Abstract

The possibility of bipolaron formation is studied taking into account both electron–phonon interaction and direct Coulomb repulsion. Starting from the Bethe–Salpeter equation with a rather general interaction of the form V(k,ω) = 4πe2/ε(k,ω), and using spectral representations for both the bipolaron wave function and the interaction, the effective Schrödinger-type equation is obtained with the new effective potential, which is non-local and which parametrically depends on the binding energy. It is shown that, if the static response function l/ε(K:,0) is non-negative, then there is no bound state, i.e. in this case bipolarons do not form (electron–lattice interaction is not sufficient to overcome direct Coulomb repulsion). Possible ways out are discussed, among them the possibility of a negative static dielectric function or more general form of the effective electron–electron interaction.

Introduction

The problem of the state of electrons in crystals with strong electron–phonon interaction is now attracting considerable attention. It is well known that one of the possibilities in this case is the formation of polarons [1,2]. The conditions for their existence and their properties have been studied in numerous publications.

Much less studied (and more controversial) is the next possible step – formation of bipolarons in certain cases. The possibility of bipolaron formation was probably first pointed out by Vinetskii and Giterman [3]; later, bipolrons were suggested as possible candidates to explain some properties of Ti4O7 [4]. The problem of the existence of bipolarons has recently acquired special significance in view of the suggestions that they may exist in cuprates and may possibly explain the phenomenon of high-temperature superconductivity in them (see especially [5–7]).