样品的磁场"过热"与"过冷"现象, 以及介观超导样品边界对涡旋结构分布的影响. 关键词： 涡旋结构 双能带 含时Ginzburg-Landau理论 超导     

Effect of supercurrent injection on vortex penetration and expulsion fields in mesoscopic superconducting squares

We report an experimental study on the effect of supercurrent injection on vortex states in mesoscopic superconductors. The sample consists of an Al square with side of 1.1 μm, which is directly connected to Al leads for current injection. The vortex penetration/expulsion is detected by the voltage change across a small tunnel junction attached to the square. We find that the vortex penetration/expulsion fields are significantly influenced by the external current of the order of 10 μA. The shift of the vortex penetration/expulsion fields is interpreted in terms of the forces exerted by the external current.     

Structure, melting, and potential barriers in mesoscopic clusters of repulsive particles

This paper discusses two-dimensional mesoscopic clusters of particles that repel according to dipole, Coulomb, and logarithmic laws and are confined by an external parabolic potential. These models describe a number of physical systems, in particular, electrons in semiconductor structures or on a liquid-helium surface allowing for image forces, indirect excitons in coupled semi-conductor dots, and a small number of vortices in an island of a second-order superconductor or in superfluid helium. Two competing forms of ordering are detected in the particles in the mesoscopic clusters-the formation of a triangular lattice or of a shell structure. The temperature dependences of the potential energy, the mean-square radial and angular deviations, the radial and angular distributions of the particles, and the distribution of the particles over the local minima are studied. Melting in mesoscopic clusters occurs in two stages: at lower temperatures, there is orientation melting, from the frozen phase into a phase with rotational reorientation of “crystalline” shells with respect to each other; subsequently, a transition occurs in which the radial order disappears. Melting in dipole macroclusters occurs in a single stage. However, in Coulomb and logarithmic macroclusters, orientation melting occurs only for the outer pairs of shells. Orientation melting is also detected in three-dimensional Coulomb clusters. A connection is established between the character of the melting and the ratio of the energy barriers that describe the breakdown of the orientational and radial structure of a cluster. Zh. éksp. Teor. Fiz. 116, 2012–2037 (December 1999)