Vortex lattice in type II superconductors under magnetic field in the presence of inhomogeneities

We investigate the structure, elastic and dynamical properties of the vortex matter in the presence of artificially created or intrinsic gradients of the critical temperature in the framework of the Ginzburg–Landau theory. The region of parameters in which vortex cores are not well separated is treated perturbatively in 1-Hc2(T)/Hc2(0)1-Hc2(T)/Hc2(0). Critical current for periodic pinning potential is obtained and general expressions for elastic moduli at long wavelength are derived. We show that it is impossible to restrict the system to lowest Landau level. We use it to provide a theory of the discontinuous peak effect in critical current which appears near Hc2(T)Hc2(T) line in low TcTc strongly type II superconductors. Influence of thermal fluctuations is also considered and we find softening of the shear modulus in the vicinity of vortex lattice melting line.