Paramagnetic intrinsic Meissner effect in a bulk

We calculate a free energy of a quasi-two-dimensional (Q2D) superconductor with $\xi_\perp<d$ in a parallel magnetic field, where $\xi_\perp$ is a perpendicular to the conducting layers coherence length and $d$ is an interlayers 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 shrinking of the Cooper pairs “sizes” in a direction perpendicular to the conducting layers. We suggest to measure this paramagnetic intrinsic Meissner effect in Q2D superconductors and superconducting super-lattices.