Ivana Mrkonjić

The Luttinger sum rule in the slave-particle theories

Abstract.The usual mean field decoupling procedure applied to the slave-particle representations of the problems with strong local interaction produces a resonant band, but violates the Luttinger sum rule for the physical single-electron propagator. The number of occupied resonant states is small and equal to the deviation from the sum rule, shedding doubt on the overall results. It is therefore argued and illustrated on the example of the Emery model for the high-Tc superconductors that, through the consistent application of the mean field procedure to the Hamiltonian and the propagators, the sum rule is restored and the resonant band conserved. In addition to the resonant band, the electron spectrum contains large number of occupied states close to the bare site-energy of the site with strong repulsion. These results are also related here to the other similar decoupling problems, which also lead to the breakdown of the Luttinger sum rule.

Chaotic Properties of the Elliptical Stadium Billiard

The two-parameter family of elliptical stadium billiards is discussed. Special attention is paid to the one-parameter subfamily inscribed into the square which interpolates between the circle and the square. It is shown that the classical dynamics of such system is mixed for all values of the shape parameter. For the same system the quantal spectra and wave functions are calculated, and the classical and quantal chaotic fraction values are compared. Other types of elliptical stadium billiards are briefly discussed.

Slave Boson Description of CuO2 Planes of the High-Temperature Superconductors

Slave-boson mean-field calculation is carried out analytically for doped CuO2 conduction planes, described by the extended Emery model which is parameterized by Cu–O charge transfer energy Δpd, Cu–O hopping t0, O–O hopping t′ and Coulomb repulsion U localized on Cu site, taken as infinite. At zero doping δ, finite small t′ expands the range of stability of the covalent, conducting state, characterized by renormalized band parameters Δpf and t, on the expense of insulating t=0 state, which, however, remains stable at larger Δpd. For sufficiently large Δpd, Δpf saturates at 4|t′|. Finite doping suppresses the insulating state nearly symmetrically with respect to its sign. The regime with Δpf close to 4|t′| fits remarkably well ARPES spectra of Y123, Bi2212 and LSCO, and, in the latter case, explains the observed strong doping-dependence of the effective Cu–O hopping.

Oxygen-Related Band-Features of the Extended Emerymodel for the Hts Cuprates

We examine the band properties of the extended Emery model, parameterized by Cu-O charge transfer energy Δpd, copper-oxygen overlap t0, oxygen-oxygen overlap t′ and Coulomb interaction U on the copper site. In the charge-transfer limit U ≫ Δpd > t, t′, it retains realistic three band structure, unlike the usually used Hubbard model. Neglecting the ordering of spin degrees of freedom, infinite U slave boson mean field approximation is used to calculate at small doping δ the renormalization trends of the effective band parameters Δpf and t, replacing Δpd and t0, while t′, related exclusively to oxygens, remains unchanged. It is shown that small, negative t′ expands the range of stability of the metallic phase, changing, through the higher order corrections in t′, the thermodynamical nature of the metal-insulator transition point. In the nonperturbative limit, t′ modifies qualitatively the renormalization of Δpf at zero doping, making it saturate at the value of 4|t′| and keeping thus the system in the regime of strong correlations. Finite doping δ suppresses the insulating t = 0 state approximately symmetrically with respect to its sign. The regime δpf ≈ 4|t′| fits very well the ARPES spectra of LSCO and also explains the evolution of the FS with doping accompanied by the spectral weight- transfer from the oxygen to the resonant band. Additionally, the values of the band- parameters Δpf /t′ and t/t′ are allowed to vary freely, in order to describe the ARPES data on LSCO, thus providing the direct insight in the role of oxygens, underestimated in the magnetic t-J limit of the large U Emery model. The important role in this theory is played by the effective Cu-O overlap t, very small in the underdoped HTS cuprates and evolving to the values of the order of t′ at larger doping.