A direct visualization of the flux distribution in a Pb film covering a five-fold Penrose array of Co dots is obtained by mapping the local field distribution with a scanning Hall probe microscope. We demonstrate that stable vortex configurations can be found for fields H~0.8H_1, H_1 and 1.6H_1, where H_1 corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H_1 corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H_1 the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H=1.6H_1 interstitial and pinned vortices arrange themselves in ring-like structures ("vortex corrals") which favor the formation of a giant vortex state at their center.
The model of the Abrikosov vortex pinning on a cylindrical defect is proposed. It is shown that in the limit $\varkappa \gg 1$ the potential for the vortex core excitations can be treated in terms of the zero-range potentials method. Using the variational method the estimates for the energy of pinning, the pinning force and the density of critical current defect are obtained.
Quasiperiodic pinning arrays, as recently demonstrated theoretically and experimentally using a five-fold Penrose tiling, can lead to a significant enhancement of the critical current Ic as compared to "traditional" regular pinning arrays. However, while regular arrays showed only a sharp peak in Ic(Phi) at the matching flux Phi1 and quasiperiodic arrays provided a much broader maximum at Phi<Phi1, both types of pinning arrays turned out to be inefficient for fluxes larger than Phi1. We demonstrate theoretically and experimentally the enhancement of Ic(Phi) for Phi>Phi1 by using non-Penrose qu…
We numerically show that a vortex pinning occurs in superconducting quasicrystal without impurities and defects. This vortex pinning is intrinsic since the superconducting order parameter in quasicrystal is always inhomogeneous due to the lack of the translational symmetry. We propose that experiments influenced by vortex pinning effects can detect the atomic-scale inhomogeneous superconducting order parameter in quasicrystals. We develop a numerical method to solve the Bogoliubov-de Gennes equations and gap equations in large systems, which is based on the localized-Krylov subspace and a spar…
The influence of random pinning on the vortex dynamics in a periodic square potential under an external drive is investigated. Using theoretical approach and numerical experiments, we found several dynamical phases of vortex motion that are different from the ones for a regular pinning potential. Vortex transfer is controlled by kinks and antikinks, which either preexist in the system or appear spontaneously in pairs and then propagate in groups. When kinks and antikinks collide, they annihilate.
We report on the systematic evolution of vortex pinning behavior in isovalent doped single crystals of BaFe2(As1-xPx)2. Proceeding from optimal doped to ovedoped samples, we find a clear transfor- mation of the magnetization hysteresis from a fishtail behavior to a distinct peak effect followed by a reversible magnetization and Bean Livingston surface barriers. Strong point pinning dominates the vortex behavior at low fields whereas weak collective pinning determines the behavior at higher fields. In addition to doping effects, we show that particle irradiation by energetic protons can tune vo…
We use local and global magnetometry measurements to study the influence of magnetic domain width w on the domain-induced vortex pinning in superconducting/ferromagnetic bilayers, built of a Nb film and a ferromagnetic Co/Pt multilayer with perpendicular magnetic anisotropy, with an insulating layer to eliminate proximity effect. The quasi-periodic domain patterns with different and systematically adjustable width w, as acquired by a special demagnetization procedure, exert tunable vortex pinning on a superconducting layer. The largest enhancement of vortex pinning, by a factor of more than 10…
Within the Ginzburg-Landau theory we consider Abrikosov vortex pinning on a columnar defect with the characteristic size of the cross-section much smaller than the coherence length. We present an extension of the electrostatic analogies method, which proved to be useful for calculations of the pinning force for large cavities, to the case of small defects. The pinning potential for an elliptic cavity is derived analytically. Also, we determine the depinning current for a circular defect.
We performed systematic AC susceptibility and magnetic moment measurements to investigate the vortex dynamics and pinning in the $EuRbFe_4As_4$ single crystal as a function of temperature, frequency, and DC magnetic field. The vortex solid-liquid line was determined and it fits well with $H(T_p)=H_0(1-t_p)^β$ using $β$=1.74-1.91, for $H\parallel ab$. It indicates a rather high pinning strength of the vortex system. The activation energy $U_0$ was determined from thermally activated flux creep theory and reached 6700 K at low fields, suggesting strong vortex pinning. A field dependence of $U_0(…
Phase-Locking of Vortex Lattices Interacting with Periodic Pinning
我们研究Shapiro步骤的涡旋晶格相互作用的周期性钉扎阵列驱动的交流和直流电流。涡流是由间隙涡运动通过周期性势而产生的，周期性势是由被钉扎在钉扎部位的涡产生的。在B_B < B < 2.25B_B的情况下，观察到Shapiro台阶，其中最显著的台阶出现在间隙涡晶格具有高度对称性的情况下。锁相电流阶跃的宽度作为交流驱动的幅度的函数被发现遵循与理论一致的贝塞尔函数。
We have investigated the vortex dynamics in superconducting thin film devices with non-uniform patterns of artificial pinning centers (APCs). The magneto-transport properties of a conformal crystal and a randomly diluted APC pattern are compared with that of a triangular reference lattice. We have found that in both cases the magneto-resistance below the first matching field of the triangular reference lattice is significantly reduced. For the conformal crystal, the magneto-resistance is below the noise floor indicating highly effective vortex pinning over a wide magnetic field range. Further,…
In this report, we comprehensively study the effect of H$^+$ irradiation on the critical current density, $J_c$, and vortex pinning in FeSe single crystal. It is found that the value of $J_c$ for FeSe is enhanced more than twice after 3-MeV H$^+$ irradiation. The scaling analyses of the vortex pinning force based on the Dew-Hughes model reveal that the H$^+$ irradiation successfully introduce point pinning centers into the crystal. We also find that the vortex creep rates are strongly suppressed after irradiation. Detailed analyses of the critical current dependent pinning energy based on the …
The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for th…
Nanowires of two-dimensional (2D) crystals of type-II superconductor NbSe$_2$ prepared by electron-beam lithography were studied, focusing on the effect of the motion of Abrikosov vortices. We present magnetoresistance measurements on these nanowires and show features related to vortex crossing, trapping, and pinning. The vortex crossing rate was found to vary non-monotonically with the applied field, which results in non-monotonic magnetoresistance variations in agreement with theoretical calculations in the London approximation. Above the lower critical field, $H_{c1}$, the crossing rate is …
We identify a scalable, practical route to fabricating a superconducting diode. The device relies for its function on the barrier to flux vortex entry being reduced at the substrate interface of a superconducting pinning enhanced YBa2Cu3O7-d nano-composite film. We show that these composite systems provide a practical route to fabricating a useful superconducting diode and demonstrate the rectification of an alternating current.
We use a magnetic force microscope (MFM) to investigate single vortex pinning and penetration depth in NdFeAsO$_{1-x}$F$_x$, one of the highest-$T_c$ iron-based superconductors. In fields up to 20 Gauss, we observe a disordered vortex arrangement, implying that the pinning forces are stronger than the vortex-vortex interactions. We measure the typical force to depin a single vortex, $F_{\mathrm{depin}} \simeq 4.5$ pN, corresponding to a critical current up to $J_c \simeq 7 \times 10^5$ A/cm$^2$. Furthermore, our MFM measurements allow the first local and absolute determination of the supercond…
The interrelation between heterogeneity and flux pinning is studied in Ba(Fe1-xCox)2As2 single crystals with widely varying Co-content x. Magnetic Bitter decoration of the superconducting vortex ensemble in crystals with x = 0:075 and x = 0:1 reveal highly disordered vortex structures. The width of the Meissner belt observed at the edges of the crystals, and above the surface steps formed by cleaving, as well as the width of the intervortex distance distribution, indicate that the observed vortex ensemble is established at a temperature just below the critical temperature Tc. The vortex intera…
We have studied vortex pinning and dynamics in a Sr0.6K0.4Fe2As2 superconducting tape with critical current density Jc~0.1 MA/cm2 at 4.2 K and 10 T. It is found that grain boundary pinning is dominant in the vortex pinning mechanism. Furthermore, we observe large density of dislocations which can also serve as effective pinning centers. We find that the temperature dependence of critical current density is in agreement with the model of vortices pinned via spatial fluctuation of charge carrier mean free path. Magnetic relaxation measurement indicates that the magnetization depends on time in a…
We report measurements of the field and angular dependences of Jc of truly epitaxial Co-doped BaFe2As2 thin films grown on SrTiO3/(La,Sr)(Al,Ta)O3 with different SrTiO3 template thicknesses. The films show Jc comparable to Jc of single crystals and a maximum pinning force Fp(0.6Tc) > 5 GN/m3 at H/Hirr ~ 0.5 indicative of strong vortex pinning effective up to high fields. Due to the strong correlated c-axis pinning, Jc for field along the c-axis exceeds Jc for H//ab plane, inverting the expectation of the Hc2 anisotropy. HRTEM reveals that the strong vortex pinning is due to a high density of n…
We show that a remarkable variety of dynamical phenomena, including switching, polarization, symmetry locking, and dynamically induced pinning, can occur for vortices in type-II superconductors in the presence of a honeycomb pinning array and an ac or combined ac and dc drive. These effects occur at the second matching field where there are two vortices per pinning site, and arise due to the formation of vortex dimer states in the interstitial regions of the honeycomb array. The orientation of the pinned and moving vortex dimers can be controlled externally by the application of a drive. We te…
We analyze the vortex dynamics in superconducting thin films with a periodic array of pinning centers. In particular, we study the effect of anisotropy for a Kagomé pinning network when longitudinal and transverse transport currents are applied. By solving the equations of motion for the vortex array numerically at zero temperature we find different phases for the vortex dynamics depending on the pinning and driving force. An unusual sequence of peaks along and perpendicular to the main hexagonal lattice axes is observed for the differential resistance reflecting the anisotropy of the transpor…
Strong vortex pinning in FeSe could be useful for technological applications and could provide clues about the coexistence of superconductivity and nematicity. To characterize the pinning of individual, isolated vortices, we simultaneously apply a local magnetic field and image the vortex motion with scanning SQUID susceptibility. We find that the pinning is highly anisotropic: the vortices move easily along directions that are parallel to the orientations of twin domain walls and pin strongly in a perpendicular direction. These results are consistent with a scenario in which the anisotropy ar…
We report herein a high and isotropic critical-current density Jc for BaFe2(As,P)2 epitaxial films. The isotropy of Jc with respect to the magnetic-field direction was improved significantly by decreasing the film growth rate to 2.2 Å/s. The low growth rate served to preferentially align dislocations along the c-axis, which work well as c-axis vortex-pinning centers. Because of the intentional introduction of effective pinning, the absolute Jc at 9 T was larger than that obtained for other iron-based superconductors and conventional alloy superconducting wires.
The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density jc at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to "weak collective pinning" and a magnetic field-independent …
