Dynamic Phase Transitions in Superconductivity

In this Letter, the dynamic phase transitions of the time-dependent Ginzburg-Landau equations are analyzed using a newly developed dynamic transition theory and a new classification scheme of dynamics phase transitions. First, we demonstrate that there are two type of dynamic transitions, jump and continuous, dictated by the sign of a nondimensional parameter R. This parameter is computable, and depends on the material property, the applied field, and the geometry of domain that the sample occupies. Second, using the parameter R, precise analytical formulas for critical domain size, and for critical magnetic fields are derived.