Phase diagram of randomly pinned vortex matter in layered superconductors: Dependence on the details of the point pinning

Abstract

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 superconductors with tilted columnar pinning centers

“…We have ρ n,i ≡ ρ n (r i )A 0 where A 0 = h 2 √ 3/2 is the area of the in-plane computational cell of lattice constant h. The computational lattice is of size N 2 × N L . As in previous work 7,8,9,16,17,18 we take h = a/16 where a = 1.99a 0 is the equilibrium value 16 of the lattice constant of the system in the absence of pinning at the chosen value of B z . The minimization procedure we use 23 ensures the non-negativity of the variables ρ n,i .…”

“…To shed some light on this problem, we have studied the structural and thermodynamic properties of a system of pancake vortices in a strongly anisotropic, layered superconductor in the presence of tilted columnar pinning, using a mean-field, free-energy based numerical method developed in our earlier studies 7,8,9,16,17,18 of vortex matter with different kinds of pinning. In this method, the free energy of a system of pancake vortices interacting among themselves and with pinning centers is written as a functional of the time-averaged local areal density of the vortices.…”

“…As in previous work 7,8,9,16,17,18 we take h = a/16 where a = 1.99a 0 is the equilibrium value 16 of the lattice constant of the system in the absence of pinning at the chosen value of B z . The minimization procedure we use 23 ensures the non-negativity of the variables ρ n,i .…”

“…The value N L of the number of layers in the computational lattice has to be 17 at least several hundred. There are of course computational limitations: in our recent 18 work on point pinning the total number of computational lattice sites attainable was N C = N 2 N L = 2 23 . But the main problem here is that the periodic boundary conditions in the z direction impose, computationally, an effective "quantization condition" on the values of ψ that can be used and, indirectly, on the range of c that can be studied.…”

Muon-Spin Rotation Measurements of an Unusual Vortex-Glass Phase in the Layered SuperconductorBi2.15Sr1.85CaCu2O8+δHeron1, Ray2, Lister3 et al. 2013Phys. Rev. Lett.14080View full textAdd to dashboardCite

“…This region has proved notoriously difficult to equilibrate via numerical simulations [5,22,23]. By contrast, the glass and lattice phases at higher and lower field are clearly seen in the simulations.…”