Magnetic breakdown in a normal-metal–superconductor proximity sandwich

We study the magnetic response of a clean normal-metal slab of finite thickness in proximity with a bulk superconductor. We determine its free energy and identify two (meta)stable states, a diamagnetic one where the applied field is effectively screened, and a second state, where the field penetrates the normal-metal layer. We present a complete characterization of the first-order transition between the two states which occurs at the breakdown field $H_b\mathrm{}\left(T\right)\mathrm{}$, including its spinodals, the jump in the magnetization, and the latent heat. The bistable regime terminates at a critical temperature $T_{\mathrm{crit}}$ above which the sharp transition is replaced by a continuous crossover. We compare the theory with experiments on normal superconducting cylinders.