Resonant pairing isotope effect in polaronic systems

Abstract

The intermediate coupling regime in polaronic systems, situated between the adiabatic and the anti-adiabatic limit, is characterized by resonant pairing between quasi-free electrons which is induced by an exchange interaction with localized bipolarons. The onset of this resonant pairing takes place below a characteristic temperature T * and is manifest in the opening of a pseudogap in the density of states of the electrons. The variation of T * is examined here as a function of (i) the typical frequency ω0 of the local lattice modes, which determines the binding energy of the bipolarons, and (ii) the total concentration of charge carriers ntot = nF + nB, where nF and nB are the densities of free electrons and bipolarons, respectively. The variation of either of these quantities induces similar changes of the value of nB with respect to that of nF , in this way leading to a shift of T * . For finite, but small values of nB (≤ 0.1 per site), we find negative and practically doping independent values of the corresponding isotope coefficient α * . Upon decreasing ntot such that nB becomes exponentially small, we find a rapid change in sign of α * . This is related to the fact that the system approaches a state which is more BCS-like, where electron pairing occurs via virtual excitations into bipolaronic states and where T * coincides with the onset of superconductivity.

Isotope effect in the pseudogap of high-temperature superconducting copper oxides

“…We expect them to reveal a smaller isotope effect in the pseudogap (if visible) compared to the hole-doped side, but a substantial e-ph effect on quasiparticles. This is different from what predicted by the resonant pairing scenario [5], in which the isotope coefficient is essentially doping independent.…”

“…This represents an unusual dependence, having conventional BCS theory in mind. Some possible scenarios for its explanation have been proposed: Assuming that the pairing in cuprates is directly mediated by phonons [5] so that the pseudogap is associated to the binding of two polarons with no long-range phase coherence, Ranninger calculated the isotope shift of T * and found good qualitative agreement with experiments. The main drawback of this approach is that a small electronic repulsion is enough to make bipolaron formation energetically highly unfavorable, and in cuprates local Coulomb repulsion can by no means be neglected.…”

Local dynamical lattice instabilities: Prerequisites for resonant pairing superconductivity

“…55,56 Its lattice-driven origin became apparent in the isotope effect experimentally observed 57 on the temperature T ‫ء‬ at which the pseudogap opens up. 58 Within the same scenario, the onset of the pseudogap feature was found to be related to a change from single-particle transport at temperature above the onset of the pseudogap ͑T Ն T ‫ء‬ ͒ to one which is controlled primarily by bound charge-carrier pairs below T ‫ء‬ , upon approaching T c from above. These bound pairs then acquire free-particle-like dispersion, which results in a transient Meissner effect 59 ͑experimentally verified 60 ͒ and remnant Bogoliubov shadow modes in the pseudogap phase.…”

“…Such systems should be close to an insulator-tosuperconductor transition, 35,36 the insulator being represented by phase-uncorrelated pair fluctuations and the superconductor by spatially phase-correlated ones with a T c controlled by phase and not amplitude fluctuations. As far as superconductivity is concerned, our approach to this problem 34,35,36,56,58 differs from any standard Eliashberg formulation. 63 In the Boson-Fermion Model scenario superconductivity comes about via a center of mass motion of dynamically fluctuating pairs.…”