Polarons and Bipolarons in High-Tc Superconductors and Related Materials

Abstract

The BSC theory is extended to strong electron–phonon coupling for λ > 1. In this limit carriers are charged 2e bosons (singlet and triplet inter-site bipolarons). The Anderson localisation of the bosons resulting from disorder is also considered. Several non Fermi-liquid features of copper-based high-Tc oxides, in particular the spin gap in NMR and neutron scattering, the temperature dependent Hall effect, linear resistivity and divergent Hc2(T) are explained.

The strong-coupling extension of the BCS theory

The electron–phonon coupling constant λ in the BCS theory is the ratio of the characteristic interaction energy V = 2Ep of carriers with a bosonic field, for instance of phonons, which is responsible for the coupling to their kinetic energy EF, λ ⋍ V/(2EF). At the point λ ⋍ 1 the characteristic potential energy due to the local lattice deformation exceeds the kinetic energy. This is a condition of small-polaron formation which has been known for a long time as a solution for a single electron on a lattice coupled with lattice vibrations. So long as λ > 1 the kinetic energy remains smaller than the interaction energy and a self-consistent treatment of a many-electron system strongly coupled with phonons is possible with the ‘1/λ’ expansion technique [1]. This possibility results from the fact, which has been known for a long time, that there is an exact solution for a single electron in the strong-coupling limit λ rarr; infin. Following Lang and Firsov (1962) one can apply the canonical transformation exp (S1) to diagonalise the single-electron Fröhlich Hamiltonian (under the ‘Fröhlich Hamiltonian’ we assume that any electron–phonon interaction occurs with its matrix element depending on the phonon momentum).