I am a condensed matter theorist at Iowa State University, working on various problems in strongly correlated electronic systems. I tend to be interested in translating abstract theoretical ideas to real materials, and vice versa. I was an undergraduate in physics at Caltech, a graduate student in the condensed matter theory group at Rutgers University and most recently a Simons Postdoctoral Fellow in the condensed matter theory group at MIT. My curriculum vitae. |
The search for fundamentally new states of matter is a major driving force in condensed matter, and the peculiar regime between local and itinerant physics is one of the most fruitful places to look. Here, strong electronic correlations realize exotic phases not simply related to free electrons or their Fermi surface instabilities. Instead, these phases are characterized by new broken symmetries or even topological order, and these materials can carry low energy collective modes that fractionalize the electron's charge and spin. For example, spin liquids are magnetic states that break no symmetries, and yet form a highly correlated topologically ordered state with neutral spin 1/2 excitations. There are now several good spin liquid candidates, but it is necessary to examine how realistic models affect the spin liquid physics. Currently, I am interested in the possible chiral spin liquid in Pr_{2}Ir_{2}O_{7} and in how to realize the J_{1}-J_{2} honeycomb lattice spin liquid in real d-electron materials. Heavy fermion materials also realize a variety of exotic phases; these materials combine electrons from the two extremes: localized electrons, which form magnetic moments or spins, and itinerant electrons, which form a metallic band. At low temperatures, these two species become strongly entangled as the itinerant electrons screen the local moments, effectively melting the spins to form a heavy Fermi liquid. When there are two, competing screening channels instead of one, the two channels ultimately cooperate to melt the spins into an exotic symmetry-breaking phase composite pair superconductivity, which is a purely local mechanism for d-wave superconductivity relevant to the 115 materials, and hastatic order, a time-reversal symmetry breaking phase without any large moments that describes the hidden order in URu_{2}Si_{2}. I am currently working to extend these ideas to Pr based materials. |
The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded identification. Here we argue that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor hybridization order parameter that breaks double time-reversal symmetry by mixing states of integer and half-integer spin. Such "hastatic order" (hasta:[Latin]spear) hybridizes Kramers conduction electrons with Ising, non-Kramers 5f2 states of the uranium atoms to produce Ising quasiparticles. The development of a spinorial hybridization at 17.5K accounts for both the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. This paper develops the theory of hastatic order in detail, providing the mathematical development of its key concepts. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states. |
The recent observation of fully-gapped superconductivity in Yb doped CeCoIn_{5} poses a paradox, for the disappearance of nodes suggests that they are accidental, yet d-wave symmetry with protected nodes is well established by experiment. Here, we show that composite pairing provides a natural resolution: in this scenario, Yb doping drives a Lifshitz transition of the nodal Fermi surface, forming a fully-gapped d-wave molecular superfluid of composite pairs. The T^{4} dependence of the penetration depth associated with the sound mode of this condensate is in accord with observation. |
The London penetration depth, lambda(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd and Yb down to Tmin = 50 mK (Tc/Tmin > 50) using a tunnel-diode resonator. In the cleanest samples lambda(T) is best described by the power law, lambda(T) , with n = 1, consistent with line nodes. Substitutions of Ce with La, Nd and Yb lead to similar monotonic suppressions of Tc, however the effects on lambda(T) differ. While La and Nd doping results in an increase of the exponent to n = 2, as expected for a dirty nodal superconductor, Yb doping leads to n>3, inconsistent with nodes, suggesting a change from nodal to nodeless superconductivity where Fermi surface topology changes were reported, implying that the nodal structure and Fermi surface topology are closely linked. |
The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu2Si2. 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 anisotropic 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 URu2Si2. |
The hidden order developing below 17.5K in the heavy fermion material URu2Si2 has eluded identification for over twenty five years. This paper will review the recent theory of ``hastatic order,'' a novel two-component order parameter capturing the hybridization between half-integer spin (Kramers) conduction electrons and the non-Kramers 5f^2 Ising local moments, as strongly indicated by the observation of Ising quasiparticles in de Haas-van Alphen measurements. Hastatic order differs from conventional magnetism as it is a spinor order that breaks both single and double time-reversal symmetry by mixing states of different Kramers parity. The broken time-reversal symmetry simply explains both the pseudo-Goldstone mode between the hidden order and antiferromagnetic phases and the nematic order seen in torque magnetometry. The spinorial nature of the hybridization also explains how the Kondo effect gives a phase transition, with the hybridization gap turning on at the hidden order transition as seen in scanning tunneling microscopy. Hastatic order also has a number of new predictions: a basal-plane magnetic moment of order .01\mu_B, a gap to longitudinal spin fluctuations that vanishes continuously at the first order antiferromagnetic transition and a narrow resonant nematic feature in the scanning tunneling spectra. |
Adding a second Kondo channel to heavy fermion materials reveals new exotic symmetry breaking phases associated with the development of Kondo coherence. In this paper, we review two such phases, the "hastatic order" associated with non-Kramers doublet ground states, where the two-channel nature of the Kondo coupling is guaranteed by virtual valence fluctuations to an excited Kramers doublet, and "composite pair superconductivity," where the two channels differ by charge 2e and can be thought of as virtual valence fluctuations to a pseudo-isospin doublet. The similarities and differences between these two orders will be discussed, along with possible realizations in actinide and rare earth materials like URu2Si2 and NpPd5Al2. |
We introduce the idea of emergent lattices, where a simple lattice decouples into two weakly-coupled lattices as a way to stabilize spin liquids. In LiZn2Mo3O8, the disappearance of 2/3rds of the spins at low temperatures suggests that its triangular lattice decouples into an emergent honeycomb lattice weakly coupled to the remaining spins, and we suggest several ways to test this proposal. We show that these orphan spins act to stabilize the spin-liquid in the J_{1}-J_{2} honeycomb model and also discuss a possible 3D analogue, Ba2MoYO6 that may form a "depleted fcc lattice." * Editor's suggestion |
Motivated by the potential chiral spin liquid in the metallic spin ice Pr_{2}Ir_{2}O_{7}, we consider how such a chiral state might be selected from the spin ice manifold. We propose that chiral fluctuations of the conducting Ir moments promote ferro-chiral couplings between the local Pr moments, as a chiral analogue of the magnetic RKKY effect. Pr_{2}Ir_{2}O_{7} provides an ideal setting to explore such a chiral RKKY effect, given the inherent chirality of the spin-ice manifold. We use a slave-rotor calculation on the pyrochlore lattice to estimate the sign and magnitude of the chiral coupling, and find it can easily explain the 1.5K transition to a ferro-chiral state. * Editor's Suggestion |
The development of collective long-range order via phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry while superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5K in the heavy fermion compound URu_{2}Si_{2} has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu_{2}Si_{2} results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such hastatic order hybridizes conduction electrons with Ising 5f^{2} states of the uranium atoms to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states. |
The microscopic nature of the hidden order state in URu_{2}Si_{2} is dependent on the low-energy configurations of the uranium ions, and there is currently no consensus on whether it is predominantly 5f^{2} or 5f^{3}. Here we show that measurement of the basal-plane nonlinear susceptibility can resolve this issue; its sign at low-temperatures is a distinguishing factor. We calculate the linear and nonlinear susceptibilities for specific 5f^{2} and 5f^{3} crystal-field schemes that are consistent with current experiment. Because of its dual magnetic and orbital character, a ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â½ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã¢â‚¬Å“_{5} magnetic non-Kramers doublet ground-state of the U ion can be identified by ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚ÂÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡_{1}^{c}(T)/ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚ÂÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡_{3}^{ab}(T) where we have determined the constant of proportionality for URu_{2}Si_{2}. |
Motivated by recent quantum oscillations experiments on URu_{2}Si_{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 this 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 ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â½ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã¢â‚¬Å“_{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_{2}Si_{2}. |
The possible discovery of s_{ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Â¦Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â±} superconducting gaps in the moderately correlated iron-based superconductors has raised the question of how to properly treat s_{ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€šÃ‚Â ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¾Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¾ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¦ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€šÃ‚Â ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¾Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Â¦Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€šÃ‚Â¦ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Â¦Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â±} gaps in strongly correlated superconductors. Unlike the d-wave cuprates, the Coulomb repulsion does not vanish by symmetry, and a careful treatment is essential. Thus far, only the weak correlation approaches have included this Coulomb pseudopotential, so here we introduce a symplectic N treatment of the t-J model that incorporates the strong Coulomb repulsion through the complete elimination of on-site pairing. Through a proper extension of time-reversal symmetry to the large N limit, symplectic-N is the first superconducting large N solution of the t-J model. For d-wave superconductors, the previous uncontrolled mean field solutions are reproduced, while for s_{ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Â¦Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â±} superconductors, the SU(2) constraint enforcing single occupancy acts as a pair chemical potential adjusting the location of the gap nodes. This adjustment can capture the wide variety of gaps proposed for the iron based superconductors: line and point nodes, as well as two different, but related full gaps on different Fermi surfaces. |
Using a two-channel Anderson model, we develop a theory of composite pairing in the 115 family of heavy fermion superconductors that incorporates the effects of f-electron valence fluctuations. Our calculations introduce ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â‚¬Å¾Ã‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¡ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Â ÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â€šÂ¬Ã…Â¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¦ÃƒÆ’Ã†â€™Ãƒâ€ Ã¢â‚¬â„¢ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã†â€™Ãƒâ€šÃ‚Â¢ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã‚Â¡ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â¬ÃƒÆ’Ã†â€™ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â¦ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬Ãƒâ€¦Ã¢â‚¬Å“symplectic Hubbard operators" an extension of the slave boson Hubbard operators that preserves both spin rotation and time-reversal symmetry in a large N expansion, permitting a unified treatment of anisotropic singlet pairing and valence fluctuations. We find that the development of composite pairing in the presence of valence fluctuations manifests itself as a phase-coherent mixing of the empty and doubly occupied configurations of the mixed valent ion. This effect redistributes the f-electron charge within the unit cell. Our theory predicts a sharp superconducting shift in the nuclear quadrupole resonance frequency associated with this redistribution. We calculate the magnitude and sign of the predicted shift expected in CeCoIn_{5}. |
We consider the internal structure of a d-wave heavy-fermion superconducting condensate, showing that it necessarily contains two components condensed in tandem: pairs of quasiparticles on neighboring sites and composite pairs consisting of two electrons bound to a single local moment. These two components draw upon the antiferromagnetic and Kondo interactions to cooperatively enhance the superconducting transition temperature. This tandem condensate is electrostatically active, with an electric quadrupole moment predicted to lead to a superconducting shift in the nuclear quadrupole resonance frequency. |
Here, we introduce a new class of large-N expansion that uses symplectic symmetry to protect the odd time-reversal parity of spin and sustain Cooper pairs as well-defined singlets. We show that when a lattice of magnetic ions exchange spin with their metallic environment in two distinct symmetry channels, they can simultaneously satisfy both channels by forming a condensate of composite pairs between local moments and electrons. We then discuss the application of this two channel Kondo model to the heavy fermion superconductors, PuCoGa_{5} and NpPd_{5}Al_{2}. The inclusion of spin-orbit coupling and the crystal fields predicts a g-wave superconducting order parameter. |
In this paper, we develop a new large N treatment of the Heisenberg model based on symplectic-N, represent the spins by Schwinger bosons, which allows us study the boundaries between short-range and long-range order. This limit treats ferromagnetic and antiferromagnetic correlations simultaneously, exacting an energy cost for frustrating antiferromagnetic bonds. As an example, we treated the two dimensional J1-J2 model, where the symplectic-N phase diagram improves over previous large N treatments both at zero and finite temperatures. |
Ca_{3}Co_{2-x}Mn_{x}O_{6}(x ~ 0.96) is a multiferroic with spin-chains of alternating Co^{2+} and Mn^{4+} ions. The spin state of Co^{2+} remains unresolved, as there is a discrepancy between high temperature X-ray absorption (S= 3/2) and low temperature neutron (S= 1/2) measurements. Here we study the high-field magnetization using magnetic modeling and confirm the small Co moment. With crystal-field analysis, we show that neither spin orbit coupling nor Jahn-Teller distortions yield a small effective moment with large anisotropy at low temperatures within the high spin (S = 3/2) scenario, while the low spin (S=1/2) can explain both the small moment and large anisotropy. In order to unify the experimental results, we propose a spin-state crossover, and make a number of specific predictions for experiment. |
Strongly correlated electrons provide a unique challenge to theorists as they sit at the intersection of the kinetic and potential energy scales, where traditional, perturbative many body techniques fail. To make progress, we must develop non-perturbative methods. One method that has had some success here is large N theory, which generalizes the number of components of the electron spin from 2 to N, providing an artificial perturbation expansion about a strongly correlated state which, if chosen properly, captures the essential physics. Large N has been heavily used in both the Kondo lattice and in frustrated magnetism, where SU(2N) is the traditional generalization of the electron spin group, SU(2). In choosing the large N group, we chose which symmetries to preserve and which to discard. Unfortunately, SU(2N) inadvertently loses the time inversion and charge conjugation properties of SU(2); while some generators invert under time reversal like spins, $\vec{S} \rightarrow -\vec{S}$, and remain neutral under charge conjugation, the others behave more like electric dipoles: neutral under time reversal and flipped by charge conjugation. To treat phenomena like frustrated magnetism and superconductivity, which relies on the formation of Cooper pairs, we must restrict ourselves to the subgroup of spin-like generators, SP(2N), a large N limit we call symplectic-N. This limit differs from the SP(2N) limit introduced by Sachdev and Read, which breaks the SU(2N) symmetry of the Hamiltonian down to SP(2N) in that the interaction Hamiltonian is constricted solely from symplectic spins. Symplectic-N has been successfully applied to frustrated magnetism, where it treats ferromagnetic and antiferromagnetic correlations simultaneously, and to the two channel Kondo model, where it treats the Kondo effect and superconductivity simultaneously. We are currently working to develop symplectic-N Hubbard operators to treat the t-J and Anderson models. |