Supersymmetric BCS: Effects of an external magnetic field and spatial fluctuations of the gap

Recently an N=1 supersymmetric model of BCS superconductivity was proposed realizing spontaneous symmetry breaking of a U(1)_R symmetry. Due to scalar contributions the superconducting phase transition turned out to be first order rather than second order as in standard BCS theory. Here we consider the effects of an external magnetic field and spatial fluctuations of the gap in that model. This allows us to compute the magnetic penetration length and the coherence length, and also to distinguish between type I and type II superconductors. We compare the supersymmetric and standard relativistic BCS results, where the main differences come from the different orders of the phase transition.