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arXiv:cond-mat/0510388 · The European Physical Journal B

Pairing correlations in finite systems: from the weak to the strong fluctuations regime

M Fernández, J.L. Egido

Published Dec 1, 2005• 12 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2005-00405-y

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By analyzing simple models of fermions in lattice potentials we argue that the zero-temperature pairing instability of any ideal band-insulator occurs at a finite momentum. The resulting supersolid state is known as "pair density wave". The pairing momentum at the onset of instability is generally incommensurate as a result of phase-space restrictions and relative strengths of interband and intraband pairing. However, commensurate pairing occurs in the strong-coupling limit and becomes a Cooper-channel analogue of the Halperin-Rice exciton condensation instability in indirect bandgap semiconductors. The exceptional sensitivity of incommensurate pairing to quantum fluctuations can lead to a strongly-correlated insulating regime and a non-BCS transition, even in the case of weak coupling as shown by an exact renormalization group analysis.
After a short review of the different physics in the weak and strong coupling regime, resulting in amplitude fluctuation controlled Cooper pair superconductivity and phase fluctuation controlled superfluidity of tightly bound local polaron pairs, we suggest a scenario for the cross-over regime between those two. It is based on the idea of resonating Bipolarons inside a Fermi sea of uncorrelated electrons, similar to the Feshbach resonance in Fermionic gases in optical traps. Due to the competition between amplitude and phase correlations such systems in the cross-over regime can exhibit a superconductor to insulator transition upon varying the strength of that resonance.
Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.