Critical Currents and Melting Temperature of a Two-Dimensional Vortex Lattice with Periodic Pinning

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 the hexagonal pinning lattice and anisotropic for both pinning arrays. This anisotropy is stronger with temperature for the hexagonal array. For the Kagomé pinning lattice, our analysis shows a multi stage phase melting; that is, as we increase the temperature, each different dynamic phase melts before reaching the melting temperature. Both the melting temperature and critical currents are larger for the hexagonal lattice, indicating the role for the interstitial vortices in decreasing the pinning strength.     

Dynamics of Vortex Lattice Formation in a Rotating Bose-Einstein Condensate with an Optical Lattice Potential

We study dynamics of quantized vortex lattice formation in a rotating Bose-Einstein condensate with a square blue-detuned optical lattice by solving the Gross-Pitaevskii equation. This dynamics depends on the depth of the optical lattice. Vortices tend to form a triangular lattice under the rotation, while an optical lattice likes to pin vortices at their peaks. Such a competition of two effects makes this system more interesting and complicated.     

Incommensurate and Commensurate Density-Wave in the Two-Dimensional Lattice

We have investigated anisotropic density-wave phase with arbitrary ordering wave vector (Q) and estimated the value of Q that corresponds to the minimum of the free energy. We have found that for a wide range of model parameters the commensurate d-density-wave (DDW) is actually the most stable density-wave state. However, for moderate doping the commensurate DDW state is stable only at finite temperatures and disappears when the temperature is sufficiently low. These features may assist in clarification of the mechanism of the pseudogap.     

Spontaneous Vortex Lattices in Quasi 2D Dipolar Spinor Condensates

Motivated by recent experiments (Vengalattore et al. in Phys. Rev. Lett. 100: 170403, 2008; Vengalattore et al., arXiv:0901.3800), we study quasi 2D ferromagnetic condensates with various aspect ratios. We find that in zero magnetic field, dipolar energy generates a local energy minimum with all the spins lie in the 2D plane forming a row of circular spin textures with alternating orientation, corresponding to a packing of vortices of identical vorticity in different spin components. In a large magnetic field, the system can fall into a long lived dynamical state consisting of an array of elliptic and hyperbolic Mermin-Ho spin textures, while the true equilibrium is an uniaxial spin density wave with a single wave-vector along the magnetic field, and a wavelength similar to the characteristic length of the long lived vortex array state.     

Vortex Lattice Structures of a Bose-Einstein Condensate in a Rotating Lattice Potential

We study vortex lattice structures of a trapped Bose-Einstein condensate in a rotating lattice potential by numerically solving the time-dependent Gross-Pitaevskii equation. By rotating the lattice potential, we observe the transition from the Abrikosov vortex lattice to the pinned vortex lattice. We investigate the transition of the vortex lattice structure by changing conditions such as angular velocity, strength, and lattice constant of the rotating lattice potential.     

Vortex Lattice Dynamics in a Dilute Gas BEC

We study the dynamics of large vortex lattices in a dilute gas Bose–Einstein condensate. Rapidly rotating condensates are created that contain vortex lattices with up to 300 vortices. The condensates are held in a parabolic trapping potential, and rotation rates exceeding 99% of the radial trapping frequency are achieved. By locally suppressing the density while maintaining the phase singularities, we create vortex aggregates. To illustrate the underlying Coriolis force driven dynamics, oscillation frequencies of the vortex aggregate area are measured. A related technique also enables us to excite and directly image Tkachenko modes in a vortex lattice. These modes provide evidence for the shear strength that a vortex lattice in a superfluid can support.     

Feedback Spin Exciton Formation in Unconventional Superconductors

The superconducting feedback resonance in inelastic neutron scattering (INS) has now been found in numerous unconventional superconductors of the cuprate, ferropnictide, and heavy fermion classes. The collective spin excitation appears below T _c at an energy less than the quasiparticle threshold with momentum Q provided the gap changes sign under translation by Q. The resonance has been found in the heavy fermion (HF) superconductors CeCu₂Si₂, CeCoIn₅, and UPd₂Al₃, and recently in Fe-pnictide Ba_1−x K _x Fe₂As₂, BaFe_2−x Co _x As₂, BaFe_2−x Ni _x As₂, and FeSe_1−x Te _x compounds and may be a more general phenomenon. Of particular interest is the interaction of the 3d spin exciton with the 4f crystalline electric field (CEF) excitations in rare earth based unconventional superconductors like CeFeAsO_1−x F _x pnictide and Nd_2−x Ce _x CuO₄ cuprate where a coupling between 3d spin resonance and 4f CEF excitations leads to intriguing interaction effects observed experimentally by INS.     

High-Field and Multi-Frequency ESR in the Quasi Two-Dimensional Triangular-Lattice Antiferromagnet CuCrO2

We have performed high-field and multi-frequency electron spin resonance (ESR) and magnetization measurements in magnetic fields up to about 53 T on single crystals of a delafossite triangular-lattice antiferromagnet CuCrO₂, which has been proposed to show an out-of-plane 120° spiral spin structure below about 24 K. We calculated ESR resonance modes and magnetization curves assuming an Ising-like Heisenberg Hamiltonian with a spiral spin structure by a mean-field theory. The experimental results can be well reproduced using the following parameters, the intralayer exchange constant J/k _B=26.9 K, the easy-axis anisotropy D/k _B=?0.47 K, and the in-plane g-factor g _ab =2.0.     

D-Wave Superconductivity and Coulomb Correlations in the Two-Dimensional Hubbard Lattice

We considered anisotropic superconductivity within the two-dimensional Hubbard model extended by pairing correlations originating from the electron–phonon interaction. To discuss the onset of superconductivity close to the insulator–metal transition, we used the Hubbard I approximation to account for the formation of the insulating gap and see the role of Coulomb correlations for superconducting pairing. It has been shown that the Hubbard I approximation reflects effective pairing interactions genuine for correlated electron systems and leads to the stabilization of the superconductivity in the d-wave channel. One may expect the cooperation of phonon-free and phonon-induced mechanism in the formation of thed-wave superconducting state.     

NMR Lineshape in Anisotropic Superconductors with Nonregular Vortex Lattice

The nuclear magnetic resonance line shapes within a primitive cell of the vortex lattice of the type II anisotropic superconductors in a case when a vortex is displaced on small distance a from a regular position in a primitive cell are constructed. The results of the numerical calculations show that displacement of the flux line lattice essentially changes the NMR lineshape. The derivative of the power of the absorption energy with respect to the magnetic field is calculated. It allows to obtain more detailed information about the real vortex lattice of a superconductor.     

Depinning of Two-Dimensional Vortex System with Square Pinning Array at the Second Matching Field

Depinning of a two-dimensional vortex system at the second matching field B=2B _? in the presence of square pinning array was studied by molecular dynamics simulations. The annealed ground structures and depinning properties are found to be dependent on pinning strength. For strong pinning, we find a two-step depinning transition with a lower depinning force F _c1 and a higher one F _c2. At F _c1 only the interstitial vortices start to move, while at F _c2 the vortices at pinning sites are depinned and all vortices move.     

Exciton Self–Trapping and Lattice Defect Creation in Rare Gas Solids and Other Insulators

We have studied the possible creation of stable lattice defects induced by exciton self–trapping (STE) in solid neon. Generally speaking, the STE–bubbles accompanied with a plastic deformation are found to be at lower energies than a pure STE–bubble. Those with two vacancies in the first atomic shell have the lowest energy. Some of the vacancy–interstitial atom pairs escaped mutual annihilation as the electronic sub–system returned to the ground state, thereby stable lattice defects resulted. The emission energy changes of lattice defect–associated STE have been evaluated and are found to be in reasonable agreement with observed data. Much has been learned recently on the role of the STE in radiation damage creation of ionic halides. We have made a brief comparison of the ionization induced defect formation processes in the two types of materials. In both cases, the excited electron is the prime driver of the process. In solid neon the excited electron is directly attracted to the localized hole on Ne, but repelled by the ground state Ne atoms. In the halides the excited electron is attracted to the Madelung potential at an anion site instead. In rare gas solids, the Frenkel pair is a purely structural defect in the lattice with the electronic subsystem in its ground state. In ionic halides, the pair of F center and H center is not only an interstitial atom–vacancy pair in the halogen sublattice, but also represents an electronically excited state. Because of this difference the way the created Frenkel defects are stabilized in the two types of material is distinct.     

Oblique Vortex Lattice Implies Unconventional Pairing Symmetry in High Temperature Superconductors

The symmetry of order parameters of YBa₂Cu₃O_{7 –} high temperature superconductor was studied with the Ginzburg–Landau theory. The vortex lattice of a YBa₂Cu₃O₇ superconductor is oblique at a temperature well below the transition temperature T _c, where the mixed s– state is expected to have the lowest energy, whereas very close to T _c, the -wave is slightly lower in energy, and a triangular vortex lattice recovers. The coexistence and the coupling between the s- and d-waves would account for the unusual behaviors such as the upward curvature of the upper critical field curve H _C2(T).     

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?Cvortex and the vortex?Cnanodot 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.     

Dynamics of the Cluster of Vortex Points in Two-Dimensional Superfluid 4He

We have simulated the dynamics of cluster of quantized vortex points with the same circulation in two-dimensional superfluid ⁴He. In two-dimensional quantum turbulence, vortices are always distributed uniformly, but often form some clusters. We study the dynamics of a cluster at zero temperature and finite temperatures. At zero temperature the cluster rotates. The radius and the density of the cluster hardly change because of the conservation of the energy and the angular momentum. On the other hand, at finite temperatures, the cluster rotates with forming a lattice structure and expanding because of the mutual friction.     

Vortex Formation in Neutron-Irradiated Rotating Superfluid 3He-B

A convenient method to create vortices in meta-stable vortex-free superflow of ³He-B is to irradiate with thermal neutrons. The vortices are then formed in a rapid non-equilibrium process with distinctive characteristics. Two competing explanations have been worked out about this process. One is the Kibble-Zurek mechanism of defect formation in a quench-cooled second order phase transition. The second builds on the instability of the moving front between superfluid and normal ³He, which is created by the heating from the neutron absorption event. The most detailed measurements with single-vortex resolution have been performed at temperatures close to T_c. In the first half of this report we summarize the two models and then show that the experimentally observed vortices originate from the Kibble-Zurek mechanism. In the second half we present new results from low temperatures. They also weakly support the Kibble-Zurek origin, but in addition display superfluid turbulence as a new phenomenon. Below 0.6 T_c the damping of vortex motion from the normal component is reduced sufficiently so that turbulent vortex dynamics become possible. Here a single absorbed neutron may transfer the sample from the meta-stable vertex-free to the equilibrium vortex state. The probability of a neutron to initiate a turbulent transition grows with increasing superflow velocity and decreasing temperature. PACS numbers: 47.32, 67.40, 67.57, 98.80.     

Vortex Nucleation and Array Formation in a Rotating Bose-Einstein Condensate

We study the dynamics of vortex lattice formation of a rotating trapped Bose-Einstein condensate by numerically solving the two-dimensional Gross-Pitaevskii equation, and find that the condensate undergoes elliptic deformation, followed by unstable surface-mode excitations before forming a quantized vortex lattice. The dependence of the number of vortices on the rotation frequency is obtained.     

Plastic and Elastic Symmetry Transformations Induced in the Vortex Lattice of Anisotropic and Layered Superconductors

We make a comparative analysis of the response of the three-dimensional vortex lattice in Bi₂Sr₂CaCu₂O₈ and NbSe₂ to the presence of square arrays of pinning sites localized at one extremity of the vortex crystals. The absence of the hexagonal to square symmetry transformation and the induction of a distorted hexagonal symmetry in the vortex lattice of NbSe₂ contrast to the observed symmetry change in Bi₂Sr₂CaCu₂O₈. The dissimilar response in both cases is explained taking into account the vortex structure solidification mechanisms in both materials: The plastic response in the case of the layered material Bi₂Sr₂CaCu₂O₈ is suggested to be a result of the simultaneity of solidification and coupling of bidimensional pancake vortices whereas a viscous solidification is the responsible for the three-dimensional elastic response in NbSe₂.     

Finite-temperature Effect in Phase Transition to Superfluidity for Bose–Einstein Condensates in a 1-D Optical Lattice

We experimentally study the phase transition of ⁸⁷Rb Bose–Einstein condensates adiabatically loaded to a combined trap of a 1D optical lattice and a magnetic trap. The phase coherence property of this system is probed by recording the interference pattern of the expanded atomic cloud suddenly released from the combined trap. We show that as the temperature is sufficiently low (below the critical temperature T _C ), an interference pattern has a “peak on a peak” feature which is a true signature of macroscopic superfluid states. The normal gas only contributes to the broad background and three wide peaks in an interference pattern. These observations qualitatively agree with the recent theoretical predictions (Diener et al. in Phys. Rev. Lett. 98:180404, 2007; Kato et al. in Nat. Phys. 4:617, 2008). We also computed both the critical temperature and the interference pattern for a practical combined trap as ours in the tight-binding limit, and the numerical results are consistent with our experimental observations.