The Spin Gap in the Context of the Boson-Fermion Model for High TcT_c Superconductivity

The issue of the spin gap in the magnetic susceptibility $\chi''(q,\omega)$ in high T_c superconductors is discussed within a scenario of a mixture of localized tightly bound electron pairs in singlet states (bi-polarons) and itinerant electrons. Due to a local exchange between the two species of charge carriers, antiferromagnetic correlations are induced amongst the itinerant electrons in the vicinity of the sites containing the bound electron pairs. As the temperature is lowered these exchange processes become spatially correlated leading to a spin wave-like spectrum in the subsystem of the itinerant electrons. The onset of such coherence is accompanied by the opening of a pseudo gap in the density of states of the electron subsystem whose temperature dependence is reflected in that of $\chi'' (q,\omega)$ near $q =(\pi,\pi)$ where a ``spin gap'' is observed by inelastic neutron scattering and NMR.Comment: 9 pages Latex, 3 figures available upon request. To appear in Physica

Hole Localization in Underdoped Superconducting Cuprates Near 1/8th Doping

Measurements of thermal conductivity versus temperature over a broad range of doping in YBa$_2$Cu$_3$O$_{6+x}$ and HgBa$_2$Ca$_{n-1}$Cu$_n$O$_{2n+2+\delta}$ ($n$=1,2,3) suggest that small domains of localized holes develop for hole concentrations near $p$=1/8. The data imply a mechanism for localization that is intrinsic to the CuO$_2$-planes and is enhanced via pinning associated with oxygen-vacancy clusters.Comment: 4 pages, 4 eps fig.'s, to be published, Phys. Rev.

Spectral and transport properties of doped Mott-Hubbard systems with incommensurate magnetic order

We present spectral and optical properties of the Hubbard model on a two-dimensional square lattice using a generalization of dynamical mean-field theory to magnetic states in finite dimension. The self-energy includes the effect of spin fluctuations and screening of the Coulomb interaction due to particle-particle scattering. At half-filling the quasiparticles reduce the width of the Mott-Hubbard `gap' and have dispersions and spectral weights that agree remarkably well with quantum Monte Carlo and exact diagonalization calculations. Away from half-filling we consider incommensurate magnetic order with a varying local spin direction, and derive the photoemission and optical spectra. The incommensurate magnetic order leads to a pseudogap which opens at the Fermi energy and coexists with a large Mott-Hubbard gap. The quasiparticle states survive in the doped systems, but their dispersion is modified with the doping and a rigid band picture does not apply. Spectral weight in the optical conductivity is transferred to lower energies and the Drude weight increases linearly with increasing doping. We show that incommensurate magnetic order leads also to mid-gap states in the optical spectra and to decreased scattering rates in the transport processes, in qualitative agreement with the experimental observations in doped systems. The gradual disappearence of the spiral magnetic order and the vanishing pseudogap with increasing temperature is found to be responsible for the linear resistivity. We discuss the possible reasons why these results may only partially explain the features observed in the optical spectra of high temperature superconductors.Comment: 22 pages, 18 figure