We report on the interplay of localized and extended degrees of freedom in the metallic state of high-temperature superconductors in a multiband setting. Various ways in which the bare magnetic response may become incommensurate are measured against both phenomenological and theoretical requirements. In particular, the pseudogap temperature is typically much higher than the incommensurability temperature. When microscopic strong-coupling effects with real-time dynamics between copper and oxygen sites are included, they tend to restore commensurability. Quantum transport equations for low-dimensional multiband electronic systems are used to explain the linear doping dependence of the dc conductivity and the doping and temperature dependence of the Hall number in the underdoped LSCO compounds. Coulomb effects of dopands are inferred from the doping evolution of the Hartree-Fock model parameters.

The single-band current-dipole Kubo formula for the dynamical conductivity of heavily doped graphene from Kupčić [Phys. Rev. B 91, 205428 (2015)] is extended to a two-band model for conduction π electrons in lightly doped graphene. Using a posteriori relaxation-time approximation in the two-band quantum transport equations, with two different relaxation rates and one quasiparticle lifetime, we explain a seemingly inconsistent dependence of the dc conductivity σ dc αα of ultraclean and dirty lightly doped graphene samples on electron doping, in a way consistent with the charge continuity equation. It is also shown that the intraband contribution to the effective number of conduction electrons in σ dc αα vanishes at T = 0 K in the ultraclean regime, but it remains finite in the dirty regime. The present model is shown to be consistent with a picture in which the intraband and interband contributions to σ dc αα are characterized by two different mobilities of conduction electrons, the values of which are well below the widely accepted value of mobility in ultraclean graphene. The dispersions of Dirac and π plasmon resonances are reexamined to show that the present, relatively simple expression for the dynamical conductivity tensor can be used to study simultaneously single-particle excitations in the dc and optical conductivity and collective excitations in energy loss spectroscopy experiments. PACS numbers: 72.80.Vp, 72.10.Di, 78.67.Wj, 71.45.Gm Keywords: quantum transport equations, lightly doped graphene, dc and optical conductivity, energy loss spectroscopy , (8) J J µ J J ν µ ν J J ν µ J J ν µ J J ν µ FIG. 2: The Bethe-Salpeter expression for the 4 × 4 currentcurrent correlation function πµν (q, i νn) [14, 21]. 2A 2B 2 J J µ ν J J µ ν J J µ ν J J µ ν 2A 1 J J µ ν

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The role of the oxygen degree of freedom in the cuprates' superconducting planes is analyzed in detail. Structural and photoemission results are reviewed to show that the most sparse description of the in-plane electronic states requires explicit control of the oxygens. For metallic states, the relative contributions of oxygen and copper vary along the Fermi surface (FS), with the arc metallicity dominantly oxygen-derived. For the magnetic responses, we find that the observed incommensurability arises naturally if one keeps separate the roles of the two sites. For the charge order in LBCO, we propose a scenario, based on magnetic interactions in the plane. We stress the need for further experimental investigations of the evolution of the intracell charge distribution with doping, and for a better theoretical understanding of the large particle-hole-symmetry breaking required for successful phenomenologies, but difficult to reconcile with ab initio calculations.

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