Langevin dynamics of the two-stage melting transition of vortex matter inBi2Sr2CaCu2O8+δin the presence of straight or tilted columnar defects

Abstract

In this paper, we use London-Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on dynamical measurements in the presence of a current that clearly identifies the irreversibility line and the second stage delocalization transition. In addition to CDs aligned along the $c$ axis, we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for CDs tilted by 45\ifmmode^\circ\else\textdegree\fi{} with respect to the $c$ axis show that the locations of the melting and delocalization transitions are not affected by the tilt when the ratio of flux lines to CDs remains constant. On the other hand, we argue that some dynamical properties and, in particular, the position of the irreversibility line, should be affected.