Paramagnetic intrinsic Meissner effect in a bulk

We calculate the free energy of a quasi-two-dimensional (Q2D) superconductor with ξ_⊥ < d in a parallel magnetic field, where ξ_⊥ is a perpendicular to the conducting layer coherence length and d is the interlayer distance. It is shown to be different from that in the famous Lawrence-Doniach model. In particular, at high enough magnetic fields, the Meissner currents are found to create an unexpected paramagnetic moment due to the shrinking of the Cooper pairs "sizes" in a direction perpendicular to the conducting layers. We suggest measuring this paramagnetic intrinsic Meissner effect in Q2D superconductors and superconducting superlattices.