Suprafroth in type-I superconductors

The structure and dynamics of froths have been subjects of intense interest owing to the desire to understand the behaviour of complex systems where topological intricacy prohibits exact evaluation of the ground state. The dynamics of a traditional froth involves drainage and drying at the cell boundaries; thus, it is irreversible. Here, we report a new member of the froth family: suprafroth, in which the cell boundaries are superconducting and the cell interior is normal, or non-superconducting. Despite having a very different microscopic origin, topological analysis of the structure of the suprafroth shows that the same statistical laws, such as those of von Neumann and of Lewis apply to a suprafroth. Furthermore, for the first time in the analysis of froths, there is a global measurable property, the magnetic moment, which can be directly related to the suprafroth structure. We propose that this suprafroth is a model system for the analysis of the complex physics of two-dimensional froths—with magnetic field and temperature as external (reversible) control parameters. Froths and foams are complex structures, particularly those that disappear irreversibly. Superconducting froth, however, can be reversibly controlled by several external parameters, so it may help quantify froth dynamics across different systems.