Vortex Lattice Melting Transition Research Articles

Molecular Dynamics Simulation on Vortex Lattice Melting in Meso-scopic Superconductors

Vortex lattice melting transitions in meso-scopic superconductors are studied using the molecular dynamics method for vortices. Temperature dependence of vortex dynamics comes from the fluctuation force and penetration dependence in the vortex-vortex interaction. Using the standard deviation of the positions of vortices, we can determine the melting temperature. Changing the vortex numbers, the melting temperature oscillates with increasing the vortex number.

Tilted vortex lattice in irradiate Bi2Sr2CaCu2O8+δ single crystals

In order to enlighten the structure of vortex matter in irradiated layered Bi2Sr2CaCu2O8+δ single crystals, the interaction of Josephson vortices and pancake vortices in was investigated by means of the local ac-magnetic permeability measurements by using the miniature local coils, while vortex matter in pristine crystals was studied by in-plane resistivity measurements. The transition anomaly, separating the strong pinning phase and the weak pinning vortex phase was found by both techniques deep in the vortex solid phase solid near ab-plane, indicating crossover from the vortex chains + lattice phase to tilted vortex chains phase. While the columnar defects affect strongly the first-order vortex-lattice melting transition, the magnetic permeability anomaly, associated with the crossover from vortex chains + lattice phase to tilted lattice, is surprisingly still clear, deep in the vortex solid phase. However, the stronger columnar defects eventually affect the crossover anomaly that it disappears too.

Partially ordered vortex lattices in the high-field low-temperature mixed state of quasi-two-dimensional organic superconductors

We report the results of high-field, low-temperature $\ensuremath{\mu}\mathrm{SR}$ measurements of the quasi-two-dimensional organic superconductors $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$, and $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}[\text{N}{(\mathrm{CN})}_{2}]\mathrm{Br}$. The $\ensuremath{\mu}\mathrm{SR}$ lineshapes for these compounds indicate the existence of partially ordered vortex lattice phases in the high-magnetic-field regime, up to 2.5 T for the former compound and 4 T for the latter compound. The observed sharp loss of order is found to be consistent with a vortex-lattice melting transition that is predicted by numerical simulations of weakly coupled layers of pancake vortices. It is argued that the robustness of the partially ordered vortex lattice phases could be due to strong flux-line pinning by a dilute ensemble of defects.

Oscillatory behavior of vortex-lattice melting transition line in mesoscopic Bi_{2}Sr_{2}CaCu_{2}O_{8+y} superconductors.

The vortex-lattice melting transition of a limited number of vortices confined in mesoscopic square superconductors was studied by c-axis resistance measurements using stacks of intrinsic Josephson junctions in Bi_{2}Sr_{2}CaCu_{2}O_{8+y}. In contrast to the melting transition in bulk crystals, we have first found a clear oscillatory behavior in the field dependence of the melting temperature in small samples of 5-10 μm square. The periods of the oscillations roughly obey the regularity of the matching conditions of square vortex lattices surrounded by a square boundary and the melting temperatures are enhanced around the vortex number of i^{2} (where i is an integer). The results suggest that a confinement effect by the square boundary stabilizes square lattice structures which are realized around i^{2} vortex number even in competition with the favorable Abrikosov triangular lattice in the bulk.

Examination of Doping Change by C-axis Current Injection in Bi2Sr2CaCu2O8+y and the Influence on Vortex States

It has recently been found that a large c-axis current injection into a stack of the intrinsic Josephson junctions (IJJs) of Bi2Sr2CaCu2O8+y makes the doping level change reversibly and controllably [Y. Koval et al., Appl. Phys. Lett. 96, (2010) 082507]. This can be one of promising in-situ methods to control superconducting properties, such as superconducting critical temperature Tc of high-Tc superconductors. We re-examined this doping process with changing the number of IJJs in a stack, and studied the influence on the vortex state, especially vortex lattice melting transition. Increase of the melting transition fields was observed by the current injection doping, suggesting the reduction of the anisotropy γ (=λc/λab). Dependence of the threshold voltage for the current injection doping on the number of IJJs, relaxation of the c-axis resistance in room-temperature undoping process, and the change of the anisotropy were evaluated.

Cyclotron resonance study of quasiparticle mass and scattering rate in the hidden-order and superconducting phases ofURu2Si2

The observation of cyclotron resonance in ultra-clean crystals of URu2Si2 [S. Tonegawa et al., PRL 109, 036401 (2012)] provides another route besides quantum oscillations to the determination of the bulk electronic structure in the hidden order phase. We report detailed analyses of the resonance lines, which fully resolve the cyclotron mass structure of the main Fermi surface sheets. A particular focus is given to the anomalous splitting of the sharpest resonance line near the [110] direction under in-plane magnetic-field rotation, which implies peculiar electronic structure in the hidden order phase. The results under the field rotation from [110] toward [001] direction reveal that the splitting is a robust feature against field tilting from the basal plane. This is in sharp contrast to the reported frequency branch alpha in the quantum oscillation experiments showing a three-fold splitting that disappears by a small field tilt, which can be explained by the magnetic breakdown between the large hole sphere and small electron pockets. Our analysis of the cyclotron resonance profiles reveals that the heavier branch of the split line has a larger scattering rate, providing evidence for the existence of hot-spot regions along the [110] direction. These results are consistent with the broken fourfold rotational symmetry in the hidden-order phase, which can modify the interband scattering in an asymmetric manner. We also extend our measurements down to 0.7 K, which results in the observation of cyclotron resonance in the superconducting state, where novel effects of vortex dynamics may enter. We find that the cyclotron mass undergoes no change in the superconducting state. In contrast, the quasiparticle scattering rate shows a rapid decrease below the vortex-lattice melting transition temperature, which supports the formation of quasiparticle Bloch state in the vortex lattice phase.

Vortex States of Exfoliated Bi2Sr2CaCu2O8+y Thin Films with and without Micro-Hole Array

To investigate vortex states in exfoliated Bi2Sr2CaCu2O8+y high-Tc superconductor with and without micro-hole arrays, the in-plane resistance in the vortex states has been measured. In exploration of vortex-lattice melting transition in pristine films, signs of the transition have been successfully found in the films as thin as a few hundred nm. A comparison of irreversibility lines in both samples indicates that influence of artificial micro holes is masked at low temperatures due to the native residual pinnings.

Vortex lattice melting andHc2in underdoped YBa2Cu3Oy

Vortices in a type-II superconductor form a lattice structure that melts when the thermal displacement of the vortices is an appreciable fraction of the distance between vortices. In an anisotropic high-Tc superconductor, such as YBa2Cu3Oy, the magnetic field value where this melting occurs can be much lower than the mean-field critical field Hc2. We examine this melting transition in YBa2Cu3Oy with oxygen content y from 6.45 to 6.92, and fit the data to a theory of vortex-lattice melting. The quality of the fits indicates that the transition to a resistive state is indeed the vortex lattice melting transition, with the shape of the melting curves being consistent with the known change in penetration depth anisotropy from underdoped to optimally doped YBa2Cu3Oy. From the fits we extract Hc2(T = 0) as a function of hole doping. The unusual doping dependence of Hc2(T =0) points to some form of electronic order competing with superconductivity around 0.12 hole doping.

Estimates for the thermodynamic signatures of vortex-lattice melting in conventional superconductors

The first-order nature of the vortex-lattice melting transition in copper-based layered high-Tc superconductors is well established. The associated discontinuities in magnetization have been extensively studied, for example, in YBa2Cu3O7[1,2] and Bi2Sr2CaCu2O8[3], while the respective latent heats have been systematically investigated only in YBa2Cu3O7 and related compounds [4–13]. The apparent absence of such signatures in conventional superconductors such as Nb raises the question whether or not the concept of vortex-lattice melting is applicable at all in such materials [14]. Based on available literature to describe the vortex-state and using the Lindemann criterion, we estimate quantitatively the order of magnitude for the expected latent heats of melting and the associated discontinuities in magnetization, respectively, as functions of a few known material parameters. It turns out that both thermodynamic quantities are not strictly vanishing even in isotropic materials as long as κ>1/2, but they are small and may often be beyond the available experimental resolution.

Vortices in superconducting nano-networks with anti-dots array

AbstractVortices (magnetic flux quanta) in the superconducting networks perforated with anti-dots (holes) arrays behave as electrons in atomic lattice of crystals. Repulsive and attractive interaction among vortices and anti-dots resemble to those among electrons and atoms in crystals. To confirm the variety of the vortex physics similar to the solid state physics, we have fabricated such superconducting networks with antidots array in metallic, inter-metallic and high-T c superconductors (HTSCs), and have measured magneto-resistance of vortex-flow. In these materials, we have observed integer-matching at the matching fields and fractional-matching effect between them. Most of them are well explained by commensurability between Abrikosov vortex lattice and anti-dots array. Furthermore, the effect of the anti-dots array in HTSCs appears as another kind of phase transitions instead of to the first-order melting transition of vortex lattice in pristine samples.

Vortex states of Bi2Sr2CaCu2O8+y with antidot array probed by c-axis transport measurements

To study the vortex states in Bi2Sr2CaCu2O8+y (Bi2212) high- T c superconductor with periodic array of antidots, we have measured the c -axis critical current in a stack of the intrinsic Josephson junctions with a square lattice of antidots, which gives us information on the c -axis correlation of the pancake vortices. Without the antidot array, the c -axis critical current can probe the first-order vortex lattice melting transition. Additionally, a suppression of the critical current in the vicinity of zero magnetic field is found, which may be related to the instability of vortex lattice under the parallel current flow. With the square lattice of antidots, enhancements of the critical current due to the matching effect are observed in both the integer and fractional matching fields. By mapping the critical current on H - T diagram, the influence of the matching effect on the phase boundary of vortex solid and liquid is shown.

Vortex lattice melting in two-dimensional superconductors in intermediate fields

To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the melting transition in higher fields is significantly weakened with decreasing the field. Nevertheless, a genuine crossover to the consecutive continuous melting picture intervened by a hexatic liquid is not found within the use of the GL model.

Absence of vortex lattice melting in a high-purity Nb superconductor

The state of the vortex lattice extremely close to the superconducting to normal transition in an applied magnetic field is investigated in high purity niobium. We observe that thermal fluctuations of the order parameter broaden the superconducting to normal transition into a crossover but no sign of a first order vortex lattice melting transition is detected in measurements of the heat capacity or the small angle neutron scattering (SANS) intensity. Direct observation of the vortices via SANS always finds a well ordered vortex lattice. The fluctuation broadening is considered in terms of the Lowest Landau Level theory of critical fluctuations and scaling is found to occur over a large H_{c2}(T) range.

Vortex-lattice melting in magnesium diboride in terms of the elastic theory

In the framework of elastic theory, we study the vortex-lattice melting transitions in magnesium diboride for magnetic fields both parallel and perpendicular to the anisotropy axis. Using the parameters from experiments, the vortex-lattice melting lines in the H– T diagram are located systematically by various groups of Lindemann numbers. It is observed that the theoretical result for the vortex melting with parallel and perpendicular fields agrees well with the experimental data. Therefore, it is suggested that the phenomenological elastic theory is universal to various type-II superconductors, including two- and multi-band superconductors.

Tunneling microscope maps the melting transition of a two-dimensional vortex lattice

Tunneling microscope maps the melting transition of a two-dimensional vortex lattice

Elastic theory for the vortex-lattice melting in iron-based high-Tc superconductors

The vortex-lattice melting transitions in two typical iron-based high-Tc superconductors Ba(Fe1−xCox)2As2 (122-type) and Nd(O1−xFx)FeAs (1111-type) for magnetic fields parallel and perpendicular to the anisotropy axis are studied within the elastic theory. Using the parameters from experiments, the vortex-lattice melting lines in the H–T diagram are located systematically by various groups of Lindemann numbers. It is observed that the theoretical results for the vortex melting on both superconductors Ba(Fe1−xCox)2As2 and Nd(O1−xFx)FeAs for parallel fields agree well with the recent experimental data. The future experimental results for the vortex melting can be compared with the present theoretical prediction by tuning reasonable Lindemann numbers.

Vortex lattice melting in the ultraclean heavy-fermion superconductor URu2Si2

The vortex states and the quasiparticle dynamics in the ultraclean heavy-fermion superconductor URu2Si2 (Tc0=1.45 K) are studied by the electronic and thermal transport measurements. We find that a distinct vortex lattice melting transition, which is similar to that in high-Tc cuprates, occurs well below the mean-field upper critical field. The thermal fluctuations are exceptionally enhanced by very low carrier number with heavy mass even at sub-Kelvin temperatures. Additionally, we find a thermal conductivity anomaly below the melting transition, indicating enhancement of the quasiparticle mean free path possibly due to the formation of a novel quasiparticle Bloch state.

Observation of first-order transitions of the vortex lattice in MgB2 single crystals

Measurements of reversible magnetization have been performed on high quality MgB2 single crystals using torque magnetometry combined with the 'vortex shaking' technique. At high temperatures above 26 K, a step like decrease in the magnetization curve is observed at Hm with and without shaking. This anomaly can be ascribed to the first order vortex lattice melting transition. At low temperature below 25 K, where the irreversible magnetization curve reveals the peak effect, we succeed in suppressing the hysteresis completely by shaking and observing the clear step in the reversible magnetization curve at the field H* for the peak effect. The entropy change, estimated from the step of the reversible magnetization at Hm is 2–3 times larger than that at H*.

Angular dependence of vortex matter phase transition in MgB 2 single crystal

The vortex matter phase transitions and intrinsic pinning effect were investigated in an MgB 2 single crystal using the torque magnetometry. For the field directions apart from the ab plane, we succeed in the observation of the vortex lattice melting transitions, which are transformed from the order–disorder transitions at low temperatures. Both transition fields with field directions can be describe by the GL effective mass model. For the field direction along the ab plane, these transitions become unobservable. Instead, the sudden increase in the hysteresis of magnetization curve occurs, indicating the existence of the intrinsic pinning coming from the layer structure.

Vortex lattice melting induced by force-free current inBi2Sr2CaCu2O8+y

To investigate the melting transition of the vortex lattice under a force-free current parallel to the $c$ axis, we have measured the field dependence of $c$-axis resistance, critical current, and $I\text{\ensuremath{-}}V$ characteristics in vortex states of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+y}$ single crystals. The melting transition field ${H}_{m}$ observed in the critical current measurements was almost 20% smaller than ${H}_{m}$ determined by the resistance measurements. Furthermore, it was found that ${H}_{m}$ is reduced as the parallel current increases by measurements of the differential resistance with various bias currents. We have first demonstrated to induce the vortex-lattice melting transition by the force-free current. Although monotonical decrease of ${H}_{m}$ with increasing current is consistent with the theoretical expectations, the whole behavior of the current dependence of ${H}_{m}$ does not obey them.