Lindemann criterion and vortex lattice phase transitions in type-II superconductors (original) (raw)
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Physical Review B, 2007
We study the thermodynamic and structural properties of the superconducting vortex system in high temperature layered superconductors, with magnetic field normal to the layers, in the presence of a small concentration of strong random point pinning defects via numerical minimization of a model free energy functional in terms of the time-averaged local density of pancake vortices. Working at constant magnetic induction and point pinning center concentration, we find that the equilibrium phase at low temperature (T ) and small pinning strength (s) is a topologically ordered Bragg glass. As T or s is increased, the Bragg glass undergoes a first order transition to a disordered phase which we characterize as a "vortex slush" with polycrystalline structure within the layers and interlayer correlations extending to about twenty layers. This is in contrast with the pinned vortex liquid phase into which the Bragg glass was found to melt, using the same methods, in the case of a large concentration of weak pinning centers: that phase was amorphous with very little interlayer correlation. The value of the second moment of the random pinning potential at which the Bragg glass melts for a fixed temperature is very different in the two systems. These results imply that the effects of random point pinning can not be described only in terms of the second moment of the pinning potential, and that some of the unresolved contradictions in the literature concerning the nature of the low T and high s phase in this system are likely to arise from differences in the nature of the pinning in different samples, or from assumptions made about the pinning potential.
Phase diagram of vortex matter in layered high-temperature superconductors with random point pinning
Physical Review B, 2006
We study the phase diagram of the superconducting vortex system in layered high-temperature superconductors in the presence of a magnetic field perpendicular to the layers and of random atomic scale point pinning centers. We consider the highly anisotropic limit where the pancake vortices on different layer are coupled only by their electromagnetic interaction. The free energy of the vortex system is then represented as a Ramakrishnan-Yussouff free energy functional of the time averaged vortex density. We numerically minimize this functional and examine the properties of the resulting phases. We find that, in the temperature (T ) -pinning strength (s) plane at constant magnetic induction, the equilibrium phase at low T and s is a Bragg glass. As one increases s or T a first order phase transition occurs to another phase that we characterize as a pinned vortex liquid. The weakly pinned vortex liquid obtained for high T and small s smoothly crosses over to the strongly pinned vortex liquid as T is decreased or s increased -we do not find evidence for the existence, in thermodynamic equilibrium, of a distinct vortex glass phase in the range of pinning parameters considered here. We present results for the density correlation functions, the density and defect distributions, and the local field distribution accessible via µSR experiments. These results are compared with those of existing theoretical, numerical and experimental studies.
Physical Review B, 2004
We study the melting transition of the low-temperature vortex solid in strongly anisotropic layered superconductors with a concentration of random columnar pinning centers small enough so that the areal density of the pins is much less than that of the vortex lines. Both the external magnetic field and the columnar pins are assumed to be oriented perpendicular to the layers Our method, involving numerical minimization of a model free energy functional, yields not only the free energy values at the local minima of the functional but also the detailed density distribution of the system at each minimum: this allows us to study in detail the structure of the different phases. We find that at these pin concentrations and low temperatures, the thermodynamically stable state is a topologically ordered Bragg glass. This nearly crystalline state melts into an interstitial liquid (a liquid in which a small fraction of vortex lines remain localized at the pinning centers) in two steps, so that the Bragg glass and the liquid are separated by a narrow phase that we identify from analysis of its density structure as a polycrystalline Bose glass. Both the Bragg glass to Bose glass and the Bose glass to interstitial liquid transitions are first-order. We also find that a local melting temperature defined using a criterion based on the degree of localization of the vortex lines exhibits spatial variations similar to those observed in recent experiments.
2014
The vortex lattice in a Type II superconductor provides a versatile model system to investigate the order-disorder transition in a periodic medium in the presence of random pinning. Here, using scanning tunnelling spectroscopy in a weakly pinned Co0.0075NbSe2 single crystal, we show that at low temperatures, the vortex lattice in a 3-dimensional superconductor disorders in two steps across the peak effect. At the onset of the peak effect, the equilibrium Bragg glass transforms into an orientational glass through the proliferation of dislocations. At a higher field, the dislocations dissociate into isolated disclination giving rise to an amorphous vortex glass. We also show the existence of a variety of additional non-equilibrium metastable states, which can be accessed through different thermomagnetic cycling.
Disordered type-II superconductors: a universal phase diagram for low-Tc systems
Physica C: Superconductivity, 2001
A universal phase diagram for weakly pinned low-T c type-II superconductors is revisited and extended with new proposals. The low-temperature``Bragg glass'' phase is argued to transform ®rst into a disordered, glassy phase upon heating. This glassy phase, a continuation of the high-®eld equilibrium vortex glass phase, then melts at higher temperatures into a liquid. This proposal provides an explanation for the anomalies observed in the peak eect regime of 2H±NbSe 2 and several other low-T c materials which is independent of the microscopic mechanisms of superconductivity in these systems.
Pramana-journal of Physics, 2006
We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe2 and CeRu2 with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe2, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe2 which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.
Journal of Experimental and Theoretical Physics Letters, 1997
The phase transition ''triangular lattice-vortex liquid'' in layered high-T c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (Ӎ3 K͒ into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (Ӎ8 K for T c ϭ84 K͒, the boundaries of the ''islands'' become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point ''triangular lattice-rotating lattice'' decreases slightly ͑to Ӎ2 K͒ and the temperature of the phase transition ''rotating lattice-vortex liquid'' increases substantially (Ӎ70 K͒.
Journal of Superconductivity and Novel Magnetism, 2007
We describe quantitatively the combined effects of both the thermal fluctuations and of the quenched disorder via the replica trick applied to the Ginzburg-Landau (GL) theory. We show that the vortex state can appear in either of the three disordered phases: (i) unpinned vortex liquid, (ii) amorphous vortex glass (pinned), and (iii) the crystalline (pinned but not containing topological defects) Bragg glass. The formation of the vortex glass is associated with the continuous replica symmetry breaking (RSB) reflecting the hierarchial structure of the potential barriers in a vortex glass state. An earlier analysis in the framework of London approximation have established that activation barriers controlling vortex dynamics obey the extreme value statistics within roughly the same domain of the phase diagram. We show that the disordered GL model in which only the coefficient at the quadratic term |ψ| 2 is random, first considered by Dorsey et al., exhibits, in the gaussian approximation, an additional nonhierarchical state possessing certain glassy properties like nonzero Edwards-Anderson order parameter. We associate this state with the "marginal glass phase" predicted in the earlier work of one of the authors; the marginal glass state being characterized by the marginally glassy dynamics. We show further that when the random component of the coefficient of the quartic term |ψ| 4 in GL free energy is taken into account, RSB effects appear. Application of the obtained results to description of various disorder-generated phenomena in vortex matter are briefly considered. The location of the glass transition line is determined and compared to experiments. This line is clearly different from both the melting line and the second peak line describing the translational and rotational symmetry breaking at high and low temperatures respectively. The phase diagram is separated by these two lines into the four phases described above.
Magnetic Phase Diagram of Weakly Pinned Type-II Superconductors
1999
The phenomenon of superconductivity was discovered in 1911, however, the methodology to classify and distinguish type-II superconductivity was established only in late fifties after Abrikosov's prediction of a flux line lattice in 1957. The advent of high temperature superconductors (HTSC) in 1986 focused attention onto identifying and classifying other possible phases of vortex matter in all classes of superconductors by a variety of techniques. We have collated evidences in support of a proposal to construct a generic phase diagram for weakly pinned superconducting systems, based on their responses to ac and dc magnetic fields. The phase diagram comprises quasi-glassy phases, like, the Bragg glass, a vortex glass and a reentrant glass in addition to the (completely) amorphous phases of pinned and unpinned variety. The characteristic metastability and thermomagnetic history dependent features recognized amongst various glassy vortex phases suggest close connections between vortex matter and other disordered condensed matter systems, like, spin glasses, super cooled liquids/ structural glasses, etc. A novel quenched random disorder driven fracturing transition stands out amongst other noteworthy facets of weakly vortex pinned vortex matter.
Phase diagram of vortex matter in layered superconductors with random point pinning
Phys Rev B, 2006
We study the phase diagram of the superconducting vortex system in layered high-temperature superconductors in the presence of a magnetic field perpendicular to the layers and of random atomic scale point pinning centers. We consider the highly anisotropic limit where the pancake vortices on different layer are coupled only by their electromagnetic interaction. The free energy of the vortex system is then represented as a Ramakrishnan-Yussouff free energy functional of the time averaged vortex density. We numerically minimize this functional and examine the properties of the resulting phases. We find that, in the temperature ($T$) -- pinning strength ($s$) plane at constant magnetic induction, the equilibrium phase at low TTT and sss is a Bragg glass. As one increases sss or TTT a first order phase transition occurs to another phase that we characterize as a pinned vortex liquid. The weakly pinned vortex liquid obtained for high TTT and small sss smoothly crosses over to the strongly pinned vortex liquid as TTT is decreased or sss increased -- we do not find evidence for the existence, in thermodynamic equilibrium, of a distinct vortex glass phase in the range of pinning parameters considered here. %cdr We present results for the density correlation functions, the density and defect distributions, and the local field distribution accessible via mu\mumuSR experiments. These results are compared with those of existing theoretical, numerical and experimental studies.