Pinning of vortices and penetration of the magnetic field into a periodically modulated long Josephson contact

The upper field of the Meissner regime, H _up, and overheat field H′_c1, above which vortices start penetrating into a Josephson contact, are calculated throughout the range of pinning parameter I. The stability of likely configurations is investigated. It is shown that H _up = H′_c1 at any I. The existence of a single vortex centered at the extreme cell in the contact is demonstrated to be a possibility. At I > 3.69, such a vortex may exist even in a zero magnetic field. At 1.48 < I < 3.69, this vortex can exist in an external field in the range from some H _v to H _up. At I < 1.48, the vortex cannot exist under any conditions. From the equality of H _up and H′_c1 at any I, the conclusion is drawn that penetration of vortices into any Josephson medium is conditioned by the need to satisfy flux quantization conditions. Here, not the forces of vortex pinning at defects in the medium but quantization requirements are of major importance, which are satisfied in specific quantum ways rather than by meeting equilibrium conditions for vortices, forces, etc.     

On the Meissner effect in gauge theories

The phase structure of spontaneously broken scalar electrodynamics in an external electromagnetic field is analyzed. With no external field, the spectrum comprises a scalar boson of mass m_H and a vector boson of mass m_W. If m_H ≤ m_W, it is shown that in the tree approximation, as the external field is increased, a first order phase transition to a restored symmetry phase occurs, and the critical field strength is calculated. Below the critical point the external field is completely screened, this being the analogue of the Meissner effect in superconductivity. If m_H > m_W, a third phase, characterized by vortex solutions of the field equations, occurs. Quantum effects, such as pair production in an electric field, are considered at the one (and two) loop level in the massless theory (the Coleman-Weinberg model). The leading correction to the critical magnetic field strength is calculated, and it is shown that for an external electric field the phase transition does not exist.     

Site selection NMR study on electronic state in and near vortex core of YBa2Cu4O8

We report a site-selective ¹⁷O spin-lattice relaxation rate T₁⁻¹ in the vortex state of YBa₂Cu₄O₈. We found that T₁⁻¹ at the planar sites exhibits an unusual nonmonotonic NMR frequency dependence. Based on T₁⁻¹ in the vortex core region, we establish strong evidence that the local density of states within the vortex core is strongly reduced.     

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.     

Effects of Meissner surface current on the microwave surface resistance of type-II superconductors

Influence of the Meissner current on the field-induced variations of the microwave (mw) surface resistance in type-II superconductors is demonstrated to be well reproduced by exploiting different critical state models. R_s(B)/R_n versus B_a curves have been obtained using Kim and exponential type J_c(B) considering Meissner current circulating at the surface of the superconducting specimen.     

On the emergence of superconductivity and hysteresis in a cylindrical type I superconductor

One-dimensional vortex-free solutions of the system of Ginzburg-Landau equations (the so-called precursor states) are studied. These states describe the emergence of superconductivity in a long cylindrical type I superconductor, which was initially in the supercooled normal state in a magnetic field, and are formed upon subsequent reduction of the external field. The precursor states are responsible for the magnetic hysteresis in type I superconductors (for which κ < κ_c, where κ_c (R) is the critical value of the parameter κ in the Ginzburg-Landau theory, which is a function of radius). The range of fields is determined in which precursor states exist along with the Meissner state (and a hysteresis is possible) in the dependence of the cylinder radius R and parameter κ.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Mixed state in a superlattice

Presented in this paper is a theoretical calculation of the vortex solution in a chosen superlattice (Nb/NbZr) using the Gibbs free energy of an inhomogeneous superconductor. The eigenvalue obtained in this geometry from de Gennes-Werthamer proximity coupling theory is first examined according to a set of experimental data, while the correspondent eigenfunctions are then used to construct vortex solutions with either square lattice or triangle lattice symmetry. The Gibbs free energy is calculated in terms of the vortex solutions of both symmetries. The effective Ginzburg-Landau parameter,K _NS , for this superlattice is determined asK _NS =0.218 by requiring a consistency between the microscopic and macroscopic theoretical calculations. Of particular importance is a new mechanism revealed by this calculation that a highly localized state of superconducting condensate in its hosting layer, despite the spatially rapid varying characteristic of its correspondent nucleating order parameter, provides a lower eigenvalue state, which results in a dimensional crossover. A further examination of this mechanism is carried out in the mixed state calculation. Finally, a generalization of the present theoretical results to a large class of superlatices is discussed.     

Vortex structure in Sr2RuO4

The vortex structure in p-wave superconductors is investigated by the Bogoliubov–de Gennes theory on a tight-binding model. We calculate the temperature dependence of the electronic state at each site in the vortex lattice state, and show the difference between sin p_x+i sin p_y-wave and sin p_x−i sin p_y-wave superconducting state. Furthermore the relation of the electronic structure and the site-dependence of the nuclear magnetic relaxation time is also discussed.     

Stability of solitons on vortex filaments

A vortex filament is a filament on which fluid vorticity is concentrated. This concept is particularly important in superfluidity and turbulence. This Letter focuses on the vortex filament equation (VFE), which is a model for the motion of a vortex filament in an incompressible and inviscid fluid. The VFE soliton solutions are considered and their spectral stability is proven by developing a straightforward method to solve the corresponding eigenvalue problem. A similar analysis is performed on the planar vortex filament equation. We discuss the applicability of the methods introduced in this Letter to other physically relevant curve equations and other types of solutions.     

Meissner-London currents in superconductors with rectangular cross section

Exact analytic solutions are presented for the magnetic moment and screening currents in the Meissner state of superconductor strips with rectangular cross section in a perpendicular magnetic field and/or with transport current. The extension to finite London penetration is achieved by an elegant numerical method which works also for disks. The surface current in the specimen corners diverges as l(-1/3) where l is the distance from the corner. This enhancement reduces the barrier for vortex penetration and should increase the nonlinear Meissner effect in d-wave superconductors.     

Doping dependence of Meissner effect in cuprate superconductors

Within the t–t′–J model, the doping dependence of the Meissner effect in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. Following the linear response theory, it is shown that the electromagnetic response consists of two parts, the diamagnetic current and the paramagnetic current, which exactly cancels the diamagnetic term in the normal state, and then the Meissner effect is obtained for all the temperature T ? T_c throughout the superconducting dome. By considering the two-dimensional geometry of cuprate superconductors within the specular reflection model, the main features of the doping and temperature dependence of the local magnetic field profile, the magnetic field penetration depth, and the superfluid density observed on cuprate superconductors are well reproduced. In particular, it is shown that in analogy to the domelike shape of the doping dependent superconducting transition temperature, the maximal superfluid density occurs around the critical doping δ ≈ 0.195, and then decreases in both lower doped and higher doped regimes.     

Eigenschaften der Lösungen der nichtlinearisierten Ginsburg-Landau-Gleichungen in Zylindersymmetrie

Solutions of the nonlinear Ginzburg-Landau equations in cylindrical symmetry have been computed for a type I superconductor. From these solutions the behaviour of a circular cylinder of infinite length in a magnetic field parallel to its axis has been deduced. For a series of values of the magnetic field solutions are given in two cases. The first case was calculated with the assumption of no fluxoid frozen in (fluxoid quantum number n=0), whereas in the second case a vortex with fluxoid quantum numbern=1 was assumed on the axis of the cylinder. For both series of solutions investigation of the thermodynamic stability was carried out. This and further thermodynamic considerations led to the result that in a gedankenexperiment the transition from the normal to the superconducting state and vice versa can be performed in a reversible manner. The expulsion of the magnetic field from the sample during the reversible transition to the superconducting state (Meissner-Effect) is also described by the solutions. Further results are the existence of a supercooled state down to a magnetic fieldH _c2=κ√2H_cb and of a superheated state up to a fieldH _c1>H _cb. The value ofH _c1 depends on the radius of the cylinder. If a condensation to the superconducting state takes place at a fieldH ₀ whereH _c2<H ₀<H _cb, condensation withn=0 seems to be preferred in comparison to that withn=1.     

Penetration of the magnetic field into a 3D ordered Josephson medium at very small values of the pinning parameter

The Meissner state of a 3D Josephson medium is analyzed for stability against small fluctuations of phase discontinuities at contacts. For any form of fluctuations, there exists value I ₀ of pinning parameter I such that the Meissner configuration remains stable if I < I ₀. Reasons why the configuration remains stable at small I are considered. Instability arises when the quadratic form of the second variation of Gibbs potential G is not a positively definite quantity. At small I, the contribution of the Josephson energy to G is small. The second variation of the magnetic energy, the other component of G, is always a positively definite quadratic form. Therefore, instability may arise only if I has a finite value. This statement holds true not only for the Meissner but also for any equilibrium configuration. At I < I ₀, stability persists up to the boundary of the Meissner state. Then, a sequence of plane vortices parallel to the boundary appears throughout the sample. Thus, vortices appearing at I < I ₀ are plane vortices rather than linear. The configurations of currents and the magnetic field profile inside the sample are calculated for I < I ₀. Calculation is based on analyzing the continuous variation of the current configuration toward a decrease in the Gibbs potential.     

Magnetic transition and Meissner shielding in ferromagnetic high-Tc superconductor RuSr2Gd1.4Ce0.6Cu2O10-δ

The magnetic superconductor RuSr₂Gd_1.4Ce_0.6Cu₂O_{10- δ} was studied by means of detailed magnetization measurements in order to clarify its complex magnetic and superconducting properties. Our experiments agree with a model indicating that the in-plane component of the Ru moment might transform from a spin-glass ground state to a ferromagnetically coupled excited state by application of a small magnetic field below the magnetic transition temperature. The experiments also show that a full Meissner state is present at the low temperature, the low magnetic field region of the phase diagram. This is in contrast to the previous prediction that no Meissner state exists in this material for an internal magnetic field of several hundred Oersteds in the CuO₂ planes exerted by the Ru sublattice and exceeding the lower critical field.     

Vortex imaging in Co-doped BaFe2As2

We review superconducting vortex imaging in Co-doped BaFe₂As₂ by Bitter decoration and small-angle neutron scattering (SANS). At all measured fields a highly disordered vortex configuration is observed, which is attributed to strong pinning. Further support of this conclusion comes from the absence of a Meissner rim in decoration images obtained close to the sample edge. The evolution of the SANS scattering vector with increasing applied field indicates vortex lattice domains of (distorted) hexagonal symmetry. This is consistent with the decoration images which show small, six fold coordinated ordered vortex domains. The SANS scattered intensity is found to decrease rapidly with increasing field, exceeding the rate expected from estimates of the upper critical field. This is consistent with the large degree of vortex “lattice” disorder.     

A quantitative analysis of magnetic vortices in Permalloy nanoparticles characterized by electron holography

The present work investigates experimentally curling magnetic configurations locally observed in almost dispersed Permalloy nanoparticles in the remanent state. Magnetic analysis is performed in a field emission TEM using off-axis electron holography. Particularly, electron holography is used to characterize the magnetic microstructure of Fe₃₀Ni₇₀ nanoparticles, whose average diameter (50 nm) is expected to be close to the critical size for a curling magnetic structure (vortex) formation. The vortex core diameter D_core and the bulk magnetic profile of the vortex are measured and compared with a “rigid vortex” micromagnetic model. The connection between vortex structure and the characteristic micromagnetic length of the system deduced from magnetization curve measurements is discussed.     

Hole core in superconductors and the origin of the Spin Meissner effect

It is proposed that superconductors possess a hidden ‘hole core’ buried deep in the Fermi sea. The proposed hole core is a small region of the Brillouin zone (usually at the center of the zone), where the lowest energy states in the normal state reside. We propose that in the superconducting state these energy states become singly occupied with electrons of a definite spin helicity. In other words, that holes of a definite spin helicity condense from the top to the bottom of the band in the transition to superconductivity, and electrons of that spin helicity ‘float’ on top of the hole core, thus becoming highly mobile. The hole core has radius q₀ = 1/2λ_L, with λ_L the London penetration depth, and the electrons expelled from the hole core give an excess negative charge density within a London penetration depth of the real space surface of the superconductor. The hole core explains the development of a spin current in the transition to superconductivity (Spin Meissner effect) and the associated negative charge expulsion from the interior of metals in the transition to superconductivity, effects we have proposed in earlier work to exist in all superconductors and to be at the root of the Meissner effect.     

Ab initio investigation of phase separation in Ca1−xZnxO alloys

First-principles study of the ground-state properties and the stability of Ca_1−xZn_xO solid solutions is presented using the full-potential linearized augmented plane wave (FP-LAPW) method. We employed the local density approximation (LDA) to the exchange-correlation potential. It is found that the structural parameters, i.e., lattice constants and bulk moduli deviate from the linear function of the composition x. We determined the equation of state of the alloys and showed an increasing compressibility function of composition. The formation energy is viewed as an energetic balance between pure structural constraints and quantum chemical effects. Thus, a phase separation over the whole range of concentration is expected. The origin of the miscibility gap has a chemical nature. Also, the thermodynamic stability of the alloys was investigated.     

Growth temperature dependence of flux pinning properties in ErBa2Cu3Oy thin films with nano-rods

Irreversibility lines and distributions of local critical current density (J_cl) based on the percolation transition model were affected by the growth temperature (T_s) in 3.5 wt.%-BaNb₂O₆-doped ErBa₂Cu₃O_y thin films. The vortex-Bose-glass-like state appeared by the introduction of nano-rods, and this vortex state was affected by T_s. The shape and width of the J_cl distribution strongly depended on T_s. These results are probably caused by variations of the density and the growth direction for nano-rods reflecting T_s. The growth temperature is an important factor to achieve higher critical current properties under magnetic fields for coated conductors of rare-earth-based cuprates with nano-rods.