Magnetic screening and specific heat of an anisotropic Coulomb Bose-gas as a model for the superconducting state

The thermodynamics of the Coulomb Bose-gas (CBG) is studied using the Bogoliubov approximation. Within the's approximation the condensate density did not tend to zero as the transition temperature, T-c, was approached, but remained finite, resulting in a first order phase transition. By the use of the condensate density as the only temperature dependent feature of the electromagnetic screening the London penetration depth is derived. The free energy of the system and the specific heat are calculated. We report a well defined lambda-point transition in the specific heat. Comparisons are made with the experimental results for YBCO, a high temperature superconductor. We also report recient findings of the Bose-Einstein condensation of CBG in a magnetic field at ultra-low temperatures and ultra-high magnetic fields. A low-temperature dependence of the upper critical field H-c2(T) is obtained both for the particle-impurity and particle-particle scattering.