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On the melting of the nanocrystalline vortex matter in high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced low concentration of columnar defects satisfying $B_ϕ\le B$. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.