Intermediate Phase in the Superconducting Cuprates.

It has long been speculated that upon doping the Mott-Hubbard insulator may go through an intermediate phase before becoming a Fermi-liquid metal. If there is such a phase its structure may be intimately connected to the mechanism of the pseudogap and superconductivity. The only well-defined and popular option has been the spin-charge stripe phase, but the strongly one-dimensional nature of the stripe phase is at odds with the highly two-dimensional CuO$_{2}$ plane. We propose a superlattice of $2\sqrt 2 \times 2\sqrt 2 $ in the $a-b$ plane as an alternative candidate for the intermediate phase. In this phase the Mott-Hubbard states and the Fermi-liquid phase coexist in different Brillouin sub-zones. The presence of such a phase is consistent with the recent results of the ARPES at a high energy scale (J. Graf, \textit{et al.}, \textit{cond-mat/}0607319), dispersion of Cu-O bond-stretching phonon mode in YBCO, pulsed neutron PDF analysis of LSCO, and our recent observation of the supperlattice peaks in YBa$_{2}$Cu$_{4}$O$_{8}$ single crystal by x-ray diffraction. The intensity of the superlattice peaks in YBa$_{2}$Cu$_{4}$O$_{8}$ decreases below 250K. This is an unusual behavior for the ordering peak, suggesting the interplay with superconductivity.