Lindemann criterion and vortex lattice phase transitions in type-II superconductors

We discuss the destruction of vortex lattice order in type-II superconductors by random point pinning and thermal fluctuations based on Lindemann criteria. The location of the melting line and the order-disorder transition, which marks the destruction of the topologically ordered Bragg glass phase and is the reason for the second peak effect, is calculated. We focus on a comparative discussion of different versions of Lindemann criteria and, with regard to experiment, on a comparative discussion of three classes of type-II superconductors—low-T_c, anisotropic high-T_c, and layered high-T_c materials. Specific attention is paid to the role of nonlocal magnetic interlayer couplings and the softening of elastic moduli at high magnetic fields, which is crucial for low-T_c materials. We also discuss in detail the competing mechanisms of thermal depinning and temperature dependence of the pinning strength through microscopic parameters as well as the crossover between single vortex and bundle pinning for low-T_c materials.