Flux melting in BSCCO: Incorporating both electromagnetic and Josephson couplings

Abstract

Multilevel Monte Carlo simulations of a BSCCO system are carried out including both Josephson as well as electromagnetic couplings for a range of anisotropies. A first order melting transition of the flux lattice is seen on increasing the temperature and/or the magnetic field. The phase diagram for BSCCO is obtained for different values of the anisotropy parameter $\gamma$. The best fit to the experimental results of D. Majer {\it et al.} [Phys. Rev. Lett. {\bf 75}, 1166 (1995)] is obtained for $\gamma \approx 250$ provided one assumes a temperature dependence ${\lambda }^2(0)/{\lambda }^2(T)=1-t$ of the penetration depth with $t=T/T_c$. Assuming a dependence ${\lambda }^2(0)/{\lambda }^2(T)=1-t^2$ the best fit is obtained for $\gamma \approx 450$. For finite anisotropy the data is shown to collapse on a straight line when plotted in dimensionless units which shows that the melting transition can be satisfied with a single Lindemann parameter whose value is about 0.3. A different scaling applies to the $\gamma =\infty$ case. The energy jump is measured across the transition and for large values of $\gamma$ it is found to increase with increasing anisotropy and to decrease with increasing magnetic field. For infinite anisotropy we see a 2D behavior of flux droplets with a transition taking place at a temperature independent of the magnetic field. We also show that for smaller values of anisotropy it is reasonable to replace the electromagnetic coupling with an in-plane interaction represented by a Bessel function of the second kind ($K_0$), thus justifying our claim in a previous paper.

arXiv comment12 figures, revtex4

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• On the melting of the nanocrystalline vortex matter in high-temperature superconductors
• Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O${}_{8+\delta }$ in the presence of straight and of tilted columnar defects
• Molecular Dynamics of pancake vortices with realistic interactions: Observing the vortex lattice melting transition
• Rapid evaluation of the periodic Green's function in d dimensions