Qimiao Si

Normal state properties in the cuprates and their Fermi liquid based interpretation

Abstract A central issue in the field of high temperature superconductivity is the nature of the normal state. Here we review normal state transport, thermodynamic, magnetic and spectroscopic data and discuss their interpretation within a Fermi liquid based framework. Comparison with other highly correlated systems, such as the heavy fermnion metals and the quantum liquid 3 He, is also presented. It is demonstrated that the cuprate data are not consistent with canonical Fermi liquid behavior. However, if the Fermi liquid is characterized by low energy scales, arising from narrow bandwidths or soft spin fluctuations, then canonical behavior is not expected at the relatively “high” temperatures of the normal state. In this way anomalies above T c may be reconciled with a Fermi liquid (ground state) picture. Here we review the two main Fermi liquid based schools and their interpretation of the data. These are the ”almost localized” and “almost magnetic” Fermi liquid descriptions. The dichotomy between these two nearinstabilities has appeared in the context of the heavy fermoins as well as liquid 3 He and seems to be generally associated with highly correlated systems. Both approaches have addressed the data with some success and it is clear that they are, in many respects, closely related. The relationship between other Fermi-liquid-like, as well as more unconventional schemes is also addressed. Here it is claimed that the strongest support for a Fermi liquid based approach to the cuprates derives from the comparison with other strongly correlated Fermi liquid systems, which exhibit similar normal state anomalies.

Microscopic Fermi liquid theory of NMR relaxation and neutron scattering in the metallic copper oxides

Abstract We calculate the NMR relaxation rates for the Cu and O sites, the temperature dependent magnetic susceptibility and the inelastic neutron scattering cross section using the dynamical RPA susceptibility derived previously. This approach is a Fermi liquid based scheme in which the Cu d electrons are (on the basis of considerable experimental evidence) assumed to be quasi-localized. These narrow band effects lead to low energy scales, T coh below which the Cu d electrons are fully coherent and a “one component” picture is applicable. Above this characteristic temperature the d electrons begin to lose their coherence, although they are still strongly coupled to the p orbitals. This coherence energy scale, along with the exchange interactions J H completely determine the characteristic temperatures and frequencies which appear in NMR and neutron data. Our calculations of 1/ T 1 on the Cu sites suggest that the cuprates are not as close to a magnetic instability as has been assumed elsewhere. This is because the coherence energy scale (which appears in the “bare” Lindhard function for the renormalized band structure) already provides an intrinsic “soft” frequency. Consequently, we find that antiferromagnetic interactions are playing a less dominant (but not insignificant) role in magnetic measurements. Analysis of the oxygen relaxation suggests that the sharp antiferromagnetic peaks invoked elsewhere to yield form factor cancellation effects may not be sufficiently robust to explain the data. Indeed, careful numerical calculations yield some degree of non-Korringa behavior on the oxygen sites due to imperfect cancellations of the transfer-hyperfine-coupling induced relaxation. Finally, our calculations of the neutron cross section show incommensurate peaks in the diagonal ( q, q ) and off-diagonal ( q , π) directions, which are found to reflect the detailed Fermi surface geometry of the LaSrCuO system. These peaks become increasingly more incommensurate as the hole concentration increases. These predictions and their comparison with future experiments may help to determine the applicability of Fermi liquid based approaches to the cuprates.

Theory of contrasting spin dynamics in YBa2Cu3O7-δ and La2-xSrxCuO4

Abstract We demonstrate that the commensurate peaks observed in neutron experiments on YBa 2 Cu 3 O 7−δ and the incommensurate structure found for La 2−x Sr x CuO 4 reflect differences in the fermiology of these two cuprates. Strong Coulomb effects, responsible for the Mott insulating parent compound, are essential for our analysis. Agreement with the q and ω, T dependence of the neutron cross section is found as a function of hole concentration for both cuprates, provided antiferromagnetic exchange interactions of moderate strength are included.

Theory of spin dynamics in YBa2Cu3O7−δ: Fermiology effects

Abstract We reconcile the Fermi surface shape observed in photoemission experiments in YBa 2 Cu 3 O 7−δ with recent neutron data. A peak at Q 0 = ( π / a , π / a ) is found for δ = 0.3 as a consequence of the q -dependent exchange interaction. The associated correlation length is roughly T independent, and the T , ω dependences of the peak height are found to be in reasonable agreement with experiment. We present predictions for the (even smaller) peak structure associated with the fully oxygenated system and demonstrate agreement with Cu NMR for both δ values.

Magnetic interactions in the metallic phase of the copper oxides

Abstract The Cu Cu spin interactions arising from a mediating itinerant oxygen band is derived. Using a formalism similar to that which has been applied to heavy fermion metals, we solve for the concentration dependence of both superexchange and RKKY interactions. The former falls off dramatically with increasing dopant concentration, while the latter undergoes a sign change.

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

Abstract The magnetic interactions in the metallic phase of the copper oxides and associated dynamical susceptibility are calculated within a Fermi liquid scheme in which the Cu electrons are nearly localized and the oxygen bandwidth assumes physical values. Both superexchange (JS) and RKKY interactions (JR) emerge from our diagrammatic formalism on a similar footing. With increasing carrier concentration, JS decreases rapidly, while JR abruptly increases from zero. These self consistently determined interactions and “renormalized” bandstructure lead to an enhanced stability of the Fermi liquid phase.

Current Status of Fermi Liquid Based Approaches to the Cuprates

A central issue in the field of high temperature superconductivity is the nature of the normal state. Here we review normal state transport, thermodynamic, magnetic and spectroscopic data and discuss their interpretation within a Fermi liquid based framework. It is demonstrated that the cuprate data are not consistent with canonical Fermi liquid behavior. However, if the Fermi liquid is characterized by low energy scales, arising from narrow bandwidths or soft spin fluctuations, then canonical behavior is not expected at the relatively “high” temperatures of the normal state. We discuss two main Fermi liquid based schools, i.e., the “almost localized” and “almost magnetic” descriptions. Both approaches have addressed the data with some success and it is clear that they are, in many respects, closely related. Here it is claimed that the strongest support for a Fermi liquid based approach to the cuprates derives from the comparison with other strongly correlated Fermi liquid systems, which exhibit similar normal state anomalies.

Metallic copper oxide as an almost localized fermi liquid

Abstract In view of recent photoemission data, a Fermi liquid description of the metallic copper oxides must be taken as a serious contender for a theory of the normal state. We summarize evidence to support a picture in which the Fermi liquid consists of quasi-localized d electrons. The associated electronic and magnetic structure is discussed.

Competition between magnetic and Fermi liquid phases in the copper oxides

Abstract We study the competition between the (hybridized) Fermi-liquid phase and magnetic order using the Cu Cu spin interaction J H derived in the previous paper. The insulating state arises through magnetically driven localization. Within the Fermi-liquid phase spin-spin interactions are predominantly RKKY in nature and may have either sign. While the spin-liquid phase is not discussed, the fact that J H is negative for a range of concentrations will have implications for this phase.