Frequency Evolution of Neutron Peaks Below Tc: Commensurate and Incommensurate Structure in LaSrCuO and YBaCuO

We study the evolution of the neutron cross-section with variable frequency $\omega$ and fixed $T$ below $T_c$ in two different cuprate families. Our calculations, which predominantly probe the role of d-wave pairing, lead to generic features, independent of Fermi surface shapes. Among our findings, reasonably consistent with experiment, are (i) for $\omega$ near the gap energy $\Delta$, both optimal {LaSrCuO} and slightly underdoped YBCO exhibit (comparably) incommensurate peaks (ii) peak sharpening below $T_c$ is seen in {LaSrCuO}, (iii) quite generically, a frequency evolution from incommensurate to commensurate and then back to incommensurate structure is found with increasing $\omega$. Due to their narrow $\omega$ regime of stability, commensurate peaks in {LaSrCuO} should be extremely difficult to observe.Comment: RevTex 5pages, 4figures; Manuscript rewritten, figures revised, and direct comparisons with experiments adde

Commensurate and Incommensurate Structure of the Neutron Cross Section in LaSrCuO and YBaCuO

We study the evolution of the d-wave neutron cross-section with variable frequency \omega and fixed T (below and above Tc) in two different cuprate families. The evolution from incommensurate to commensurate to incommensurate peaks is rather generic within an RPA-like scheme. This behavior seems to be in reasonable accord with experiments, and may help distinguish between this and the "stripe" scenario.Comment: 2 pages; submitted to Proceedings of M2S-HTSC-V

Hole dynamics in an antiferromagnet across a deconfined quantum critical point

We study the effects of a small density of holes, delta, on a square lattice antiferromagnet undergoing a continuous transition from a Neel state to a valence bond solid at a deconfined quantum critical point. We argue that at non-zero delta, it is likely that the critical point broadens into a non-Fermi liquid `holon metal' phase with fractionalized excitations. The holon metal phase is flanked on both sides by Fermi liquid states with Fermi surfaces enclosing the usual Luttinger area. However the electronic quasiparticles carry distinct quantum numbers in the two Fermi liquid phases, and consequently the limit of the ratio A_F/delta, as delta tends to zero (where A_F is the area of a hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. We demonstrate that the electronic spectrum at this transition is described by the `boundary' critical theory of an impurity coupled to a 2+1 dimensional conformal field theory. We compute the finite temperature quantum-critical electronic spectra and show that they resemble "Fermi arc" spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.Comment: 33 pages, 8 figures, Longer version of cond-mat/0611536, with additional results for electron spectrum at non-zero temperatur

Superconducting Order Parameter in Bi-Layer Cuprates: Occurrence of π\pi Phase Shifts in Corner Junctions

We study the order parameter symmetry in bi-layer cuprates such as YBaCuO, where interesting $\pi$ phase shifts have been observed in Josephson junctions. Taking models which represent the measured spin fluctuation spectra of this cuprate, as well as more general models of Coulomb correlation effects, we classify the allowed symmetries and determine their associated physical properties. $\pi$ phase shifts are shown to be a general consequence of repulsive interactions, independent of whether a magnetic mechanism is operative. While it is known to occur in d-states, this behavior can also be associated with (orthorhombic) s-symmetry when the two sub-band gaps have opposite phase. Implications for the magnitude of $T_c$ are discussed.Comment: 5 pages, RevTeX 3.0, 9 figures (available upon request

Quantum Criticality and Global Phase Diagram of Magnetic Heavy Fermions

Quantum criticality describes the collective fluctuations of matter undergoing a second-order phase transition at zero temperature. It is being discussed in a number of strongly correlated electron systems. A prototype case occurs in the heavy fermion metals, in which antiferromagnetic quantum critical points have been explicitly observed. Here, I address two types of antiferromagnetic quantum critical points. In addition to the standard description based on the fluctuations of the antiferromagnetic order, a local quantum critical point is also considered. It contains inherently quantum modes that are associated with a critical breakdown of the Kondo effect. Across such a quantum critical point, there is a sudden collapse of a large Fermi surface to a small one. I also consider the proximate antiferromagnetic and paramagnetic phases, and these considerations lead to a global phase diagram. Finally, I discuss the pertinent experiments on the antiferromagnetic heavy fermions, briefly address the case of ferromagnetic heavy fermions, and outline some directions for future studies.Comment: (v2) reference added, and typos corrected; (v1) 10 pages, 2 figures, based on a plenary talk given at the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden

Magnetic interactions in the metallic phase of the copper oxides: A Fermi-liquid description

One of the central issues in the field of high-temperature superconductivity is whether the normal state can be described by Fermi-liquid theory. Recent photoemission experiments along with a growing body of Fermi-liquid-based theoretical work have provided some support for this viewpoint. However, one major concern in ascertaining the validity of a Fermi-liquid approach is whether the magnetic interactions in the metallic cuprates are sufficiently strong so as to undermine the usual Fermi-liquid description. In this paper we address this question by examining the nature of the magnetic interactions in the metallic state. These interactions, which are dominantly between the Cu spins, arise via the intermediating oxygenlike states. Since the oxygen character changes as the hole doping is increased, it is expected that the Cu-Cu interactions are doping sensitive and evolve away from their value in the insulating limit. We deduce these interactions within a physical picture in which the Cu d electrons are nearly localized and the oxygen bandwidth assumes a finite value. While our qualitative results are general, we use a 1/N expansion as a convenient theoretical tool. In the extended Hubbard Hamiltonian the exchange terms are evaluated at order (1/N2). Both superexchange (JS) and Ruderman-Kittel-Kasuya-Yosida interactions (JR) emerge on a similar footing. With increasing carrier concentration, JS decreases rapidly, while JR abruptly increases from zero. We find that, because of the reduction in the strength of the superexchange, there is an enhanced stability of the Fermi-liquid phase. The dynamical susceptibility is also calculated within this scheme and the consequences for NMR and neutron experiments are discussed elsewhere

Phenomenological description of the copper oxides as almost localized Fermi liquids

We demonstrate that a variety of normal-state properties of the cuprates are similar to what is observed in heavy-fermion metals, provided that the temperature or frequency are rescaled. This leads to a characteristic energy scale Tcoh 150 K and suggests that the non-Fermi-liquid-like behavior of the cuprates is related to the high-temperature breakup of coherence of a Fermi-liquid ground state. We propose a concrete physical picture for future theories and give predictions which can be tested

Comparison of spin dynamics in YBa2Cu3O7-δ and La2-xSrxCuO4: Effects of Fermi-surface geometry

Neutron experiments have indicated that the structure factor S(q,ω) for the two cuprates YBa2Cu3O7-δ and La2-xSrxCuO4 has a different q dependence. Commensurate peaks at (π/a,π/a) are observed in the former case, whereas clearly incommensurate peaks are seen in the latter, for metallic hole concentrations. We attribute this contrasting q dependence to differences in the Fermi-surface geometry, obtained in band-structure approaches, and (for the YBaCuO system) also corroborated by photoemission experiments. Using a large Coulomb-U, Fermi-liquid-based scheme, we present results for the q,ω and temperature dependence of the neutron cross section as well as for the temperature dependence of the NMR relaxation, in both cuprate families at various hole concentrations. When antiferromagnetic quasiparticle interactions of moderate strength are included, these calculations compare favorably with experiment. It should be stressed that the Fermi-surface shape must be accurately represented in both systems in order to produce this good agreement with the neutron data. We conclude that the close correspondence found, thus far, between band-structure-derived spin dynamics and the detailed fermiology of both cuprates provides support for Fermi-liquid-based schemes. Furthermore, this correspondence suggests important constraints which should be included in theoretical schemes ranging from the marginal and nearly antiferromagnetic Fermi liquid to more exotic scenarios for the normal state. Within this context, it is extremely important to determine the characteristic energy scales of the Fermi liquid. Comparison of our calculations with the measured energy scales of the spin dynamics indicates that these are sufficiently low so that one can reconcile deviations from canonical behavior above Tc with a Fermi-liquid ground state. Explicit effects of these low-energy scales are discussed in the context of the quasiparticle lifetime as a function of frequency and temperature. Our detailed studies also yield predictions for future experiments which will help to test futher the validity of this approach

NMR relaxation and neutron scattering in a Fermi-liquid picture of the metallic copper oxides

Using a Fermi-liquid formalism in which the Cu d electrons are quasilocalized, we calculate the NMR relaxation for the Cu and O sites, the temperature-dependent magnetic susceptibility, and the neutron-scattering cross section. Our microscopic calculations of the dynamical susceptibility help to decouple narrow-band phenomena from spin-fluctuation effects. The former lead to a low (coherence) energy scale and considerable structure in the Lindhard function. The latter help to enhance these effects

Theory of Neutron Scattering in the Normal and Superconducting State of YBCO

We analyze neutron experiments on \ybco at various stoichiometries in the superconducting state, within the context of a bi-layer theory which yields good agreement with the normal state Cu-NMR and neutron data as a function of \omega, q and T. A d-wave superconducting state exhibits peaks at q = ( \pi , \pi , \pi ) and sharp maxima as a function of \omega, at twice the gap frequency. This behavior may have been observed experimentally. The counterpart behavior for other choices of order parameter symmetry is discussed.Comment: uuencoded postscript file for the entire paper enclose