Topologically interesting superconductors

Cooper pairs with orbital angular momentum -- p-wave or d-wave -- have order parameters that are potentially more interesting than the U(1) order parameter of a BCS superconductor. The basic idea is that there are three p orbitals, five d orbitals, etc. instead of a single s orbital; therefore, e.g., p_x + i p_y and p_x - i p_y are equally good orbitals to Cooper pair in. In superconductors, the underlying crystal lattice picks out the axes and reduces the orbital symmetry group to a discrete one: e.g., in strontium ruthenate, one has domains of p_x + ip_y and of p_x - ip_y, separated by what appear to be domain walls. However, if one could make p- or d-wave pairs with cold fermions, one would presumably have Cooper pairs spontaneously breaking a large continuous symmetry, and this, in principle, could give rise to interesting sorts of topological defects. (e.g. triplet superfluids have half-quantum vortices, in which the orbital and spin parts each rotate by pi when you go around a loop, so that the total wavefunction returns to itself but the spatial part doesn't. These vortices turn out to be interesting for quantum computation.)

There are two new arxiv papers on this topic; the first is from Nigel Cooper and Gora Shlyapnikov, both quite well-known:

---

Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
N. R. Cooper, G. V. Shlyapnikov
http://arxiv.org/abs/0907.3080

Abstract: We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.

---

The idea here is something like this. You trap a bunch of dipolar molecules in a 2D trap and impose an external magnetic field to line up the dipoles. Next, you use microwaves to have the make the dipole moments precess (a la NMR); if you do this right, the time-averaged dipole-dipole interaction is attractive and you get Cooper pairing. The authors don't offer an intuitive explanation of why p-wave pairing is preferred; I assume it has to do with the fact that dipolar-molecule systems are naturally ferromagnetic because of the external fields keeping the dipoles lined up, so the natural ground state tends to have all spins lined up pointing along the field, which favors spin-triplet pairing and therefore p-wave pairing.

The other paper is about d-wave pairing:

---

Textures and non-Abelian vortices in atomic d-wave paired Fermi condensates
Authors: H. M. Adachi, Y. Tsutsumi, J. A. M. Huhtamäki, K. Machida
http://arxiv.org/abs/0907.2972

Abstract: We report on fundamental properties of superfluids with d-wave pairing symmetry. We consider neutral atomic Fermi gases in a harmonic trap, the pairing being produced by a Feshbach resonance via a d-wave interaction channel. A Ginzburg-Landau (GL) functional is constructed which is symmetry constrained for five component order parameters (OP). We find OP textures in the cyclic phase and stability conditions for a non-Abelian fractional 1/3-vortex under rotation. It is proposed how to create the intriguing 1/3-vortex experimentally in atomic gases via optical means.

---

The 1/3-quantum vortex is interesting even if it isn't realizable. What seems to me most interesting about this paper is that it carefully accounts for the influence of the harmonic trap on vortex energetics -- that defects which would be energetically unstable in bulk might be stable in a trap is an interesting possibility.