Vortex Lattice Configurations Research Articles

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit (SO)- and coherently-coupled spin-1 Bose–Einstein condensates (BECs) trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, SO and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, we illustrate that a boson in these rotating SO- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials under specific coupling and rotation strengths. In the presence of mean-field interactions, using the coupled Gross–Pitaevskii formalism at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. On rapid rotation, we further find that the spin-expectation per particle of an antiferromagnetic spin-1 BEC approaches unity indicating a similarity in the response with ferromagnetic SO-coupled condensates.

Rotational transition, domain formation, dislocations, and defects in vortex systems with combined sixfold and twelvefold anisotropic interactions

We introduce a new model for a pairwise repulsive interaction potential of vortices in a type-II superconductor, consisting of superimposed six- and 12-fold anisotropies. Using numerical simulations we study how the vortex lattice configuration varies as the magnitudes of the two anisotropic interaction terms change. A triangular lattice appears for all values, and rotates through 30 degrees as the ratio of the six- and 12-fold anisotropy amplitudes is varied. The transition causes the VL to split into domains that have rotated clockwise or counter-clockwise, with domain boundaries that are "decorated" by dislocations consisting of five- and seven-fold coordinated vortices. We also find intra-domain dislocations and defects, and characterize them in terms of their energy cost. We discuss how this model could be generalized to other particle-based systems with anisotropic interactions, such as colloids, and consider the limit of very large anisotropy where it is possible to create cluster crystal states.

Broken time-reversal symmetry in the topological superconductor UPt3

The topological superconductor UPt3, has three distinct vortex phases, a strong indication of its unconventional character. Using small-angle neutron scattering we have probed the vortex lattice in the UPt3 B phase with the magnetic field along the crystal c-axis. We find a difference in the vortex lattice configuration depending on the sign of the magnetic field relative to the field direction established upon entering the B phase at low temperature in a field sweep, showing that the vortices in this material posses an internal degree of freedom. This observation is facilitated by the discovery of a field driven non-monotonic vortex lattice rotation, driven by competing effects of the superconducting gap distortion and the vortex-core structure. From our bulk measurements we infer that the superconducting order parameter in the UPt3 B phase breaks time reversal symmetry and exhibits chiral symmetry with respect to the c-axis.

Upper Frequency Limits for Vortex Guiding and Ratchet Effects

The guided and rectified motion of magnetic flux quanta are important effects governing the magnetoresistive response of nanostructured superconductors. While at low ac frequencies these effects are rather well understood, their manifestations at higher ac frequencies remain poorly investigated. Here, we explore the upper frequency limits for guided and rectified net motion of superconducting vortices in epitaxial $\mathrm{Nb}$ films decorated with ferromagnetic nanostripes. By combining broadband electrical spectroscopy with resistance measurements, we reveal that the rectified voltage vanishes at a geometrically defined frequency of about 700 MHz. By contrast, a vortex-guiding-related low-ac-loss response persists up to about 2 GHz. This value corresponds to the depinning frequency ${f}_{d}^{s}$ associated with the washboard pinning potential induced by the nanostripes, which exhibits peaks for commensurate vortex-lattice configurations. By applying a sum of dc and microwave ac currents at an angle $\ensuremath{\alpha}$ with respect to the nanostripes, the angle dependence of ${f}_{d}^{s}(\ensuremath{\alpha})$ is found to be correlated with the angle dependence of the depinning current. In all, our findings suggest that superconductors with higher ${f}_{d}^{s}$ should be favorable for efficient vortex manipulation in the gigahertz ac frequency range.

Exotic Vortex Lattices in Binary Repulsive Superfluids.

We investigate a mixture of two repulsively interacting superfluids with different constituent particle masses: m_{1}≠m_{2}. Solutions to the Gross-Pitaevskii equation for homogeneous infinite vortex lattices predict the existence of rich vortex lattice configurations, a number of which correspond to Platonic and Archimedean planar tilings. Some notable geometries include the snub-square, honeycomb, kagome, and herringbone lattice configurations. We present a full phase diagram for the case m_{2}/m_{1}=2 and list a number of geometries that are found for higher integer mass ratios.

Improvements of high-field pinning properties of polycrystalline Fe(Se,Te) material by heat treatments

We present the fabrication of FeSe0.5Te0.5 polycrystalline samples by self-flux method, showing the presence of the peak-effect in the vortex lattice configuration. To improve the performances at high magnetic fields for this iron-based superconductor of the 11-family, the two-step solid-state reaction process has been successfully modified by increasing the temperature of the heat treatment and by slowing down the cooling rate. The magnetic field-temperature phase diagram has been investigated by magneto-resistance, magnetization, and heat capacity measurements in applied magnetic fields up to 18 T. The magnetization curves exhibit an enhancement of the peak-effect whose position shifts by varying the temperature, following a similar dependence than that previously reported in high-temperature superconducting materials such as YBa2Cu3O7-δ. The presence of the peak-effect can be correlated to the sample manufacture, since by tuning a proper heat treatment it becomes observable ever more in the magnetic field-temperature phase diagram. This fabrication route paves the way to a systematic increase in the critical current density thus becoming relevant for applications.

Anomalous reduction in the long-time flux creep relaxation in superconducting Ca10(Pt4As8)((Fe1−xPtx)2As2)5 (x ≈ 0.05) single crystals

We report the vortex dynamics of superconducting a Ca10(Pt4As8)((Fe1−xPtx)2As2)5 (x ≈ 0.05) single crystal with Tc = 26 K investigated by performing magnetic measurements. The field dependence of the magnetization displays a second peak (SPM), typically related to a crossover between elastic and plastic vortex relaxation in a weak pinning scenario. Long-time flux creep relaxation measurements for fields smaller that of the SPM show that the vortex dynamics can be separated in two different regions. For magnetic fields smaller than the lower end of the SPM, glassy relaxation (with a characteristic glassy exponent μ) is observed. For magnetic fields between the lower end and the SPM, the flux creep rate decreases systematically to values below to the ones predicted by the collective theory. This effect can be understood by considering a stable vortex lattice configuration. As the field position of the SPM can be adjusted by modifying the quenched potential, our results suggest that extremely low flux creep relaxation rate may be tuned in many other superconducting materials.

Metastability and hysteretic vortex pinning near the order-disorder transition in NbSe2 : Interplay between plastic and elastic energy barriers

We studied thermal and dynamic history effects in the vortex lattice (VL) near the order-disorder transition in clean NbSe$_2$ single crystals. Comparing the evolution of the effective vortex pinning and the bulk VL structure, we observed metastable superheated and supercooled VL configurations that coexist with a hysteretic effective pinning response due to thermal cycling of the system. A novel scenario, governed by the interplay between (lower) elastic and (higher) plastic energy barriers, is proposed as an explanation for our observations: Plastic barriers, which prevent the annihilation or creation of topological defects, require dynamic assistance to be overcome and to achieve a stable VL at each temperature. Conversely, thermal hysteresis in the pining response is ascribed to low energy barriers, which inhibit rearrangement within a single VL correlation volume and are easily overcome as the relative strength of competing interactions changes with temperature.

Dynamic Reorganization of Vortex Matter into Partially Disordered Lattices.

We report structural evidence of dynamic reorganization in vortex matter in clean NbSe(2) by joint small-angle neutron scattering and ac susceptibility measurements. The application of oscillatory forces in a transitional region near the order-disorder transition results in robust bulk vortex lattice configurations with an intermediate degree of disorder. These dynamically originated configurations correlate with intermediate pinning responses previously observed, resolving a long-standing debate regarding the origin of such responses.

In-plane gradient-magnetic-field-induced vortex lattices in spin-orbit-coupled Bose-Einstein condensations

We consider the ground-state properties of the two-component spin-orbit coupled ultracold bosons subject to a rotationally symmetric in-plane gradient magnetic field. In the non-interacting case, the ground state supports giant-vortices carrying large angular momenta without rotating the trap. The vorticity is highly tunable by varying the amplitudes and orientations of the magnetic field. Interactions drive the system from a giant-vortex state to various configurations of vortex lattice states along a ring. Vortices exhibit ellipse-shaped envelops with the major and minor axes determined by the spin-orbit coupling and healing lengths, respectively. Phase diagrams of vortex lattice configurations are constructed and their stabilities are analyzed.

Order-by-disorder degeneracy lifting of interacting bosons on the dice lattice

Motivated by recent experimental progress in the realization of synthetic gauge fields in systems of ultracold atoms, we consider interacting bosons on the dice lattice with half flux per plaquette. All bands of the non-interacting spectrum of this system were previously found to have the remarkable property of being completely dispersionless. We show that degeneracies remain when interactions are treated at the level of mean field theory, and the ground state exhibits vortex lattice configurations already established in the simpler XY model in the same geometry. We argue that including quantum and thermal fluctuations will select a unique vortex lattice up to overall symmetries based on the order-by-disorder mechanism. We verify the stability of the selected state by analyzing the condensate depletion. The latter is shown to exhibit an unusual non-monotonic behavior as a function of the interaction parameters which can be understood as a consequence of the dispersionless nature of the non-interacting spectrum. Finally, we comment on the role of domain walls which have interactions mediated through fluctuations.

Rotation of Triangular Vortex Lattice in the Two-Band Superconductor MgB2

To identify the contributions of the multiband nature and the anisotropy of a microscopic electronic structure to a macroscopic vortex lattice morphology, we develop a method based on the Eilenberger theory near \(H_{\text{c2}}\) combined with the first-principles band calculation to estimate the stable vortex lattice configuration. For a typical two-band superconductor MgB2, successive transitions of vortex lattice orientation that have been observed recently by small angle neutron scattering [Das et al.: Phys. Rev. Lett. 108 (2012) 167001] are explained by the characteristic field-dependence of two-band superconductivity and the competition of sixfold anisotropy between the σ- and π-bands. The reentrant transition at low temperature reflects the Fermi velocity anisotropy of the σ-band.

Superconducting Vortex Lattice Configurations on Periodic Potentials: Simulation and Experiment

Nb films have been fabricated on top of array of Ni nanodots. The array of periodic pinning potentials modifies the vortex lattice for specific values of the external applied magnetic field. By means of an implemented code developed from scratch, computer simulations based only on the vortex–vortex and the vortex–nanodot interactions provide the total interaction between vortices and pinning sites as well as the position of the vortices in the array unit cell. This simulation approach could be performed on square, rectangular or triangular arrays of nanodefects of different size.

Vortex Lattice Studies inCeCoIn5withH⊥c

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn5 with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H || [100], a single VL orientation is observed, while a 90 degree reorientation transition is found for H || [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Gamma = 2.0 +/- 0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H || [001]. At high fields, above which the upper critical field (Hc2) becomes a first-order transition, an increased disordering of the VL is observed.

Vortex structures of rotating spin-orbit-coupled Bose-Einstein condensates

We consider the quasi-2D two-component Bose-Einstein condensates with Rashba spin-orbit (SO) coupling in a rotating trap. An external Zeeman term favoring spin polarization along the radial direction is also considered, which has the same form as the non-canonical part of the mechanical angular momentum. The rotating condensate exhibits rich structures as varying the strengths of trapping potential and interaction. With a strong trapping potential, the condensate exhibits a half-quantum vortex-lattice configuration. Such a configuration is driven to the normal one by introducing the external radial Zeeman field. In the case of a weak trap potential, the condensate exhibits a multi-domain pattern of plane-wave states under the external radial Zeeman field.

Vortex ratchet reversal: Role of interstitial vortices

Triangular arrays of Ni nanotriangles embedded in superconducting Nb films exhibit unexpected dynamical vortex effects. Collective pinning with a vortex lattice configuration different from the expected fundamental triangular "Abrikosov state" is found. The vortex motion which prevails against the triangular periodic potential is produced by channelling effects between triangles. Interstitial vortices coexisting with pinned vortices in this asymmetric potential, lead to ratchet reversal, i.e. a DC output voltage which changes sign with the amplitude of an applied alternating drive current. In this landscape, ratchet reversal is always observed at all magnetic fields (all numbers of vortices) and at different temperatures. The ratchet reversal is unambiguously connected to the presence of two locations for the vortices: interstitial and above the artificial pinning sites.

Enhancement of synchronized vortex lattice motion in hybrid magnetic/amorphous superconducting nanostructures

Superconducting a-Mo3Si and Nb films have been grown on arrays of Ni nanodots. We have studied the vortex lattice dynamics close to critical temperatures. Different vortex lattice configurations are obtained with the same array unit cell. These different vortex lattices occur at matching conditions between the vortex lattice and the array unit cell. The interplay between the random intrinsic pinning of the superconducting films and the periodic pinning of the array govern the vortex lattice configurations. Different vortex lattice configurations and enhancement of synchronized vortex lattice motion are obtained by increasing the periodic pinning strength and decreasing the random pinning strength.

Ordered, Disordered, and Coexistent Stable Vortex Lattices inNbSe2Single Crystals

The peak effect (PE) in the critical current density of type II superconductors has been related to an order-disorder transition in the vortex lattice (VL), but its underlying physics remains a controversial issue. Intrinsic to the PE are strong metastabilities that frequently mask the stationary VL configurations. We follow shaking and thermal protocols in NbSe2 single crystals to access these configurations and examine them by linear ac susceptibility measurements that avoid VL reorganization. We identify three different regions. For T<T1(H), stable VL configurations are maximally ordered. For T>T2(H), configurations are fully disordered and no metastability is observed. In the T1<T<T2 region, we find temperature-dependent stable configurations with an intermediate degree of disorder, possibly associated with the coexistence of ordered and disordered lattices throughout the PE.

Anomalous pinning behavior in [formula omitted

In order to investigate the chiral-superconducting characteristics as well as the vortex-pinning properties, detailed magnetization measurements of the single crystal Sr 2 RuO 4 have been performed in the field parallel to the [0 0 1] direction. Anomalous pinning features are found at weak fields in the magnetization curves: Tiny flux-jumps successively appear around zero field at temperatures up to at least 0.2 K. At higher temperatures, a small peak of the hysteretic magnetization is observed below 0.1 kOe, which is so-called second magnetization peak (SMP). The magnitude of the hysteretic magnetization is strongly dependent on (independent of) the field-gradient in the field region below (above) the field where the SMP appears. Possible origins are discussed from the viewpoints of the pairing symmetry together with the topological change in the vortex-lattice configuration.

Direct observation of vortex lattice transitions in mesoscopic superconducting single crystals using STM

Superconductors containing mesoscopic artificially-engineered defects are orders of magnitude more resistant to the destructive effect of the magnetic field. We present scanning tunnelling microscopy study of the vortex lattice configurations in a mesoscopic single crystal superconductor—normal metal heterostructure. We observe co-existence of a strongly interacting multiquanta vortex lattice and interstitial Abrikosov vortices that form a composite magnetic flux distribution which undergoes a series of transitions between different topological configuration states. The vortex configuration states are strongly dependent on the nanoscale architecture of the superconductor and applied magnetic field. Scanning tunnelling spectroscopy images show the evolution of vortex topological states when the number of flux quanta in the system changes.