Band structure in autolocalization and bipolaron models of high-temperature superconductivity

Abstract

We develop the polaron theory taking into account the spatial dispersion of lattice polarizability caused by several phonon branches. This allows us to describe new effects which cannot be obtained in the classical polaron theory because of the limitations of its model medium that has only one dispersionless phonon branch interacting with the carrier. It is demonstrated that if the spatial dispersion is allowed, the carrier spectrum in a medium with many-component polarization proves to have an autolocalization band structure. It occurs due to limitation on the polaron velocity in accordance with Landau’s theory of the quantum liquid. This results in several effects. One of them is ‘‘Cherenkov’’ radiation by a sufficiently rapid polaron of the coherent medium vibrations. Owing to this radiation there exists a possibility that two polarons can couple under resonance conditions with the medium vibrations. It leads to the formation of a two-center bipolaron coupled due to the exchange of real phonons. The influence of the autolocalization band structure on the properties of a system with high carrier concentration is also studied. This is of interest as far as the properties of high-temperature superconductors are concerned. Like any complex oxides they are characterized by many-component polarization. The obtained limitation on the velocity of any autolocalized state causes both the existence of maximum polaron concentration (of the order of 1020 cm−1) and modification of the Bose-condensation condition for bipolarons.

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