The tetrahedron puzzle

(Yet another attempt to revive this blog. My experience from the other blog is that having a readership helps; however I don't think my interests overlap that strongly with anyone else's.)

On the arxiv this evening:

Local Quantum Criticality of an Iron-Pnictide Tetrahedron
T. Tzen Ong, Piers Coleman
arXiv:1109.4131

Abstract: Motivated by the close correlation between transition temperature ($T_c$) and the tetrahedral bond angle of the As-Fe-As layer observed in the iron-based superconductors, we study the interplay between spin and orbital physics of an isolated iron-arsenide tetrahedron embedded in a metallic environment. Whereas the spin Kondo effect is suppressed to low temperatures by Hund's coupling, the orbital degrees of freedom are expected to quantum mechanically quench at high temperatures, giving rise to an overscreened, non-Fermi liquid ground-state. Translated into a dense environment, this critical state may play an important role in the superconductivity of these materials.

[A little background. The pnictides/chalcogenides are of course the new iron-based superconductors; the crystal structure is such that each iron ion sits at the center of a tetrahedral cage of As-type or Se-type ions. In a plot that has now become common knowledge, a Japanese group showed [Yamada, et. al. J. Phys. Soc. Jpn 77, 083704 (2008)] that the transition temperature is highest when the tetrahedra are regular. Why should this matter? One possible line of thinking is as follows: it is either known or generally believed, from the cuprates etc., that superconducting transition temperatures are anomalously high near quantum critical points. Therefore if there were criticality associated with the perfect tetrahedral shape, you might expect criticality and hence a high transition temperature. What the Coleman paper shows is that, at least for the simplified model of a single tetrahedron in a bath, there is in fact criticality, which has to do with the degeneracy of orbitals in a perfect tetrahedron. It is a long way from proving anything directly about superconductivity but is in any case a highly interesting result.]