We have just put out a generalisation of the theory of nodal quasiparticles and used it to derive a bulk thermodynamic signature of certain topological transitions.
The theory of nodal quasiparticles has a wide range of applications, from unconventional superconductors to topological superconductors and graphene. At low temperatures, their linear dispersion away from a nodal point or line on the Fermi surface (a Dirac point or a Dirac line), leads to a characteristic power-law dependence of the specific heat:
In superconductors, such behaviour can be used to detect experimentally whether the order parameter has line nodes (n = 2) or point nodes (n = 3) and therefore to identify the Cooper pairing symmetry. In our recent preprint, [Note added: now published, see http://blogs.kent.ac.uk/strongcorrelations/2013/12/13/anomalous-power-laws-paper-published/]
Anomalous thermodynamic power laws near topological transitions in nodal superconductors
we show that other, non-integer exponents are possible. These occur when line nodes cross or near topological transitions where point nodes, line nodes, or line node crossings either appear, disappear or re-configure themselves in a non-trival way on the Fermi surface (e.g., at a line reconnection transition where the number of rings of line nodes on the Fermi surface changes). Such anomalous exponents thus provide bulk thermodynamic signatures of the topological transitions in question – which should come in handy to experimentalists wishing to study topological matter as until recently the emphasis has been on surface phenomena in topological insulators i.e. topologically-protected edge states.
Interestingly, you don’t need to be exactly at the topological transition in order to observe the anomalous exponent – merely being near the transition is enough to observe the anomalous power law down to some characteristic temperature scale 
, below which the more conventional behaviour is found – a behaviour strongly reminiscent of a quantum critical endpoint (QCEP):
