Multiple states and hysteresis for type 1 superconductors

For type I superconductors with penetration parameter λ below a certain critical value, the existence of multiple local minimizers of the energy functional is shown. The behavior of these minimizers is examined when the Ginzburg–Landau parameter is small, and a hysteresis phenomenon is demonstrated. In contrast to the case investigated by X. B. Pan [J. Math. Phys. 44, 2639 (2003)] where λ is above the critical value, the results presented in this paper show that type I superconductors with λ below the critical value have higher critical magnetic field Hc, and exhibit more complicated superconducting behavior.