Vortices everywhere

The 2026 APS Oliver E. Buckley Prize in condensed matter physics was announced this week, and it's a really interesting combination of topics that, to a lay person, may seem to be completely unrelated.  

Fig. 1 from this follow-up PRB.

On the one hand, John Reppy (at age 94!) and Dave Bishop were honored for their work examining the properties of vortices in thin films of superfluid helium-4.  Relevant papers include this one from 1977, where they used a torsion pendulum coated with the helium film to examine the transition between normal and superfluid.  When the helium becomes a superfluid, it has (at low speeds) no viscosity, so it no longer has to rotate with the torsion pendulum; this means the rotational moment of inertia goes from that of (pendulum+helium) to just (pendulum), and the period of the oscillations increases.  Really detailed measurements of the oscillations and their damping allowed Reppy and Bishop to compare with models of the superfluid transition based on work by Kosterlitz and Thouless (and Berezinskii).  See the image for a diagram of the experimental setup - very clever and intricate.  

The key idea here is the role of vortices.  Superfluidity in helium is described by an order parameter that looks like a wavefunction - it has an amplitude, \(\Psi_{0}\), and a phase \(\phi\), so that \(\Psi(\mathbf{r}) = \Psi_{0} \exp(i \phi)\).   That order parameter is supposed to be single-valued, meaning if you go around a closed loop of some kind, that phase will either remain the same or ramp by some integer multiple of \(2\pi\).  The gradient of the phase is related to the velocity of the superfluid, so if the phase winds by \(2\pi\), that implies there is a circulation of flow and orbital angular momentum that has to be an integer multiple of \(\hbar\).  In the BKT theory, the demise of the superfluid phase as the system is warmed happens through the creation and unbinding of vortex-antivortex pairs.

On the other hand, the other recipients of the Buckley Prize were Gwendal Fève, Mike Manfra, and Steve Kivelson, for their work (experiments here and here) regarding the braiding statistics of anyons in fractional quantum Hall systems.  I'd written about anyons here.  For electrons in 2D, the wavefunctions of excitations of the fractional quantum Hall system look like vortices.  The phase of the electronic wavefunction can wind due to circulation, and because electrons are charged, the phase can also wind due to magnetic flux attached to the little whirlpool.  It's the combination of these phase effects that can lead to those excitations acting like anyons (so that when two are physically swapped or braided around one another, the wavefunction picks up a phase factor that is not just the \(+1\) of bosons or the \(-1\) of fermions).  

As my friend Dan Arovas pointed out, there was a hope back in the early 1980s that perhaps vortices in superfluid helium would also act like anyons and have fractional statistics.  However, this paper by Haldane and Wu disproved that possibility.  

Vortex shedding, from here.

Because of the relationship between quantum phase winding and actual flow of (density) currents, vortices show up in lots of places in hard condensed matter physics.  Classical vortices are also physically nontrivial objects - they're topological and often seem to have very counterintuitive properties and motions.  Heck, Lord Kelvin was so taken by this that he thought (pre-quantum) that maybe everything is really vortices of some kind.  

Perhaps it is fitting that I am posting this on the 85th anniversary of the Tacoma Narrows bridge collapse.  That classic civil engineering failure was caused by vortex shedding by the bridge coupling to its torsional resonance frequency.  Vortices can have big consequences!