Formation of Stripelike Flux Patterns Obtained by Freezing Kinematic Vortices in a Superconducting Pb Film

Abstract

We demonstrate experimentally and theoretically that the dissipative state of superconducting samples with a periodic array of holes at high current densities consists of flux rivers resulting from a short-range attractive interaction between vortices. This dynamically induced vortex-vortex attraction results from the migration of quasiparticles out of the vortex core (kinematic vortices). We have directly visualized the formation of vortex chains by scanning Hall probe microscopy after freezing the dynamic state by a field cooling procedure at a constant bias current. Similar experiments carried out in a sample without holes show no hint of flux river formation. We shed light on this nonequilibrium phenomena modeled by timedependent Ginzburg-Landau simulations. Self-organization and its associated pattern morphologies belong to the most striking phenomena in nature. Usually periodic, such features are often the result of competing interactions. One of the most common structures is stripe patterns, which are found in magnetic, colloidal, or biological systems [1]. In most of them, the longrange (dipolarlike) repulsion is balanced by a short-range attraction, with an origin specific to each system. An interesting analogue can be found in superconductivity. Although this state of matter is magnetophobic, the magnetic field can penetrate (type-II) superconductors in the form of vortices with each bearing a flux quantum È 0 . Since the magnetic energy increases when vortices approach each other [2], their interaction is purely repulsive, and they form a triangular lattice. However, an attractive component in the vortex-vortex interaction may appear even in type-II superconductors. For example, such phenomenon is observed in anisotropic superconductors with a magnetic field tilted away from the principal symmetry axes [3][4][5], or as a result of the nonlocal relationship between supercurrents and vector potential in clean and low-materials [6]. Another example can be found in the case of type-1.5 superconductors where two weakly coupled order parameters, each of which belong to a different type of superconductivity, coexist in the same material [7,8]. In all cases when vortex attraction is present, a vortex chain formation is observed.However, the formation of vortex chains in isotropic type-II superconductors is still energetically unfavorable due to purely repulsive interactions [9]. The only instance where vortex chains are predicted to attract each other in type-II isotropic superconductors is when they are out of equilibrium. Namely, in an applied dc drive, fast moving vortices due to a Lorentz force create an excess of quasiparticles behind themselves generating a wake of depleted order parameter [10,11]. This effect gives rise to the socalled kinematic vortices characterized by a very anisotropic vortex core elongated in the direction of motion [11]. Under these circumstances, vortices attract the following vortices and interconnect into a ''vortex river.'' This directional interaction between kinematic vorti...

Onset, evolution, and magnetic braking of vortex lattice instabilities in nanostructured superconducting films

“…This particular case, with one of the principal axes coinciding with the Lorentz force, has been discussed in Ref. 17. Concerning the symmetry of the individual pinning motifs, by using a triangular symmetry we are able to demonstrate that, as we stated above, the details of the dynamic phases are influenced by the particular geometry of the holes.…”

“…This prediction has been indeed observed in many different superconducting materials, [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] thus demonstrating the universal character of this phenomenon. According to the LO model, the current density J * and the voltage V * at the point where the instability is triggered, are uniquely defined.…”

“…It was shown that the LO instability should be preceded by dynamically driven reorganizations of the vortex lattice which manifest themselves as a series of kinks in the current-voltage characteristics V (I). These reorganization transitions are followed by the development of channels of depleted order parameter populated by kinematic vortices 22 or phase-slip lines 17,23,24 which coexist with slow-moving Abrikosov vortices. The formation of channels of kinematic vortices is associated with a sudden increase of voltage.…”

Controllable morphology of flux avalanches in microstructured superconductors

“…It has been already shown that, due to the periodicity of the lattice of ADs, magnetic flux can be channeled mainly along the [10] and the [01] directions of the lattice [29,30]. This is also true for thermomagnetic avalanches, where finger-like penetration consisting of a main trunk and small branches at 90 • , has been observed in Pb and Nb samples with square arrays of antidots [18,19].…”

The position-dependent vortex dynamics in the asymmetric superconducting ring

“…17,18 The dissipative states of superconducting samples with a periodic array of holes were experimentally measured. 19,20 Special attention has also been paid to the rectification of vortex motion (ratchet effect) induced by asymmetric pinning potentials. [21][22][23][24][25][26] The effect of finite-size and temperature on vortex motion using the timedependent Ginzburg-Landau theory was reported.…”