Langevin dynamics simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced point defects as a smoothened distribution of a random potential. Both the electromagnetic and Josephson interactions among pancake vortices were included. A special shaking and annealing process was introduced to let the system approach the equilibrium configuration. We are able to see the inverse melting transition from the Bragg-glass to the amorphous vortex glass state, in agreement with recent experiments.
We study the oxygen doping dependence of the equilibrium first-order melting and second-order glass transitions of vortices in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. Doping affects both anisotropy and disorder. Anisotropy scaling is shown to collapse the melting lines only where thermal fluctuations are dominant. Yet, in the region where disorder breaks that scaling, the glass lines are still collapsed. A quantitative fit to melting and replica symmetry breaking lines of a 2D Ginzburg-Landau model further reveals that disorder amplitude weakens with doping, but to a lesser degree than thermal fluctuat…
The behavior of vortex matter in $\mathrm{Bi_{2}Sr_{2}CaCu_{2}O_{8}}$ in the presence of a low concentration of tilted columnar defects (CDs) was studied using magneto-optical measurements and molecular dynamics simulations. We find that while the dynamic properties are significantly affected by tilting the field away from CDs, the thermodynamic lines are angle independent. Our simulations reveal that vortex pancakes remain localized along CDs even at large tilting angles thus preserving the thermodynamic features, while suppression of irreversible properties is caused by vortex kink sliding.
The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local \emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking'. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid …
Precision measurements of the vortex phase diagram in single crystals of the layered superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ in oblique magnetic fields confirm the existence of a second phase transition, in addition to the usual first order vortex lattice melting line $H_{m}(T)$. The transition has a strong first order character, is accompanied by strong hysteresis, and intersects the melting line in a tricritical point ($H_{m}^{\perp}$, $H^{\parallel}_{cr}$). Its field dependence and the changing character of the melting line at the tricritical point strongly suggest that the groun…
Self-field imaging of current distribution in Ba0.6K0.4Fe2As2 superconductor is used to study the effect of drive on the low-field vortex solid to liquid melting phase transformation. At low fields, the current induced drive on the vortices aids in thermally destabilizing the vortex state thereby shifting the low field melting phase boundary. We show that the current induced drive shifts solid-liquid boundaries and prepones the vortex melting phenomenon compared to the equilibrium situation. The analysis shows that for currents above 50 mA, Joule heating effects shift the melting line while be…
Vortex matter phases and phase transitions are investigated by means of Josephson plasma resonance in under-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals in a microwave frequency range between 19 and 70 GHz. Accompanied by the vortex lattice melting transition, a jump of the interlayer phase coherence extracted from the field dependence of the plasma frequency was observed. In the solid phase, the interlayer coherence little depends on field at a temperature region well below $T_c$ while it gradually decreases as field increases toward the melting line up to just below $T_c$. As a result…
A low concentration of columnar defects is reported to transform a first-order vortex lattice melting line in BSCCO crystals into alternating segments of first-order and second-order transitions separated by two critical points. As the density of CDs is increased, the critical points shift apart and the range of the intermediate second-order transition expands. A third, low temperature critical point was also observed in one sample. The measurement of equilibrium magnetization and the mapping of the melting line down to 27K was made possible by employment of the shaking technique.
Measurements of non-local in-plane resistance originating from transverse vortex-vortex correlations have been performed on a Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} high-T_c superconductor in a magnetic field up to 9 T applied along the crystal c-axis. Our results demonstrate that a rigid vortex lattice does exist over a broad portion of the magnetic field -- temperature (H-T) phase diagram, well above the first-order transition boundary H_{FOT}(T). The results also provide evidence for the vortex lattice melting and vortex liquid decoupling phase transitions, occurring above the H_{FOT}(T).
We study the distribution of transport current across superconducting Bi$_2$Sr$_2$CaCu$_2$O$_8$ crystals and the vortex flow through the sample edges. We show that the $T_x$ transition is of electrodynamic rather than thermodynamic nature, below which vortex dynamics is governed by the edge inductance instead of the resistance. This allows measurement of the resistance down to two orders of magnitude below the transport noise. By irradiating the current contacts the resistive step at vortex melting is shown to be due to loss of c-axis correlations rather than breakdown of quasi-long-range orde…
Multilevel Monte Carlo simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced low concentration of columnar defects satisfying $B_ϕ\le B$. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in ag…
Magneto-optical observations of a second flux front, which occurs at the second peak in the magnetization of Bi_2 Sr_2 CaCu_2 O_x single crystals related to the known first order ``vortex-lattice melting'', are reconsidered. We show that, in thin samples, electrodynamics necessarily leads to an extended region in which the magnetic induction adopts a nearly constant value close to that at which the phase transition occurs at thermal equilibrium. In this region a dynamical phase mixture of vortex ``solid'' and ``liquid'' should exist. Interestingly, the observed second flux front does not mark …
Vortex matter phase transitions in the high-temperature superconductor Bi2Sr2CaCu2O8 were studied using local magnetization measurements combined with a vortex 'shaking' technique. The measurements revealed thermodynamic evidence of a first-order transition along the second magnetization peak line, at temperatures below the apparent critical point Tcp. We found that the first-order transition line does not terminate at Tcp, but continues down to at least 30 K. This observation suggests that the ordered vortex lattice phase is destroyed through a unified first-order transition that changes its …
We measured the effects of periodic surface holes, created using a focused ion beam, on the phase diagram of the vortex matter in high-T_c Bi_2Sr_2CaCu_2O_{8+δ} crystals. Differential magneto-optical measurements show that the irreversibility line is shifted to higher fields and temperatures, with respect to the pristine melting line. The irreversibility line displays weak field dependence between integer matching fields indicating multiple-flux-quanta pinning at holes. We find reduced equilibrium compressibility of the vortex matter at integer matching fields, which is strong evidence for the…
In this paper we describe a version of London Langevin molecular dynamics simulations that allows for investigations of the vortex lattice melting transition in the highly anisotropic high-temperature superconductor material Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. We include the full electromagnetic interaction as well as the Josephson interaction among pancake vortices. We also implement periodic boundary conditions in all directions, including the z-axis along which the magnetic field is applied. We show how to implement flux cutting and reconnection as an analog to permutations in the multilevel Mon…
The effect of columnar pins on the flux-lines melting transition in high-temperature superconductors is studied using Path Integral Monte Carlo simulations. We highlight the similarities and differences in the effects of columnar disorder on the melting transition in YBa$_2$Cu$_3$O$_{7-δ}$ (YBCO) and the highly anisotropic Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (BSCCO) at magnetic fields such that the mean separation between flux-lines is smaller than the penetration length. For pure systems, a first order transition from a flux-line solid to a liquid phase is seen as the temperature is increased. When…
Muon spin rotation measurements of the magnetic field distribution in the vortex state of the oxygen deficient high-Tc superconductor YBa{2}Cu{3}O{6.60} reveal a vortex-lattice melting transition at much lower temperature than that in the fully oxygenated material. The transition is best described by a model in which adjacent layers of ``pancake'' vortices decouple in the liquid phase. Evidence is also found for a pinning-induced crossover from a solid 3D to quasi-2D vortex lattice, similar to that observed in the highly anisotropic superconductor Bi{2+x}Sr{2-x}CaCu{2}O{8+y}.
The angular dependence of the first-order phase transition (FOT) in the vortex lattice in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ crystals was investigated by a low frequency AC shielding technique (with the AC field $\parallel c$), in which the static-field component parallel to $c$- ($H_{\perp}$) was varied with the in-plane field $H_{\parallel}$ held constant. The linear decrease of the FOT field $H_{\perp}^{FOT}$ with increasing $H_{\parallel}$ ends at a temperature--dependent critical value of $H_{\parallel}$. A new transition, marked by the abrupt drop of the $ab$-plane shielding current, appe…
Phase transition between the vortex glass and the Bragg glass phases in high-$T_{\rm c}$ superconductors in $\vec{B}\parallel\vec{c}$ is studied by Monte Carlo simulations in the presence of point pins. A finite latent heat and a $δ$-function peak of the specific heat are observed, which clearly indicates that this is a thermodynamic first-order phase transition. Values of the entropy jump and the Lindemann number are consistent with those of melting transitions. A large jump of the inter-layer phase difference is consistent with the recent Josephson plasma resonance experiment of Bi$_{2}$Sr$_…
The effect of a magnetic field component parallel to the superconducting layers on longitudinal Josephson plasma oscillations in the layered high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ is shown to depend on the thermodynamic state of the underlying vortex lattice. Whereas the parallel magnetic field component depresses the Josephson Plasma Resonance (JPR) frequency in the vortex solid phase, it may enhance it in the vortex liquid. There is a close correlation between the behavior of microwave absorption near the JPR frequency and the effectiveness of pancake vortex pinning, w…
Measurements of the $^{17}$O nuclear magnetic resonance (NMR) quadrupolar spectrum of apical oxygen in HgBa$_{2}$CuO$_{4+δ}$ were performed over a range of magnetic fields from 6.4 to 30\,T in the superconducting state. Oxygen isotope exchanged single crystals were investigated with doping corresponding to superconducting transition temperatures from 74\,K underdoped, to 78\,K overdoped. The apical oxygen site was chosen since its NMR spectrum has narrow quadrupolar satellites that are well separated from any other resonance. Non-vortex contributions to the spectra can be deconvolved in the ti…
