Effect of surface defects on vortex penetration in small superconducting squares

We report the dependence of the vortex penetration on the number and positions of surface defects in mesoscopic superconducting squares. The vortex penetration is detected by the change in the transport properties of small tunnel junctions attached to the sample (small-tunnel-junction method). We find that for vorticities L = 0 and 1, a defect at the center of a side facilitate the vortex penetration, while a defect at a corner does not affect the vortex penetration field. For higher vorticities, the influence of defects becomes complicated, indicating that not only the existence of surface defects but also the vortex arrangement influences the vortex penetration. Simple explanation for this mesoscopic vortex penetration effect is given.     

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.     

Phase diagram of a lattice of pancake vortex molecules

On a superconducting bi-layer with thickness much smaller than the penetration depth, λ, a vortex molecule might form. A vortex molecule is composed of two fractional vortices and a soliton wall. The soliton wall can be regarded as a Josephson vortex missing magnetic flux (degenerate Josephson vortex) due to an incomplete shielding. The magnetic energy carried by fractional vortices is less than in the conventional vortex. This energy gain can pay a cost to form a degenerate Josephson vortex. The phase diagram of the vortex molecule is rich because of its rotational freedom.     

Vortex lattice symmetry in hexagonal superconductor CaAlSi probed by small angle neutron scattering

The small angle neutron scattering diffraction patterns from the flux line lattice state in the layered hexagonal superconductor CaAlSi are observed. Under an applied magnetic field (H) parallel to the crystalline c-axis, a hexagonal vortex structure is observed over the entire temperature/field regions. On the other hand, the vortex configuration under H∥a shows an ellipsoidal arrangement of the first-order Bragg peaks due to the anisotropic penetration depth. It was inferred from these results that the vortex state characterized by penetration depth and coherence length in CaAlSi may be described by that of anisotropic uniaxial superconductor using London theory.     

Breakdown of the superheated Meissner state and spontaneous vortex nucleation in type II superconductors

The theory of local stability of the superheated Meissner state presented in an earlier paper is supplemented by an investigation of global stability in two dimensions. We conclude that flux penetration cannot be delayed beyond the fieldH _s1 where local instability sets in. Various new two-dimensional Ginzburg-Landau solutions, obtained numerically, are discussed. These include the lowest saddle point separating the Meissner from the normal and vortex state and a solution resembling the “nascent vortex state” whose existence was postulated recently by Walton and Rosenblum. Using these solutions the process of spontaneous vortex nucleation is discussed.     

Magnetic-field effects on the size of vortices below the surface of NbSe2 detected using low energy beta-NMR

A low energy radioactive beam of polarized 8Li has been used to observe the vortex lattice near the surface of superconducting NbSe2. The inhomogeneous magnetic-field distribution associated with the vortex lattice was measured using depth-resolved beta-detected NMR. Below Tc, one observes the characteristic line shape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with the magnetic field. In particular, in a low field of 10.8 mT, the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.     

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.     

Structure of the mixed state in type II superconductors and its connection with Josephson effects in long superconducting bridges

The interaction energy between vortices and the structure of the vortex lattice in superconducting layers is calculated. It is shown that the one-dimensional vortex lattice (with vortices in the centre of the layer) is stable in a relatively large interval of magnetic fields above the flux penetration field. This result is true not only for very thin layers (with dimensions smaller than the penetration depth), but also for layers withd>. The results can be helpful at explaining some unusual experimental results on Josephson effects in long superconducting bridges.     

Possibility of two-stage flux penetration in antiferromagnetic superconductors

An induced ferromagnetism in antiferromagnetic superconductors is possible, caused by a magnetic structure of vortex lines appearing in an external magnetic field strong enough to “flip over” the spins in the vortex core from their antiferromagnetic configuration. If the magnetic field is less than the “flip over” field the vortex line is entirely in the antiferromagnetic phase. Therefore the vortex interaction with the surface of a sample is altered when an applied magnetic field exceeds the “flip over” field. This mechanism makes the appearance of a new energy barrier that strongly influences the flux penetration possible. An estimation of the second critical entry field is made for DyMo₆S₈.     

Multivortex states in large pinning centers

We have studied the vortex pinning in the large centers, i.e. in the spatial regions with the characteristic size a comparable with the London lenght λ. It is shown that the type of configuration and the number of vortices in the cluster are dependent on the ration a/λ and change nonmonotonically with the temperature. The influence of such vortex clusters on the decay of magnetization and the current-voltage characteristics are discussed. The important role of the potential barrier for the penetration of vortices into the pinning center is shown. The new state of vortex cluster, “vortex polaron”, is predicted. The stability of the multivortex state is discussed.     

Shape of the magnetic resonance line in a thin film on the surface of an anisotropic superconductor

The shape of the EPR line in a thin (=λ/2, where λ is the London penetration depth of the magnetic field in the superconductor) paramagnetic film deposited on the surface of an anisotropic superconductor is calculated in an oblique magnetic field with allowance for the inhomogeneity of the local magnetic field of the Abrikosov vortex lattice. It is shown that, as the tilt angle of the external magnetic field is varied, the shape of the EPR line changes noticeably. This fact can give additional information about the superconductor parameters (the symmetry type of the vortex lattice and the anisotropy parameter of the superconductor). Fiz. Tverd. Tela (St. Petersburg) 41, 386–388 (March 1999)     

Role of surface modes in vortex formation in BEC

We study the role of surface modes in the process of vortex formation in harmonically trapped BEC. It is shown that the vortex nucleation and penetration to the inner part of the cloud occur at velocities slightly exceeding the surface mode critical velocity. Surface modes induce ripples of the order parameter; these ripples are then transformed into vortex-antivortex pairs. After this, vortices move to the inner part of the cloud, whereas antivortices go in the opposite direction     

On the method of Eilenberger for inhomogeneous superconductors

The theory of Eilenberger, modified to take into account the effect of the surface, is applied to the problem of the penetration of a weak magnetic field into a semiinfinite superconductor, and the standard result for the vector potential is derived by linearizing the Eilenberger equations. The dominant term in the asymptotic behaviour is argued to be monotonic for both large and small values of the Ginzburg-Landau parameterk _gl . ForT≠ 0, there is a small intermediate range of values ofk _gl for which the dominant term is oscillatory, but these oscillations are not related to those found by Eilenberger and Büttner in the isolated vortex problem for smallK _gl . From an analysis of these results, we conclude that the absence of the Eilenberger-Büttner oscillations in the field penetration problem cannot be used as an argument against their existence in other problems; in particular, a separate investigation is required for the isolated vortex problem.     

Magneto-optical imaging of vortex arrangements in Pb finite superconducting networks

We have fabricated finite-sized Pb superconducting networks with 10 × 10 square (each 6 × 6 μm²) holes by using the electron beam lithography and vortex arrangements are visualized by using magneto-optical imaging. We find that the vortex penetration at low temperature is controlled by defects in the network. We also find nearly regular arrangements of vortices with defects close to 1/2 and1/3 of the matching field.     

Angular dependences of the peak effect in Yba2Cu3Ox single crystals

Angular dependences of the magnetization hysteresis loops have been studied at T=77 K on YBCO single crystals exhibiting the peak effect. The peak effect is shown to be related to the pinning of longitudinal vortices along the c axis at twin boundary-type ordered defects. The behavior of the peak effect at intermediate angles is explained by anisotropic magnetic field penetration into quasi-two-dimensional superconductors. In thin crystals with a dilute ordered-defect structure this can result in an enhanced peak effect due to formation of a vortex kink structure and to “internal” pinning of transverse vortex segments at Cu-O sheets. Fiz. Tverd. Tela (St. Petersburg) 39, 425–431 (March 1997)     

Structural phase transition in the mixed state of superconducting films in a parallel magnetic field

A thin film of a second-kind superconductor in a magnetic field parallel to the surface of the film is considered in the London approximation. It has been shown that if bulk pinning is absent and the suppression of super-conductivity by the magnetic field is negligible, the splitting of a vortex chain in the film occurs as a structural phase transition either of the first or second order, depending on the ratio of the thickness of the film d to the penetration depth of the magnetic field λ. The ratio d/λ, and thereby the character of the transition in the vortex lattice, can be changed by varying the temperature. The corresponding critical thicknesses of films and field ranges in which this effect can be observed experimentally have been calculated.     

Shape of a magnetic resonance line in a thin film on the surface of anisotropic superconductor with irregularly distributed Abrikosov’s vortices

The form of an electron paramagnetic resonance (EPR) in a thin paramagnetic film (λ/10, λ-London’s depth of magnetic field penetration into superconductor) overlying the surface of an anisotropic superconductor is calculated taking into account the local magnetic field non-uniformity of an irregular Abrikosov’s vortex lattice. It is shown that the form of EPR is noticeably varied with the degree of irregularity of the superconductor vortex lattice. It is suggested that an inclusion of this circumstance into consideration may essentially change the conclusions made on the lattice type and parameters of this superconductor, which are typically derived from the analysis of the EPR form. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 49–52, January, 2007.     

Enhancing the penetration stability of plasma jet in liquid by improving the chamber structure

Two kinds of chamber structures were designed to improve the penetration stability of plasma jet in the working fluid. They are the cone-truncated chamber with an inclined wall structure and the stepped-wall chamber with an abrupt expanding structure. Based on the experiment, the penetration characteristics of plasma jet in liquid were investigated by the numerical calculation, especially the multiphase flow field structure and the jet penetration stability. In the cone-truncated chamber, the arc-like pressure wave does not evolve into the plane wave like the wave evolution rule in the traditional cylindrical chamber, and an alternating structure of arc-like wave and the plane wave is formed in the stepped-wall chamber. The stability control of stepped wall is more significant than that of inclined wall because the low-pressure vortex formed at the corner of step enhances the radial induction effect. Besides, the stepped-wall structure can restrain the moving randomness of the big vortex's core. The axial expansion speed of plasma jet in the ambient fluid is decreased exponentially and the speed estimation formula was obtained in this work.     

Anisotropy of magnetic properties of textured superconductor Bi2Sr2CaCu2O8+δ

The values of the penetration depths and their temperature dependences were measured for differentc-axis orientations of a textured 2.2.1.2. sample. The remanent magnetic flux was studied. The giant mobility of the trapped vortex structure was found above 40 K.     

Inertial mass of the Abrikosov vortex

We show that a large contribution to the inertial mass of the Abrikosov vortex comes from transversal displacements of the crystal lattice. The corresponding part of the mass per unit length of the vortex line is M(l)=(m(2)(e)c(2)/64 pi alpha(2)mu lambda(4)(L))ln((lambda(L)/xi), where m(e) is the bare electron mass, c is the speed of light, alpha=e(2)/Planck's over 2 pi c approximately 1/137 is the fine structure constant, mu is the shear modulus of the solid, lambda(L) is the London penetration length, and xi is the coherence length. In conventional superconductors, this mass can be comparable to or even greater than the vortex core mass computed by Suhl [Phys. Rev. Lett. 14, 226 (1965)]].