Vortex and critical fields in chargedBose liquids and unconventional superconductors

A single vortex in the charged Bose gas (CBG) has a charged core and its profile different from the vortex in neutral and BCS superfluids. Lower and upper critical fields of CBG are discussed. The unusual resistive upper critical field, Hc2(T ), of many cuprates and a few other unconventional superconductors is described as the Bose-Einstein condensation field of preformed bosons-bipolarons. Its nonlinear temperature dependence follows from the scaling arguments. Exceeding the Pauli paramagnetic limit is explained. Controversy in the determination of Hc2(T ) of cuprates from kinetic and thermodynamic measurements is addressed in the framework of the bipolaron theory.