Resonating Bipolarons

– Electrons coupled to local lattice deformations end up in selftrapped localized molecular states involving their binding into bipolarons when the coupling is stronger than a certain critical value. Below that value they exist as essentially itinerant electrons. We propose that the abrupt crossover between the two regimes can be described by resonant pairing similar to the Feshbach resonance in binary atomic collision processes. Given the intrinsically local nature of the exchange of pairs of itinerant electrons and localized bipolarons, we demonstrate the occurrence of such a resonance on a finite-size cluster made out of metallic atoms surrounding a polaronic ligand center. The phenomenon of resonant pairing between nucleons, atoms and molecules, characterized by a strongly enhanced scattering amplitude, has received considerable attention in the past few years, primarily in connection with the study of ultracold dilute atomic gases exhibiting various forms of condensed macroscopic coherent quantum states. The basic requirement for such so called Feshbach resonant pairing [1, 2] is that two incident particles have nearly the same energy as that required to form a shallow bound state between them. The efficiency to convert two uncorrelated atoms into a molecular state over short time intervals is then dramatically enhanced. As a result, two atoms near such a resonance oscillate between essentially uncorrelated pairs of atoms and diatomic molecular states. Experimentally such a situation can be created, provided the atoms can exist in two different spin states permitted by spin-orbit coupling. Different spin alignments of the two atoms (in form of spin singlet or triplet states) give rise to different inter-atomic interactions, which lead to either bound or scattering states. Favoring the one over the other can be monitored by applying a magnetic field which shifts the respective interaction potentials with respect to each other. We shall illustrate in this Letter, that similar effects are bound to play a role in strongly coupled electron-lattice systems with polaronic and bipolaronic charge carriers. The recently much studied high-T c cuprates, the colossal magneto-resistance manganates, the nickelates as well as the fullerenes are examples where such effects are likely to occur. It is however not c EDP Sciences