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Langevin dynamics simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced point defects as a smoothened distribution of a random potential. Both the electromagnetic and Josephson interactions among pancake vortices were included. A special shaking and annealing process was introduced to let the system approach the equilibrium configuration. We are able to see the inverse melting transition from the Bragg-glass to the amorphous vortex glass state, in agreement with recent experiments.
The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking. Two equally sharp first-order magnetization steps are revealed in a single tempe
A magnetic field applied to type-II superconductors introduces quantized vortices that locally quench superconductivity, providing a unique opportunity to investigate electronic orders that may compete with superconductivity. This is especially true
Competition with magnetism is at the heart of high temperature superconductivity, most intensely felt near a vortex core. To investigate vortex magnetism we have developed a spatially resolved probe using nuclear magnetic resonance. Our spin-lattice-
Vortex phase diagram under tilted fields from the $c$ axis in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+y}$ is studied by local magnetization hysteresis measurements using Hall probes. When the field is applied at large angles from the $c$ axis, an anomaly (
Low temperature thermal conductivity, $kappa$, of optimally-doped Bi2212 was studied before and after the introduction of point defects by electron irradiation. The amplitude of the linear component of $kappa$ remains unchanged, confirming the univer