Session Y38: Superconductivity-Vortex Lattices and Pinning Center Arrays

Vortex-lattices in quasiperiodic pinning potentials

We have investigated vortex-lattice dynamics in superconducting Nb thin films with different types of quasiperiodic arrays of magnetic pinning centers. The mixed-state magnetoresistance show minima for particular applied fields, which reveal matching effects between the vortex-lattice and the quasiperiodic array. These minima are as sharp and well defined as those found with periodic pinning arrays. Moreover, a larger number of minima are observed for quasiperiodic arrays, which in some cases indicate a high ratio of vortices per pinning site. These results suggest that matching between the vortex-lattice and the array of magnetic dots takes place on a very local scale, indicating a short local correlation-length of the vortex-lattice.   

Resistance anomaly in superconducting films containing disordered arrays of holes

Anomalous resistive peaks with values larger than the normal-state resistance has been observed in the resistance versus temperature and magnetic field curves of superconducting nanostructures of Al nanowires, nanoloops and nanodiscs. The excess resistance in these systems is believed to originate at the normal-superconducting ($N-S)$ interface and induced by dynamic phase slip centers or by different critical temperatures ($T$c) in the neighboring parts. Here we report on a new type of resistance anomaly which occurs only at high driving currents in disordered superconducting films. The samples were formed by sputtering niobium onto substrates containing arrays of irregularly distributed nanoscale holes. Resistance peaks appear as a function of temperature or magnetic field in the superconducting transition, with peak values up to 2{\%} above the typical normal-state value. We attribute the observed resistance peak effect to dissipation-induced granularity which enhances contributions from the fluctuation-induced decrease of the quasiparticle density of states. The granularity of the superconducting film arises from inhomogeneous heat-transfer due to the size variation of the Nb sections between the nanoholes.   

Origin of the resistance and critical current oscillations in superconducting films with hole arrays

The resistance and critical current of a superconducting film containing a regular array of microscale or nanoscale holes are found to oscillate with magnetic field. These oscillations are generally interpreted as commensurate pinning. On the other hand, oscillations of the critical temperature of such films with magnetic field due to the Little-Parks effect can also induce oscillations of the resistance and critical current. We present a new method to separate the contributions of commensurate pinning from the Little-Parks effect in superconducting niobium films containing triangular lattices of holes with diameter of tens of nanometers. Remarkably, we find the oscillations of the resistance and critical current with respect to field and temperature to originate purely from the Little-Parks effect. Details on sample preparation, morphological characterization and transport measurements of the critical temperature, the resistance and critical current will be reported.   

Stochastic resonance in a periodic superconducting array

Magnetic fluxon dynamics was studied in superconducting Nb films patterned with a periodic array of holes. A sum of weak harmonic and Gaussian white noise magnetic fields is applied to the sample at $T\ll T_{c}$ and the local magnetic response is measured with a scanning Hall sensor. We find that the fluxon jump rate in the array exhibits locking with the half-period of the harmonic magnetic drive at a certain \textquotedblleft optimal\textquotedblright\ non-zero amplitude of the white noise. Peaks in the resident time distribution and formation of the quasi-periodic flux patterns is observed. We explain our observations with the phenomenon of array enhanced stochastic resonance earlier seen in various driven non-linear systems with dynamic threshold. Implications of our results for the fluxon-based superconducting devices will be discussed.   

Vortex Rectification in Thickness Modulated Films

Rectification effects of Abrikosov vortices have been addressed theoretically in both one-dimensional (1D) and two-dimensional (2D) asymmetric potentials. However, experimentally, vortex ratchets have typically been realized in 2D arrays of asymmetric micropatterned features in superconducting films. Here we report vortex rectification in a smooth, 1D modulation potential fabricated by a novel method. Low- pinning granular Al films were deposited on sinusoidal glass gratings by angle evaporation to achieve an asymmetrical thickness modulation with a period $\sim 2 \mu m$. The varying thickness yields a 1D periodic pinning potential for the vortices, which is confirmed experimentally by observation of matching field effects in magneto-transport measurements. A rectified longitudinal DC voltage is generated when the sample is driven by a zero-biased AC current at $T < T_C$, which implies a unidirectional mean motion of the vortices. Weak frequency dependence up to 10 KHz signifies that the system is in the adiabatic regime. The maximum rectified voltage decreases as the applied field increases, but is detectable far above the first matching field. In some cases, a sign reversal in the DC voltage is observed, implying that the preferred direction for vortex motion can change.   

Interacting particles ratchet effect: Experiments and theoretical simulations.

Ratchet effect occurs when out of equilibrium particles move on asymmetric potentials. The outcome is a net motion without the need of being driven by non-zero average forces or temperatures gradients. This effect spans in Nature for example from molecular motors to particles separation. Most of the theoretical models have dealt with non-interacting particles. From the experimental point of view superconducting vortices are a powerful tool to study ratchet effect on interacting particles. We will present the experimental behavior of vortex lattice motion on asymmetric pinning potentials, when the asymmetric potentials are modified and extensive simulations of a two-dimensional gas of vortices in an asymmetric substrate. We simulate the vortices as Langevin particles interacting by means of a repulsive potential. The defects in the substrate are simulated as potential wells for the Langevin particles. We will analyse the experimental data in comparison with the simulations when the shape and periodicity of the asymmetric potentials are varied.   

Direct experimental visualization of magnetic flux guidance in artificially patterned YBa$_{2}$Cu$_{3}$O$_{7-x}$ thin films.

Development of new `fluxonic' devices, based on controlled motion of magnetic vortices, requires understanding of the principles of magnetic flux distribution and its dynamics in patterned superconductors. We investigated YBa$_{2}$Cu$_{3}$O$_{7-x}$ thin films equipped with various arrangements of antidots (holes of 1 $\mu $m radius) by means of real-time magneto-optical imaging. We demosntrate that 1D antidot arrays facilitate propagation of magnetic flux: each antidot concentrates the flux and tends to pass it on to the next antidot. Some flux from the antidot enters the superconductor creating a characteristic parabolic pattern. At high fields a whole line of antidots represents a cascade of parabolas with the centres in the holes. Flux `channels' and `reservoirs' were created in a superconducting strip by combining antidots of different size. We demonstrate that transfer of magnetic flux between two `reservoirs' lying parallel to the edge of the strip can be realized without applying additional transverse currents. At alternating magnetic field dynamics of the flux can be localized inside the `reservoirs'.   

Induced in-plane order in vortex liquid by regular holes array in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$

To study the influence of artificial hole defects on the vortex matter in high-$T_{c}$ superconductors, we have measured electrical transport properties in the vortex state of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+y}$ single-crystal thin films which have holes configurations with different symmetries. In samples with triangular and square holes arrays, the flow resistance of pancake vortices exhibits dips at multiples of the matching fields, while it is absent in a random hole configuration. Such matching effect occurs even in a vortex liquid phase, suggesting that the periodicity in holes configuration induces in-plane order in liquid flow.   

Niobium superconducting networks and its anisotropy

Novel properties such as an oscillating phase boundary in the magnetic field -- temperature (H-T) diagram have been reported in superconducting films containing a regular hole array where the interhole separation is comparable to the superconducting coherence length -- the superconducting networks. Aluminum is the most common material used in fabricating such superconducting networks due to its large coherence length. However, they require low He$^{3}$ refrigeration temperatures due to aluminum's low critical temperature of about 1 K. Here, we report on the fabrication of Nb superconducting networks with interhole separation down to tens of nanometers and critical temperatures up to 9K. In addition, we present results on angular dependence of the critical temperature and magnetoresistance of the superconducting networks.   

Anisotropic model for plastic flow with pinning: 3D simulations

Switching and macroscopic hysteresis are seen in the driven transport of flux liquids (and in charge density waves). Such effects are ruled out for purely elastic models of flux array transport. Results are presented for a coarse-grained model of flux arrays which generically incorporates both elastic coupling and plastic viscous coupling. This anisotropic model, describing elastic channels interacting in a plastic fashion, has a complex phase diagram with many interesting features that have been found in exact mean-field calculations, including a tricritical point which separates the non-hysteretic region from the region where there is coexistence of stuck and moving states. Our most recent work examines this coarse-grained model in finite dimensions in detail, for distinct models of couplings between the elastic channels. Strong evidence for the existence of a tricritical point has been found. The shape of the phase diagram has a shape significantly different from the mean-field calculations. Results for the critical behavior in finite dimensions will be presented.   

Flux Quantization in Thick Mesoscopic Pb Superconductors .

We present studies of novel vortex behavior on a thick triangular-shaped mesoscopic Pb crystal using ballistic micro-Hall probe magnetometry. The Pb single crystal with dimensions of 2 microns on each edge and 0.7~$\mu $m thick was placed on a 2DEG Hall sensor with a detection area of 1~$\mu $m$^{2}$ and the magnetization was studied as a function of applied magnetic field and temperature. The critical field was found to be H$_{c}$ = 78 mT and T$_{c}$ = 7.20 K, in good agreement with values of clean, bulk Pb. Above T$_{x}$~=~6.6~K, we observe a stable Meissner state for increasing field and a remarkable quantized flux entry behavior with decreasing field. Below T$_{x}$, we observe quantized flux entry (removal) with increasing (decreasing) field. These behaviors indicate that thick mesoscopic Pb superconductors can be tuned with temperature to exhibit type I or type II superconducting behavior.   

SANS Study of Edge-Contaminated Vortex States in a V$_{21at\% }$Ti Superconducting Alloy

In this talk, we report the first direct observation of edge-contaminated vortex matter using small angle neutron scattering (SANS). The vortex structures of Zero Field Cooled and Field Cooled states in a high-$\kappa $ superconducting alloy have been studied using SANS. In this sample FC states are partially ordered as shown by the coexistence of a diffuse scattering ring with two Bragg peaks. ZFC states are disordered at low fields and more disordered than FC states at all fields. For example, the ZFC vortex state at H=6 kOe gives a diffuse ring indicating an amorphous state. Upon further increasing the field, Bragg peaks emerge from the ring, indicating ordering. On increasing temperature from the disordered structure at 6 kOe, the ring gradually transforms into distinct peaks. The experiments were performed at the NIST Center For High Resolution Neutron Scattering (CHRNS).   

AC-Susceptibility and SANS Studies of the Vortex States in V$_{-21at.\% }$Ti

The vortex matter phase diagram of a binary alloy (V$_{-21at.\% }$Ti) has been mapped out using mutual-inductance ac susceptometry, and explored using small angle neutron scattering (SANS). In this sample, a peak effect (PE) appears at high fields, but disappears at low fields. The phase diagram shows a trend remarkably similar to that of a single-crystal \textit{Nb}, despite the vast differences in their respective values of \textbf{$\kappa $} and H$_{c2}$. SANS measurements of the vortex states in this sample shows the survival of quasi-long range order, suggesting the existence of a Bragg glass phase in this system. The SANS experiments were performed at the NIST Center For High Resolution Neutron Scattering (CHRNS).   

Vortex Fractionalization in a Josephson Ladder

We show numerically that in a Josephson ladder with periodic boundary conditions and subject to a suitable transverse magnetic field, a vortex excitation can break up into two or more fractional excitations. If the ladder has N plaquettes, and N is divisible by an integer q, then in an applied field of 1/q flux quanta per plaquette, the ground state is a regular lattice of one fluxon every q plaquettes. When an additional fluxon is added, it spontaneously breaks up into q fractional fluxons, each carrying 1/q units of vorticity. The fractional fluxons are basically walls between different domains of the underlying 1/q lattice. The fractional fluxons are all depinned at the same applied current and move as a unit. For certain applied fields and ladder lengths, we show that there are isolated fractional fluxons. The fractional fluxons produce a time-averaged voltage related in a characteristic way to the ac voltage frequency.