Langevin Dynamics of the vortex matter two-stage melting transition in
Bi_2Sr_2CaCu_2O8+δ​ in the presence of straight and of tilted
columnar defects
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 Bi_2Sr_2CaCu_2O8+δ​ 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 new dynamical measurements in the presence of a current that
identifies clearly 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∘ with respect to 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.Comment: 13 pages, 11 figure