Two-Step Melting of the Vortex Solid in Layered Superconductors with Random Columnar Pins (original) (raw)
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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.
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.
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.
Phase diagram of the vortex system in layered superconductors with strong columnar pinning
Physical Review B - PHYS REV B, 2005
We present the results of a detailed investigation of the low-temperature properties of the vortex system in strongly anisotropic layered superconductors with a random array of columnar pinning centers. Our method involves numerical minimization of a free energy functional in terms of the time-averaged local vortex density. It yields the detailed vortex density distribution for all local free-energy minima, and therefore allows the computation of any desired correlation function of the time-averaged local vortex density. Results for the phase diagram in the temperature vs pin concentration plane at constant magnetic induction are presented. We confirm that for very low pin concentrations, the low-temperature phase is a Bragg glass, which melts into an interstitial liquid phase via two first-order steps, separated by a Bose glass phase. At higher concentrations, however, the low-temperature phase is a Bose glass, and the melting transition becomes continuous. The transition is then c...
The phase diagram of vortex matter in layered superconductors with tilted columnar pinning centers
2009
We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, tilted with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at lower temperatures converts, via a first order transition, to a Bragg glass, while, at higher temperatures, it crosses over to an interstitial liquid. At somewhat higher concentrations, no transition to a Bragg glass is found even at the lowest temperatures studied. While qualitatively the behavior we find is similar to that obtained using the same procedures for columnar pins normal to the layers, th...
Phase diagram of vortex matter in layered superconductors with tilted columnar pinning centers
Physical Review B, 2009
We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, tilted with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at lower temperatures converts, via a first order transition, to a Bragg glass, while, at higher temperatures, it crosses over to an interstitial liquid. At somewhat higher concentrations, no transition to a Bragg glass is found even at the lowest temperatures studied. While qualitatively the behavior we find is similar to that obtained using the same procedures for columnar pins normal to the layers, there are important and observable quantitative differences, which we discuss.
Vortex Lattice Melting in Layered Superconductors with Periodic Columnar Pins
Physical Review Letters, 2001
The melting transition of the vortex lattice in highly anisotropic, layered superconductors with commensurate, periodic columnar pins is studied in a geometry where magnetic field and columnar pins are normal to the layers. Thermodynamic properties and equilibrium density distributions are obtained from numerical minimizations of an appropriate free-energy functional. We find a line of first-order transitions that ends at a critical point as the pin concentration is increased. A simple Landau theory providing a semi-quantitative explanation of the numerical results is proposed. 74.60.Ge,74.60.Jg,85.40.Ux,74.25.Ha,74.76.Db
Europhysics Letters (epl), 2002
Phase diagram of vortex states of high-$T_{\rm c}$ superconductors with {\it sparse and weak} columnar defects is obtained by large-scale Monte Carlo simulations of the three-dimensional anisotropic, frustrated XY model. The Bragg-Bose glass phase characterized by hexagonal Bragg spots and the diverging tilt modulus is observed numerically for the first time at low density of columnar defects. As the density of defects increases, the melting temperature increases owing to "selected pinning" of flux lines. When the density of defects further increases, the transition to the Bose glass phase occurs. The interstitial liquid region is observed between these two glass phases and the vortex liquid phase.
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.