Superconducting ordering in vortex states of clean type II superconductors with pinnings

Point-like pinnings inevitably exist in real and bulk type II superconductors and, even in clean limit, need to be taken into account in describing the vortex states right at and below the solidification point. Such pinning effects are considered on the basis of the superconducting fluctuation theory and putting emphasis upon a drastic pinning effect accompanying the solidification transition, i.e., the vortex-glass (VG) instability in clean limit. We point out through an examination of Gaussian VG susceptibility chi(vg) that the VG instability in clean enough systems is induced by the first-order solidification transition of vortices. It is found that the diagonal (dissipative) conductivity sigma(xx) in directions perpendicular to the field has a term becoming divergent due to the Gaussian VG instability. Our result indicates that, in any situation with no true VG transition, sigma(xx) reduces, in clean limit, to the expression in the pinning-free case, while a true VG transition certainly makes sigma(xx) divergent at the first-order solidification transition surviving the point-like pinnings. By combining this result with existing resistivity data, the presence of a 3D true VG transition line over an entire field range below H-c2(T) is expected, and possible magnetic phase diagrams of real bulk type II superconductors are proposed. Pinning effects on the Hall conductivity are also examined and found to be present once the superconducting fluctuation is included.