No abstract

No abstract

A standard perturbative expansion around the mean-field solution is used to derive the low-energy effective action for superconductors at T = 0. Taking into account the density fluctuations at the outset we get the effective action where the density ρ is the conjugated momentum to the phase θ of the order parameter. In the hydrodynamic regime, the dynamics of the superconductor is described by a time dependent non-linear Schrödinger equation (TDNLS) for the field Ψ(x) = ρ 2 e iθ . The evolution of the density fluctuations in the crossover from weak-coupling (BCS) to strong-coupling (Bose condensation of localized pairs) superconductivity is discussed for the attractive Hubbard model. In the bosonic limit, the TDNLS equation reduces to the the Gross-Pitaevskii equation for the order parameter, as in the standard description of superfluidity. The conditions under which a phase-only action can be derived in the presence of a long-range interaction to describe the physics of the superconductivity of "bad metals" are discussed.

The bipolaronic scenario for high T c superconductivity is critically examined. The underlying assumption that at low temperatures all the charge carriers exist in the form of itinerant bipolarons is shown to be incompatible on theoretical and experimental grounds. Superfluidity of such bipolarons cannot give the values of T c nor explain the fermionic nature of the quasiparticles observed in the cuprates. [S0031-9007 (98)06566-1] PACS numbers: 74.20.Mn, 71.38. + iElectron-phonon interactions in solids show up in a variety of ways: from relatively small mass renormalization of the carriers in metals due to inherently weak screened interaction to almost localized quasiparticles in ionic solids and oxides-known as small polarons -as a result of enormous mass enhancement in case of strong unscreened interaction. Although the literature [1] on polarons is vast and sometimes confusing, one calls a polaron a small polaron when it results from strong interaction with acoustic or local phonons (with a concomitant lattice distortion, localized within the unit cell). In order to explain some of the properties of amorphous chalcogenide glasses Anderson [2] in 1975 introduced the idea of on-site small bipolarons i.e., two electrons localized on the same lattice site due to intense local lattice distortion, ultimately behaving as socalled negative U centers. This idea was soon extended to intersite [3]-so-called Heitler London bipolarons which were invoked successfully to explain a host of properties in transition oxide bronzes and the insulator-metal transition in Ti 42x V x O 7 , intensively studied in Grenoble in the late 1970s [4]. About the same period one of the authors [5] pointed out that in a many electron system the ground state should continuously evolve as a function of the electronphonon coupling constant from a BCS like superconducting to an ultimately insulating ground state as the Cooper pairs localize in the form of heavy massive bipolarons. Although the discovery of high T c superconductivity [6] may owe something to these ideas, there was never any question of evoking a Bose-Enstein condensation (BEC) of bipolarons as relevant to its explanation in any of those papers. The idea published in 1981 [7] suggesting that small bipolarons may be considered as itinerant hard core bosons on a lattice which can become superfluid had lately been taken very literally by certain authors [8], suggesting it to be the reason for high T c superconductivity. We shall show in the following that extending the bipolaron theory for superconductivity to high T c materials is fallacious, that it is incompatible with experiments, and that bipolaron condensation -within the original scheme of such a theory of bipolaronic superconductivity [7]-is impossible to occur in those materials.The low carrier concentration (ϳ10 21 cm 23 ) together with the small coherence length (of the order of a few tens of angstroms) in high T c compounds is, at a first view, indeed tempting to consider a scenario where tightly bound electron pairs exist i...