Correlation bag and high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductivity

From an analysis of the normal-state properties of the high-${\mathit{T}}_{\mathit{c}}$ copper oxide superconductors the following features can be established on the basis of single-particle theories: (1) a bandwidth W\ensuremath{\approxeq}U&gt;${\mathit{E}}_{\mathit{p}}$, where U is the on-site correlation energy and ${\mathit{E}}_{\mathit{p}}$ is the pair binding energy; (2) a W\ensuremath{\approxeq}8\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}$ at the narrow-band limit for small-polaron versus itinerant-electron conduction in a mixed-valent system; (3) a W\ensuremath{\approxeq}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{\ensuremath{\sigma}}}$${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\sigma}}}^{2}$, where the covalent mixing parameter ${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\sigma}}}$ varies sensitively with the hole concentration and consequently with any local charge fluctuations in a mixed-valent system; (4) on-site and near-neighbor correlation energies that vary sensitively with the bandwidth in the region W\ensuremath{\approxeq}U. From the superconductor properties, a \ensuremath{\xi}\ensuremath{\approxeq}10 \AA{} signals an energy range of perturbed states \ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\lesssim}W, and superconductive pairs constrained to a small volume in real space which makes necessary the introduction of a nonretarded potential. These features lead us to consider charge fluctuations, induced by strong electron-lattice interactions, where U\ensuremath{\gtrsim}W\ensuremath{\approxeq}8\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{R}}$,in which ``bags'' rich in charge carriers coexist with regions poor in charge carriers together with an important modulation of the bandwidth---and hence the correlation energies---on moving from outside to inside a bag. The problems with the Alexandrov model that have been raised by De Jongh are resolved by the modulation of the correlation energies, which adds a new term to the Hamiltonian that gives an additional component to the binding energy. A bag model allows use of the spin-bag formalism but with a renormalization of the charge channel rather than the spin channel to obtain a possible solution of the new Hamiltonian. The model allows interpretation of the variation of ${\mathit{T}}_{\mathit{c}}$ with hole concentration in the p-type copper oxides as well as the pressure dependence of ${\mathit{T}}_{\mathit{c}}$ as a function of hole concentration. A bending of the Cu-O-Cu bond angles from 180\ifmmode^\circ\else\textdegree\fi{} and the degree of freedom of the Cu-O bond length normal to the ${\mathrm{CuO}}_{2}$ sheets allows identification of possible vibrational modes involved in bag formation.

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