The past few weeks I have been puzzling through the implications of some really nice experimental results on superconductivity in organic charge transfer salts. A group at Sherbrooke measured the speed of sound as a function of temperature for different polarisations. The Figure below, taken from their PRB, shows how anisotropic the elastic response is for the material κ-(BEDT-TTF)2Cu[N(CN)2]Br .
The sound is always propagating perpendicular to the layers, which lies in direction of the b axis of the crystal. C22 is the elastic constant for longitudinal sound. C44 has polarisation parallel to the c direction in the crystal which is the same direction as the t' (diagonal) hopping in the relevant Hubbard model [see picture below and this review]. C66 has polarisation in the a direction.
A few thoughts
- A really helpful succinct summary of elasticity theory and sound velocity anomalies at Tc is found in Section II of this PRB, also from Sherbrooke [I believe there is an important typo in the expression for the sound velocity in terms of the strain tensor, just below equation (5) the j and k indices on the elastic tensor need to be interchanged.]
- These variations in the sound velocity near Tc by about 0.1% may seem small, but they are actually several orders of magnitude larger than in other unconventional superconductors. The authors point this out.
- There are fluctuations which extend to temperatures far above Tc. This is consistent with Nernst effect measurements, on the same materials, reported in Nature.
- The authors perform an elegant group theoretical argument that forces them to conclude that the anomaly in C66 and other experimental results (STM and thermal conductivity) require that the superconducting order parameter for this crystal must be mixed
- I am not that convinced by the STM and thermal conductivity experiments that claim to determine the locations of the nodes in the energy gap, because these experiments are surface sensitive.
- The proposed mixed symmetries are quite inconsistent with many microscopic calculations which predict the order parameter will have here. This inconsistency is an important issue that needs to be resolved. symmetry, which competes with near when t'~t and the lattice becomes that of the isotropic triangular lattice, as discussed
- The anisotropic response is somewhat reminiscent of the anisotropy in the thermal expansion near Tc (as shown below) found by Michael Lang's group [see this PRB].
- Similar anisotropies and variations in the sound velocity and thermal expansion are also seen near the Mott transition and the crossover from a Fermi liquid to a bad metal.