Thermodynamics of a vortex system in a thin superconducting film with radiation defects

The effect of radiation defects on the thermodynamics of a system of Pearl vortices in a thin superconducting film is examined. The scenario for a Kosterlitz-Thouless transition in this system is shown to depend on the defect concentration n _d . At low concentrations, the transition takes place continuously, while at high concentrations, a range of temperatures exists in which there are two metastable states. The concentrations of free vortices and of vortices captured by defects are calculated as functions of temperature for different defect concentrations n _d . A phase diagram is constructed for the vortex system in the n _d −T plane. Zh. éksp. Teor. Fiz. 116, 1081–1090 (September 1999)     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Induced motion of a fast Josephson vortex

A relation is established between the transport current flowing through the entire S ₁ IS ₂ WS ₃ layered structure and the velocity of a fast vortex. The fast vortex exists when the Swihart velocity in the waveguide is significantly higher than that in the Josephson junction. It is demonstrated that the main contribution to the Lorentz force that induces the vortex motion is due to the current flowing through the waveguide and skin layers of the adjacent superconductors.

     

Finite vortex numbers and symmetric vortex structures in a rotating trapped Fermi gas in the BCS-BEC crossover

The ground state of a three-dimensional (3D) rotating trapped superfluid Fermi gas in the BCS-BEC crossover is mapped to finite N _v -body vortex states by a simple ansatz. The total vortex energy is measured from the ground-state energy of the system in the absence of the vortices. The vortex state is stable since the vortex potential and rotation energies are attractive while the vortex kinetic energy and interaction between vortices are repulsive. By combining the analytical and numerical works for the minimal vortex energy, the 2D configurations of N _v vortices are studied by taking into account of the finite size effects both on xy-plane and on z-direction. The calculated vortex numbers as a function of the interaction strength are appropriate to the renew experimental results by Zwierlein in [High-temperature superfluidity in a ultracold Fermi gas, Ph.D. thesis, Massachusetts Institute of Technology, 2006]. The numerical results show that there exist two types of vortex structures: the trap center is occupied and unoccupied by a vortex, even in the case of N _v < 10 with regular polygon and in the case of N _v ≥ 10 with finite triangle lattice. The rotation frequency dependent vortex numbers with different interaction strengths are also discussed.     

无序二维约瑟夫森结阵列中磁场引起的涡旋玻璃态相变

采用电阻阻错结的无序二维约瑟夫森结阵列模型,数值研究超导薄膜中垂直磁场引起的涡旋运动.通过分析磁场激发产生的涡旋度Ne及低频电压噪声S₀的变化特性,得到如下结论：在无序超导体中固定温度不变,随着磁场的减弱涡旋液态经过准有序的布拉格相,涡旋玻璃相重新进入到低磁场下的钉扎稀磁液相. 由于在涡旋玻璃相中,电流驱动下的噪声值表现出一个峰,表明系统处于无序与有序相互竞争的亚稳态,并且临界电流应有峰值效应. 计算得到噪声值的变化与Okuma等得到的无序超导Mo_xSi_1-x膜实验现象一致,并能解释磁场降低引起的重新进入钉扎的稀磁液相行为. 关键词： 约瑟夫森结阵列 磁通玻璃 重新进入 峰值效应     

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω ₀ τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B _c2/B)^1/2 due to the gap nodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 201–206 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Geometrical surface vortex pinning in superconducting films

A model is proposed for vortex pinning in a superconducting film with a rough surface. The model relates the critical current to the steepness of the surface relief and, at a high vortex concentration, to the distance between neighboring steepness maxima on the paths of vortex motion. The dependence of the critical current density on the thickness of a high-T_c superconducting film is measured in a weak magnetic field. Its behavior can be explained by the pinning at the stepped surface relief.     

Electrodynamics of the vortex lattice in untwinned YBaCuO by complex impedance measurements

We report complex impedance measurements in an untwinned YBaCuO crystal. Our broad frequency range covers both the quasi static response and the resistive response of the vortex lattice. It allow us to characterize the irreversibility line without the need of any frequency dependent pinning parameters. We confirm the validity of the two modes model of vortex dynamic, and extract both the surface critical current and the flux flow resistivity around the first order transition T_m. This latter is identified by the abrupt loss of pinning and by an unexpected step of (T) at T_m. Received 22 November 2002 / Received in final form 17 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: alain.pautrat@ismra.fr RID="b" ID="b"UMR 6508 associée au CNRS     

The effect of surface temperature on H2/D2(v = 0, j = 0)–Ni(100) scattering processes

We carry out both four-dimensional (4D×2D) and six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for H₂/D₂(v = 0,j = 0)–Ni(100) collision process. Such an effective potential was derived within a theoretical framework of mean-field approximation by considering weakly correlated interaction between molecular degrees of freedom, phonon modes and electron– hole pair (elhp) coupling through a Hartree-product-type wave function, where the initial state distribution of the surface modes and elhp coupling were introduced through Bose– Einstein and Fermi– Dirac probability factor, respectively. The temperature-dependent dissociation and state-to-state transition probabilities for H₂/D₂(v = 0,j = 0)–Ni(100) system are depicted as a function of initial kinetic energ of the incoming diatom. Though such effect appears negligibly small for H₂(v = 0,j = 0)–Ni(100) system, it is prominent in the case of D₂(v = 0,j = 0)–Ni(100) collision. It appears that the change of dissociation and transition probabilities of D₂ with the increase of surface temperature is exclusively dictated by the phonon modes directed along Z-axis, but the effect of elhp coupling particularly for transition probabilities is insignificant.     

Vortex rings and plasma toroidal vortices in a homogeneous infinite medium. I. Maximum vortex path

The maximum path L _MAX of vortex rings (toroidal vortices) in air and water before the beginning of their decay was experimentally determined in a wide variation range of their initial integral characteristics. A formula for L _MAX was derived as a function of primary characteristics of such vortices from the laws of their motion and energy variation. It was shown that this formula is in satisfactory agreement with experimental data.     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.     

Structure of the Abrikosov vortex lattice in a thin superconducting film in a parallel magnetic field

The structure of a vortex lattice in thin (d<λ, where d is the film thickness and λ is the London penetration depth) superconducting films is investigated in a magnetic field parallel to the film surface. It is shown that the stable configuration has the form of discrete vortex rows whose number changes discretely with an increase in the applied magnetic field. The entry fields H _c1 ^(N) (d) for vortex rows are calculated for N=1, 2. It is shown that the structural transition in the vortex ensemble is a second-order phase transition. A simpler method (as compared to the Monte Carlo technique) is proposed for calculating the vortex lattice parameters.     

Coherence vortex properties of partially coherent flat-topped vortex beams

The analytical propagation expression of partially coherent flat-topped vortex beams through a paraxial optical ABCD system is derived, and it then is used to investigate the coherence vortex properties of partially coherent flat-topped vortex beams in the Fourier transform and fractional Fourier transform systems. It is shown that in the Fourier transform system the coherence vortex depends on the flat-topped beam order N, spatial coherence parameter α and position (x ₁,y ₁) of the reference point, whereas in the fractional Fourier transform system the flat-topped beam order N does not affect the spectral degree of coherence. Furthermore, in both transform systems, depending on the choice of the reference point, the zero value point of the spectral degree of coherence may be present or absent. In particular, if x ₁=y ₁=0 is selected, the phase at the zero value point of the spectral degree of coherence may be determinate; thus the coherence vortex does not exist.     

Acoustic waves emitted by a vortex ring passing near a circular cylinder

Acoustic waves emitted by a vortex ring moving near a circular cylinder have been studied experimentally and theoretically. The vortex rings used in the experiments had a translational speed ν₀ in the range 26 ⪅ ν₀ ⪅ 58 m/s and a radius of about 4·7 mm comparable in size with the cylinder radius. The acoustic pressure signals were detected by four microphones in the far field, and analyzed by digital methods. The observed pressure p obeys the scaling law p ∞ ν₀³L⁻⁴, where L is the impact distance of the vortex path to the cylinder. The observed sound wave is of dipole radiation type, and the direction of the dipole axis rotates as the vortex position changes relative to the cylinder. The direction of the dipole axis is related to that of the normal to the plane of the vortex ring. The instantaneous resultant force exerted on the cylinder by the vortex motion has also been examined, and the magnitude and the direction determined experimentally as a function of time. The theory of vortex sound predicts that the wave profile is proportional to the second time derivative of the volume flux (of a hypothetical potential flow around the cylinder) through the vortex ring. The observed scaling law and dipole directivity of the pressure are in good agreement with the theoretical predictions. The pressure profiles are calculated by using the observed vortex motion. These profiles also agree well with the observed ones, confirming the validity of the theory.     

Two-Dimensional Coulomb Glass as a Model for Vortex Pinning in Superconducting Films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields B ≪ H_c2 at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase, such as InO_x, NbN, TiN, MoGe, and nanogranular aluminum, is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with a large kinetic inductance per square L_K. The distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap; i.e., the probability to find a weakly pinned vortex is extremely low.

     

Local-field anisotropy of a light wave in quasi-two-dimensional soft-matter objects

Experimental values of the Lorentz tensor components L _j for uniaxial quasi-two dimensional “soft matter” objects on substrates (bilayer lipid membranes, multilayer Langmuir films, smectics A, hexatic smectics B, submicron films of discotics Col _hd , micron anisotropic films of liquid-crystal comblike polymers and macromolecular polymers, submicron films of conjugated conductive polymers), freely suspended submicron films of smectics A, and uniaxially stretched micron films of conjugated conductive polymers have been determined using dispersion of refractive indices in the visible range. The dependences of the components L _j on the type of orientation (axial, planar) of uniaxial molecules (structural units of the film) with respect to the optical axis of the film, the film thickness, the substrate type, the chemical structure of molecules, and their long-range orientational order are established. It is revealed that the smectic A-hexatic B phase transition and two-dimensional crystallization of the smectic layer lead to changes in the components L _j due to the change in the orientational ordering of molecules as a result of the relation between the orientational and hexatic order parameters. All the above objects are characterized by isotropization of the Lorentz tensor L and the local-field tensor f with a simultaneous decrease in the birefringence of the sample and in the anisotropy of the molecular polarizability due to the change in the electronic structure of molecules. The correction for the anisotropy of the local-field tensor f to the orientational order parameter or the anisotropy of the molecular polarizability increases. The existing model approaches to calculating the components L _j for the objects under consideration are compared with the experimental data.     

Oscillating Casimir force between two slabs in a Fermi sea

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T_c, where T_c is the critical temperature of the Bose-Einstein condensation.     

Absence of dynamical crossover in the vortex creep near by the second peak effect in superconducting Hg-1201 single crystals

DC magnetic relaxation measurements in HgBa₂CuO₄ single crystals are analyzed nearby the fishtail line. It is found that in this case, it is not necessary to introduce any crossover from plastic creep to elastic creep models at the fishtail line. This type of fishtail effect comes only from a competition between a critical current at low temperature which increases versus field and the activation energy, which decreases versus field. According to the doping level of the compound, the fishtail effect can be observed or not, without any correlation with a vortex phase transition. Moreover, in this type of fishtail effect, there is no history effects as recently observed in YBaCu₂O₃ by the partial magnetization loop technique, suggesting that the transition from plastic to elastic flow is here hidden by the disorder of these materials. Received 11 January 2000     

Experimental demonstration of vortex pancake in high temperature superconductor

In order to demonstrate the existence of the vortex pancake in high temperature superconductor experimentally, a configuration in which the current and voltage electrodes lies separately on the top and bottom surface is used. The E-j relation obtained with this electrodes spatial configuration is different from the expected E-j behavior of the stiff vortex line model. Thus, the current results support the existence of the vortex pancake in high temperature superconductor.