Theoretical Statistical and Condensed Matter Physics
Equilibrium Phase Diagram of a 3D Point Disordered Type-II Superconductor
In pure single crystal samples of the high Tc superconductors, the vortex line lattice present at low magnetic fields melts into a vortex line liquid via a sharp first order phase transition, as the temperature is increased. However, even the purest samples are believed to contain intrinsic random point defects due to the random oxygen doping needed to make these materials superconducting.
As the applied magnetic field H, and hence the vortex line density, increases, the random pinning energy per unit volume increases and the disorder becomes a relevent factor in determining the nature of the vortex phase diagram.
Experimentally, as H increases, the melting transition temperature decreases, and discontinuities across this first order phase boundary steadily decrease until they vanish at what has been termed the "upper critical point". Above this "upper critical point" resistivity vanishes continuously as temperature is decreased; it is unclear if there exists a distinct second order transition to a "vortex glass" phase, or just a cross-over where the vortex liquid viscosity increases sufficiently rapidly so as to make any vortex motion undetectable. At lower temperature, measurements suggest a first order transition between the ordered vortex lattice at small H and a disordered vortex state at high H.
To investigate the effect of random pinning on the stability of the vortex lattice we have carried out numerical simulations of the 3D uniformly frustrated XY model, as a model of interacting vortex lines. Random pinning is introduced by random variations of the couplings in the model. Considering the model for varying temperature and disorder strength at fixed magnetic field, we find a phase diagram (see fig. to left) which has a single unified first order vortex lattice melting transition. At small disorder strength, the transition is driven by thermal fluctuations. As disorder increases, we find no "upper critical point", but rather that the phase boundary turns parallel to the temperature axis and continues
smoothly to lower temperatures. Here the transition is disorder driven; there are no discontinuities in energy or specific heat as the transition is crossed, but the transition remains first order. This conclusion is supported by recent experiments on the high Tc superconductor BSCCO (see Abraham et al, Nature 411, 451 (2001)). At intermediate values of disorder, we find that this first order transition is sharp locally, but from a global point of view smears out over a region of finite width in temperature, as different local regions of the system order at slightly different temperatures. This conclusion has also been reported experimentally (see Pasquini et al, Phys. Rev. Lett. 100,247003 (2008)). At large disorder strengths, above the vortex lattice melting, our model contains a sharp second order vortex glass transition, however there are suggestions that this sharp glass transition may convert to a cross-over effect once magnetic field fluctuations are included in the model.
This work has been carried out in collaboration with Prof. Peter Olsson of Umeå University, Umeå Sweden. For further details see Phys. Rev. B 79, 214503 (2009) and Phys. Rev. Lett. 87, 137001 (2001).