Discontinuous change of superconducting transition temperature from BCS type to bipolaron type in strongly coupled electron-phonon systems

Abstract

A unified theory for the superconducting transition temperature Tc of an electron-phonon coupled system has been derived, so as to clarify the nature of the intermediate region of coupling strength, as well as the weak (BCS) region and the strong (bipolaronic) one. This theory is mainly based on the polaron picture and takes the thermal fluctuation of pairing order into account within the coherent-potential approximation. In the weak-coupling limit, it reduces to the Eliashberg theory and gives a Tc that increases as the coupling increases, while in the strong-coupling region, it reduces to a pseudospin-type theory of bipolarons, and Tc decreases as the coupling increases. Thus, Tc takes its maximum in the intermediate region. It is shown, however, that this change of Tc from the BCS region to the bipolaronic one becomes discontinuous when the bandwidth of electron is greater than the phonon energy, while in the opposite case it changes continuously. The calculated results of the former case are discussed in connection with the insulator-superconductor transition of Ba1−xKxBiO3.

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