Heavy electrons and the symplectic symmetry of spin

Abstract

The recent discovery of two heavy fermion materials PuCoGa_{5} and NpPd_{5}Al_{2} which transform directly from Curie paramagnets into superconductors, reveals a new class of superconductor where local moments quench directly into a superconducting condensate. A powerful tool in the description of heavy fermion metals is the large N expansion, which expands the physics in powers of 1/N about a solvable limit where particles carry a large number (N) of spin components. As it stands, this method is unable to jointly describe the spin quenching and superconductivity which develop in PuCoGa_{5} and NpPd_{5}Al_{2}. Here, we solve this problem with a new class of large N expansion that employs the symplectic symmetry of spin to protect the odd time-reversal parity of spin and sustain Cooper pairs as well-defined singlets. With this method we show that when a lattice of magnetic ions exchange spin with their metallic environment in two distinct symmetry channels, they are able to simultaneously satisfy both channels by forming a condensate of composite pairs between between local moments and electrons. In the tetragonal crystalline environment relevant to PuCoGa_{5} and NpPd_{5}Al_{2} the lattice structure selects a natural pair of spin exchange channels, giving rise to the prediction of a unique anisotropic paired state with g-wave symmetry. This pairing mechanism predicts a large upturn in the NMR relaxation rate above T_{c}, a strong enhancement of Andreev reflection in tunneling measurements and an enhanced superconducting transition temperature T_{c} in Pu doped Np_{1-x}Pu_{x}Pd_{5}Al_{2}.Comment: This is a substantially revised version of the original paper, focussing on the high temperature heavy electron superconductors PuCoGa_5 and NpPd_5Al_2. A substantially revised supplementary online material to this paper can be found in arXiv 0710.1128v

SymplecticNand time reversal in frustrated magnetism

“…In bosonic models, this gauge symmetry reduces to the U (1) symmetry discussed earlier becauseσb † σ b † −σ = 0 on site due to symmetrization. In parallel with our current treatment of both ferromagnetism and antiferromagnetism in the Heisenberg model, we are able to treat both the Kondo effect and superconductivity within the two channel Kondo model 27 . The next step is to introduce charge fluctuations while maintaining the symplectic spin closure.…”

Composite pairing in a mixed-valent two-channel Anderson model

“…Of course, there is only one physical empty state, as becomes clear when we restrict these Hubbard operators to the physical subspace. In order to faithfully represent the symplectic spins, the sum of the spin and charge fluctuations must be fixed, [7]. While this constraint is enforced by setting Ψ = 0 in the pure spin model, here we must equate our two types of charge fluctuations, by setting…”

“…Furthermore, the paired state is an anisotropic singlet with nodes. In the case of the Ce 115 materials, this product has d-wave symmetry 7 . Again, we should consider the question of supressing s-wave superconductivity.…”

Non-Fermi liquid regimes with and without quantum criticality in Ce 1− x Yb x CoIn 5

“…Specifically, when magnetic ions in a lattice exchange a spin with their metallic environment in two distinct symmetry channels, they become overscreened, forming a condensate of composite pairs. In this picture, both the local moments and the electron pairs are involved in the formation of the superconducting condensate-hence the name composite pairing (34,35). Therefore, within the framework of composite pairing theory, it is natural to expect that the magnetic QCP will have little effect on the origin of unconventional SC.…”