Yesterday I gave a talk at a mini-programme being organised by Joseph Betouras (Loughboroguh) at the Max Planck Institut for Complex Systems, in Dresden. Sadly, I had to cancel my participation in this exciting mini-programme at the last minute, for personal reasons, however I was able to deliver my talk by video-conference and had some interesting exchanges with the audience then and also later via email.
My talk centred on nodal line re-construction topological transitions in superconductors and specifically on their specific heat signatures. I argued for the existence of a topological transition state which, far from being a special point in the phase diagram, requiring fine-tuning, dominates a vast swathe of it very much like a quantum critical point does. In fact I argued that the nodal reconstruction instablity must be a quantum critical endpoint in very much the same way that the Lifshitz transition is one [see Carr, S. T., Quintanilla, J. & Betouras, J. J. Lifshitz transitions and crystallization of fully polarized dipolar fermions in an anisotropic two-dimensional lattice. Physical Review B 82, 045110 (2010). 10.1103/PhysRevB.82.045110]. I also put forward the idea that such state may be stabilised further by a mechanism akin to the order-by-disorder and that it may even have some hiterto unexplored applications. The latter flows from recent work by Phil Whittlesea that we hope to publish soon.
Here is a link to the abstract I gave to the organisers before the talk (PDF format).