The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu$_2$Si$_2$. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such a
nisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu$_2$Si$_2$.
Here we provide the first clear evidence of Fermi-liquid breakdown in an intermediate valence system. We employ high precision magnetization measurements of the valence fluctuating superconductor beta-YbAlB4 to probe the quantum critical free energy
down to temperatures far below the characteristic energy scale of the valence fluctuations. The observed T/B scaling in the magnetization over three decades not only indicates unconventional quantum criticality, but places an upper bound on the critical magnetic field |B_c| < 0.2 mT, a value comparable with the Earths magnetic field and six orders of magnitude smaller than the valence fluctuation scale. This tiny value of the upper bound on B_c, well inside the superconducting dome, raises the fascinating possibility that valence fluctuating beta-YbAlB4 is intrinsically quantum critical, without tuning the magnetic field, pressure, or composition: the first known example of such a phenomenon in a metal.
Motivated by recent quantum oscillations experiments on URu_2Si_2, we discuss the microscopic origin of the large anisotropy observed many years ago in the anomaly of the nonlinear susceptibility in this same material. We show that the magnitude of t
his anomaly emerges naturally from hastatic order, a proposal for hidden order that is a two-component spinor arising from the hybridization of a non-Kramers Gamma_5 doublet with Kramers conduction electrons. A prediction is made for the angular anisotropy of the nonlinear susceptibility anomaly as a test of this proposed order parameter for URu_2Si_2.
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 c
ondensate. 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}.
This online material provides the technical detail for ``Heavy electrons and the symplectic symmetry of spin,(arXiv 0710.1122). Three parts. Part I - symplectic spins, their properties and gauge symmetries. Part II - derivation of two-chanel model fo
r tetragonal heavy electron systems with the view to application to PuCoGa5 and NpPd_5Al_2, symplectic-N mean field theory and computation of NMR relaxation rate. Part III - brief discussion of the application to frustrated magnetism in the J1-J2 model, mainly used to test the method.
Physicists have long debated whether the hidden order in URu2Si2 is itinerant or localized, and it remains inaccessible to direct external probes. Recent observation of an overdamped collective mode in this material (C. Weibe et al, Nature Physics 3,
96-100 (2007)), appears to resolve this outstanding issue.
