Lower critical field of a Josephson-coupled layer model of high-Tc superconductors

We calculate the lower critical field Hc1 for a magnetic field applied parallel to the layers of a Josephson-coupled layer model of high-Tc superconductors. This result is obtained by using an expression for the vortex line energy that explicitly involves the gauge-invariant phase difference between superconducting layers. We examine the behavior of Hc1 as a function of temperature and discuss the manifestation of the superconductor discreteness below a crossover temperature where the coherence length ξc(T) becomes comparable to the lattice constant c. This temperature dependence is contrasted with the standard result for Hc1 for a continuous anisotropic type-II superconductor