Vortices In High-temperature Superconductors Research Articles

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

Nuclear magnetic resonance studies of vortices in high temperature superconductors

The distinct distribution of local magnetic fields due to superconducting vortices can be detected with nuclear magnetic resonance (NMR) and used to investigate vortices and related physical properties of extreme type II superconductivity. This review summarizes work on high temperature superconductors (HTS) including cuprates and pnictide materials. Recent experimental results are presented which reveal the nature of vortex matter and novel electronic states. For example, the NMR spectrum has been found to provide a sharp indication of the vortex melting transition. In the vortex solid a frequency dependent spin-lattice relaxation has been reported in cuprates, including YBa2Cu3O7−x, Bi2SrCa2Cu2O8+δ, and Tl2Ba2CuO6+δ. These results have initiated a new spectroscopy via Doppler shifted nodal quasiparticles for the investigation of vortices. At very high magnetic fields this approach is a promising method for the study of vortex core excitations. These measurements have been used to quantify an induced spin density wave near the vortex cores in Bi2SrCa2Cu2O8+δ. Although the cuprates have a different superconducting order parameter than the iron arsenide superconductors there are, nonetheless, some striking similarities between them regarding vortex dynamics and frequency dependent relaxation.

Analysis of thermo-magnetic fluctuations above the glass-transition temperature in Bi 1.6Pb 0.5Sr 2− xEu xCa 1.1Cu 2.1O 8+ δ (0.000 ≤ x ≤ 0.180) system

The resistivity of Bi 1.6Pb 0.5Sr 2− x Eu x Ca 1.1Cu 2.1O 8+ δ (0.000 ≤ x ≤ 0.180) superconductor has been measured as a function of temperature and magnetic field. The resistivity shows a glassy behavior even at higher temperatures and magnetic fields for the Eu-doped samples as compared with the Eu free sample. The values of glass-transition temperature [ T g], magnetic field dependent activation energy [ U 0( B)] and the temperature and magnetic field dependent activation energy [ U 0( B, T)] are found to be maximum for optimal doping levels ( x = 0.135) which shows that the flux lines are effectively pinned in this sample. Also for temperatures below the superconducting transition temperature ( T C), a scaling of measured resistivity curves in magnetic field ( B = 0.4 and 0.8 T) is obtained and this scaling is quite useful for better understanding of the behavior of the flux vortices in high temperature superconductors.

Theory of disordered flux-line liquids

We study the equilibrium statics and nonequilibrium driven dynamics of flux-line liquids in the presence of a random pinning potential. Under the assumption of replica symmetry, we find in the static case using a replica Gaussian variational method that the only effect of disorder is to increase the tilt modulus and the confining ``mass'' of the internal modes of the flux lines, thus decreasing their thermal wandering. In the nonequilibrium driven case, we derive the long-scale, coarse-grained equation of motion of the vortices in the presence of disorder, which, apart from new Kardar-Parisi-Zhang nonlinearities, has the same form as the equation of motion for unpinned vortices, with renormalized coefficients. We also compute the structure factor of a disordered vortex liquid, and show that the disorder contributes an additive, Lorentzian squared term, to the structure factor of the center of mass mode, otherwise leaving the functional form of terms describing the internal modes unchanged. The expression of the static structure factor derived within our approach is consistent both with experimental data and with the standard theory of elasticity of vortices in high temperature superconductors.

Pseudogap and Vortices in High-Temperature Superconductors

The origin of the pseudogap is one of the most puzzling features of the high-temperature superconductors. There are two main scenarios: the flrst one assumes the presence of a hidden order competing or coexisting with superconductivity; within the framework of the second one the pseudogap is a precursor of the superconducting gap. In this paper we present some aspects of the hidden order pseudogap scenario. In particular, we discuss how the competing order modifles the structure of vortices in high-temperature superconductors. We demonstrate that the presence of the hidden order can explain some features of vortices observed in scanning tunneling microscopy experiments.

Local enhancement of spin and orbital antiferromagnetism around a single vortex in high-temperature superconductors

In a simple model we investigate three competing orders: d-wave superconductivity, spin and orbital antiferromagnetism (AF) in the vicinity of a single vortex in a cuprate superconductor. We find that when the potential for the orbital AF $V_{d}$ is comparatively small, the spin-density-wave (SDW) order has an enhancement at the vortex core center, and the ''d-density-wave'' (DDW) order exhibits a rather weak behavior around the core and vanishing small away from the core. However, when $V_{d}$ becomes large, globally, the SDW order decreases and the DDW order increases; locally, not only the peak of the SDW order around the core still exists, though relatively suppressed, but also a local peak for the DDW order finally appears. Similar effects are also revealed for the features when varying doping. Comparisons with experiments are discussed.

Singular and Nonsingular Vortex Structures in High-Temperature Superconductors

In this paper we focus on the comparison of the equilibrium and transport properties of singular and nonsingular vortex structures in high-temperature compounds. Using the time-dependent Ginzburg–Landau theory we study the dynamics of vortex structures in superconductors with (d+s)-wave pairing. We calculate the angular dependent correction to the viscosity tensor of a singular flux line, which appears due to the admixture of subdominant s-wave order parameter component in the vortex core. The second order phase transition between singular and nonsingular vortices in high-temperature superconductors was simulated within the time-dependent Ginzburg-Landau equations. The semiclassical analysis of the positions of gap nodes in the vortex core is performed both for singular and nonsingular flux lines.

Singular and nonsingular vortices in high-temperature superconductors

In this paper we focus on the comparison of equilibrium and transport properties of singular and nonsingular vortex structures in high-temperature compounds. Using the time-dependent Ginzburg–Landau (GL) theory we study the dynamics of vortex structures in superconductors with (d+s)-wave pairing. We calculate the angular dependent correction to the viscosity tensor of a singular flux line, which appears due to the admixture of subdominant s-wave order parameter component in the vortex core. The second order phase transition between singular and nonsingular vortices in high-temperature superconductors was simulated within time-dependent GL equations.

Interpretation of Lorentz microscopy observations of vortices in high-temperature superconductors with columnar defects

In order to interpret recent experimental observations of superconducting vortices interacting with tilted columnar defects in high-temperature superconducting materials, we have extended to the case of anisotropic materials our Fourier space approach for the calculation of the electron optical phase shift experienced by the high-energy electrons in a transmission electron microscope. The case of a London vortex having its core not perpendicular to the specimen surfaces is considered. The same configuration is also analyzed in the framework of a simplified pancake model and the influence of the number of stacks on the phase shift and images is investigated. The results obtained by the two models are compared between them and with the experimental results. The agreement between theory and experiment confirms that anisotropy plays a major role in affecting the electron microscopy images.

Charged vortices in high temperature superconductors probed by nuclear magnetic resonance

We report an experimental evidence that a vortex in the high temperature superconductors traps a finite electric charge from the high resolution measurements of the nuclear quadrupole frequencies. In slightly overdoped YBa 2Cu 3O 7 the vortex is negatively charged by trapping electrons, while in underdoped YBa 2Cu 4O 8 it is positively charged by expelling electrons. The sign of the trapped charge is opposite to the sign predicted by the conventional BCS theory. Moreover, in both materials, the deviation of the magnitude of the charge from the theory is also significant.

Strong pinning linear defects formed at the coherent growth transition of pulsed-laser-depositedYBa2Cu3O7−δfilms

Linear defects are important pinning sites for vortices in high-temperature superconductors. In ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films, the linear defects responsible for high critical currents are threading dislocations formed near the substrate interface. Investigating the first stages of growth of pulsed-lased-deposited ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ on single terminated (100) ${\mathrm{SrTiO}}_{3}$ substrates, we study the genesis of these dislocations. We find that the formation of linear defects occurs above a certain critical layer thickness at which a coherent growth transition takes place. Coherent islands are formed, surrounded by highly strained trenches. These trenches facilitate the formation of dislocation half-loops. Such half-loops relieve the misfit strain and form misfit and threading dislocations. The number of threading dislocations thus depends on the island density. This model explains both the short-range lateral order of the threading dislocations and their decreasing density at elevated substrate temperatures.

Oscillating rows of vortices in superconductors.

Superconductors can be used as dissipation-free electrical conductors as long as vortices are pinned. Vortices in high-temperature superconductors, however, behave anomalously, reflecting the anisotropic layered structure, and can move readily, thus preventing their practical use. Specifically, in a magnetic field tilted toward the layer plane, a special vortex arrangement (chain-lattice state) is formed. Real-time observation of vortices using high-resolution Lorentz microscopy revealed that the images of chain vortices begin to disappear at a much lower temperature, Td, than the superconducting transition temperature, Tc. We attribute this image disappearance to the longitudinal oscillation of vortices along the chains.

Charged vortices in high-temperature superconductors probed by NMR

We report experimental evidence that a vortex in high-temperature superconductors (HTSC) traps a finite electric charge from the high-resolution measurements of the nuclear quadrupole frequencies. In slightly overdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ the vortex is negatively charged by trapping electrons, while in underdoped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ it is positively charged by expelling electrons. The sign of the trapped charge is opposite to the sign predicted by the conventional BCS theory. Moreover, in both materials, the deviation of the magnitude of charge from the theory is also significant. These unexpected features can be attributed to the electronic structure of the vortex in HTSC.

High temperature superconductivity in the mixed state and the dynamics of charge carriers

A model to calculate the temperature and magnetic field dependence of the scattering time τ ν( H, T) of quasiparticles by bound electron states in a vortex in high-temperature superconductors is proposed. In this model, the hydrodynamic interaction of a moving gas of quasiparticles with the discrete states of the vortex velocity field is regarded as quasielastic scattering and the resulting scattering time of quasiparticles is different from scattering of individual vortices. The normalized scattering time was found to decrease exponentially with increasing temperature. This behavior is due to the suppression of the amplitude of the superconducting order parameter as the temperature increases. This model accounts for the observed temperature and field dependence of the scattering time particularly at low-field regime.

Force-free configurations of vortices in high-temperature superconductors near the melting transition

We study force-free configurations of Abrikosov flux lines in the line-liquid and line-crystal limit, near the melting transition at ${H}_{m}.$ We show that the condition for zero force configurations can be solved by appealing to the structure of chiral liquid crystalline phases.

Vortices in high temperature superconductors: role of the centrifugal and Lorentz forces

It is shown that the centrifugal force plays the dominant role in dictating the configuration of the electric charges and associated field near the vortex core in type II superconductors in weak magnetic fields.

The role of 2D pancake vortices in high-temperature superconductors

To describe vortices in the high-temperature superconductors, a multilayer model consisting of alternating superconducting and nonsuperconducting layers is useful. Superconductivity within the layers is strong, while that between superconducting layers is weak. The Lawrence-Doniach model provides a helpful starting point, in treating the in-plane superconductivity via the Ginzburg-Landau theory and the out-of-plane superconductivity via the Josephson effect. With the help of this model, one may represent a vortex line threading through the layers as a stack of 2D pancake vortices connected by Josephson strings, whose axes are confined within the nonsuperconducting layers. The magnetic fields and currents generated by a single pancake vortex can be calculated analytically in the limit of extreme anisotropy or vanishing Josephson coupling. Here, we review the results of this calculation and discuss how pancake vortices magnetically interact with each other in the absence of Josephson coupling. In this limit, pancake vortices at zero temperature strongly prefer to align themselves perpendicular to the superconducting layers. We review recent results showing that a tilted stack of 2D pancake vortices in an infinite set of Josephson-decoupled superconducting layers is unstable when the angle of tilt is greater than 52°. We also discuss the behavior of pancake vortices in a finite set of N superconducting layers. The magnetic-field and current-density distributions generated throughout the multilayer structure by a single pancake vortex in an arbitrary layer can be calculated and used to examine the stability of tilted stacks of pancake vortices, where the tilt is maintained by application of transport currents in the top or bottom superconducting layers. At a sufficiently high transport current in the top layer, we find that the pancake vortex array in this layer shears off.

Experimental evidence of a crossover in the vortex dimensionality in high-T c superconductors

Quantum motion of vortices in high-temperature superconductors (HTSCs) was studied via magnetic relaxation measurements performed with a commercial superconducting quantum interference device magnetometer. At a fixed temperature, the field dependence of the time-logarithmic magnetic relaxation rate normalized to the first magnetization value, R=‖d(M/M0)/d ln(t)‖, was investigated in different polycrystalline HTSCs: TlBaCaCuO (2212 and 2223 single phases), YBaCuO (123 phase), and (Hg,Tl)BaCaCuO (1223 phase). The results obtained for TlBaCaCuO 2223 phase and (Hg,Tl)BaCaCuO show a common trend: R increases linearly with magnetic field up to a certain value, the dimensional crossover field H3D-2D, above which it becomes field-independent. H3D-2D is a characteristic field which depends on the anisotropy parameter and the interlayer spacing of the material. The field dependence of R can be ascribed to a crossover in the dimensionality of the object involved in the quantum process: above H3D-2D, the longitudinal dimension of the tunneling object, Lc, is smaller than the interlayer distance, so the object is of two-dimensional (2D) nature (2D pancake vortices). Below H3D-2D, 2D vortices in neighboring layers become coupled, so the tunneling object becomes three-dimensional (3D) in nature (3D flux-lines). The field dependences of R obtained for TlBaCaCuO 2212 phase and YBaCuO show only the 2D and 3D vortex regimes, respectively. Well agreement between theoretical estimates and experimental values for the dimensional crossover field and normalized relaxation rates is achieved.

Charged vortices in high temperature superconductors.

It is argued that in the mixed state of a type II superconductor, because of the difference of the chemical potential in a superconducting versus normal state, the vortex cores may become charged. The extra electron density is estimated. The extra charge contributes to the dynamics of the vortices; in particular, it can explain in certain cases the change of the sign of the Hall coefficient below ${T}_{c}$ frequently observed in the high temperature superconductors.

Vortex pairs in two-dimensional superconductors

We study classical and quantum mechanics of vortex-vortex and vortex-antivortex pairs in two-dimensional superconductors. The possibility of observing quantum states of pancake vortices in high-temperature superconductors is discussed.