Huge metastability in high-T_c superconductors induced by parallel magnetic field

We present a study of the temperature-magnetic field phase diagram of homogeneous and inhomogeneous superconductivity in the case of a quasi-two-dimensional superconductor with an extended saddle point in the energy dispersion under a parallel magnetic field. At low temperature, a huge metastability region appears, limited above by a steep superheating critical field (H_sh) and below by a strongly reentrant supercooling field (H_sc). We show that the Pauli limit (H_p) for the upper critical magnetic field is strongly enhanced due to the presence of the Van Hove singularity in the density of states. The formation of a non-uniform superconducting state is predicted to be very unlikely.