Type-1.5 superconductors

Superconductors are generally classified as being type-I or type-II; Doug Natelson touched on this as part of his recent series of pedagogical posts explaining solid-state physics concepts. Type-I superconductors usually do not admit an external magnetic field in the superconducting state: they turn “normal” above a critical value of the field. Type-II superconductors do admit a magnetic field for some field strengths above the critical value, while still being able to superconduct: this is known as the “mixed” state.

In the presence of an externally-applied magnetic field, “vortices” form in a superconductor, with a normal nonsuperconducting core of size ~ (the “coherence length” over which Cooper pairs – quasiparticles consisting of pairs of ‘bound’ electrons – are extended). This is surrounded by a region of size ~ in which a supercurrent circulates (where is known as the penetration depth), and hence produces its own opposing magnetic field. Forming such a vortex requires some energy; straightforward calculations show that the interfacial energy per unit length associated with a vortex is proportional to . If , forming such vortices increases the free energy of the system, and vortices tend to attract and annihilate – as in the case of type-I superconductors. If , on the other hand, a “lattice” of repulsive vortices is formed – as in the case of the mixed state of type-II superconductors.

In some materials, electrons can exist in two different bands ( and ), reflecting different kinds of bonding. A classic example of this is graphite. The electrons in the highest occupied states in a structurally similar superconductor, MgB₂, are similarly - or -bonded. This can be thought of as resulting in two different kinds of Cooper pairs with two different values of and . The interesting thing is that in MgB₂, the quasiparticles associated with the electrons have (type-I), while the quasiparticles associated with the electrons have (type-II).

The coupling between these two different states is so weak that MgB₂ was predicted - and has now been found – to be a so-called “type-1.5″ superconductor — that is, one with behavior combining aspects of type-I and type-II superconductivity. In this case, the vortices repel each other (as in type-II superconductors) over short distances while they attract each other (as in type-I superconductors) over long distances. In a previous post, I noted that competition between long-range repulsive and short-range attractive forces often leads to spatially inhomogeneous and anisotropic phases in various systems: examples include “stripe” or “bubble” phases in blockcopolymers, “pasta phases” of the crusts of neutron stars or DNA-intercalated lipid bilayers, stripe formation in ferrofluids, and anisotropic phases in two-dimensional electron gases in the presence of moderately large magnetic fields. Similarly, one might expect the competition between short-range repulsive and long-range attractive forces between vortices to give rise to interesting pattern formation in MgB₂ at low applied fields.

This is what Moshchalkov et al. set out to explore. One way to visualize the flux vortices of a superconductor is using so-called ‘magnetic decoration’: that is, by sprinkling ferromagnetic powder onto the surface of the superconductor. The powder is then attracted by the vortex flux lines and forms a pattern representative of the flux vortices. Using this technique, Moshchalkov et al. found indeed that the vortices in MgB₂ were inhomogeneously distributed, often forming stripes separated by regions of ‘normal’ phase – thus confirming that MgB₂ is a type-1.5 superconductor.