Transition to a Superconductor with Insulating Cavities

– An extreme type II superconductor with internal insulating regions, namely cavities, is studied here. We find that the cavity-bearing superconductor has lower energy than the defectfree superconductor above a critical magnetic induction B∗ for insulating cavities but not for metallic ones. Using a numerical approach for the Ginzburg-Landau theory we compute and compare free energy densities for several cavity radii and at least for two cavity densities, assuming a cubic lattice of spherical cavities. The interface between the superconducting state and an exterior medium has a delicate energetic balance whose importance was appreciated by Abrikosov [1] in his seminal work of 1957 that predicted vortices in superconductivity. The superconducting density decays near this interface with an energy cost per area of ξH c /8π, ξ is the coherence length, H 2 c /8π the condensate energy, and Hc the superconductor’s critical field. The external applied field penetrates inside the superconducting state with an energetic cost opposite to the previous one, −λH c /8π, λ being the London penetration length. The addition of these two energies gives the energetic cost of the compound’s external physical surface and also determines the nucleation of domain walls inside this compound, which becomes a sum of superconducting and non superconducting regions. According to the above qualitative argument this nucleation is possible for a compound with a Ginzburg-Landau parameter κ = λ/ξ larger than one, which is a type II superconductors. As pointed out by Yu. N. Ovchinnikov [2] long ago, the investigation of various types of inclusions in superconducting materials is of particular interest. The question here is which inclusions can be considered as domain walls, spontaneously nucleated inside the superconductor by energetic reasons. Let us consider here an extreme type II superconductor (κ >> 1) with non-superconducting regions in its interior, that we call cavities, with typical size of ξ, and separated by a dozen of ξ. The fact that cavities introduce novel properties to the superconductor has been previously shown by Doria and Zebende [3]. However cavities can be insulating or metallic and this has important consequences for the properties of the cavity-bearing superconductor. Here we show the remarkable property that only insulating cavities can turn the superconductor into some kind of bubble system, that is, turn its coexistence with non-superconducting regions into a stable phase. For both cases the cavity-bearing superconductor share similar properties, such