Plutonium and quantum criticality (continued)

The idea of a gossamer condensate was originally introduced by Bob Laughlin to explain the relationship between superconductivity and antiferromagnetism in high-critical-temperature (high-Tc) superconductors. Subsequently, it was suggested by Laughlin’s students Zario Navario and David Santiago and me in a paper that appeared in Philosophical Magazine B in 2005 (Volume 85, Page 867) that there may be a gossamer condensate in all materials that have “metal–bad metal” transitions similar to the α -> γ transition in cerium. The quasi-particle gap for this condensate would be very small, leading to metal-like behavior for all pressures. In cases such as elemental cerium, praseodymium, and gadolinium, where the metal–bad metal transition is accompanied by “volume collapse,” a plot of the gossamer order parameter versus pressure would correspond to the van der Waals-like “loops” in the fi gure below, where the transition pressure would be determined by a Maxwell construction (the dotted lines).

In other cases, such as elemental neodymium or samarium, or cerium–thorium alloys doped with lanthanum, where the metal–bad metal transition is continuous, the transition would correspond to the critical inflection point in the figure.

The decrease in electrical conductivity in a gossamer metal is due to a decrease in the number of charge carriers rather than a decrease in carrier mobility. This is a very different picture from that of a Mott metal-insulator transition. In any case, though, the continuous “metal–bad metal” transitions in rare-earth materials cannot be Mott metal-insulator transitions since Mott transitions are always first-order transitions.

That the differences between the alpha (α) and δ forms of plutonium might be related to the α -> γ transition in cerium has been discussed for some time. Barry Cooper also pointed out in his article in the “Challenges in Plutonium Science” issue of Los Alamos Science that δ plutonium may be analogous to the critical point in the phase diagram of uranium sulfide doped with lanthanum where magnetism disappears. Doping with lanthanum changes the 5f-p/d hybridization, and at a critical dopping

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