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arXiv:2107.13805 · Physical Review Research

Resonant pair-exchange scattering and BCS-BEC crossover in a system composed of dispersive and heavy incipient bands: A Feshbach analogy

Kazunari Ochi, Hiroyuki Tajima, Kei Iida, Hideo Aoki

Published Jan 13, 2022• 16 citations
arXivHTMLPDF

Abstract

We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential $\ensuremath{\mu}$), which we call a resonant pair scattering. By elucidating the dependence of the effective interactions and gap functions on $\ensuremath{\mu}$, we can draw an analogy between the resonant pair scattering and the Feshbach resonance.

DOI
10.1103/physrevresearch.4.013032

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We theoretically show that a two-band system with very different masses harbors a resonant pair scattering that leads to novel pairing properties, as highlighted by the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover. Most importantly, the interband pair-exchange coupling induces an effective intraband attraction in each band, enhancing the superfluidity/superconductivity. The effect, a kind of Suhl-Kondo mechanism, is specifically enhanced when the second band has a heavy mass and is incipient (lying close to, but just above, the chemical potential \ensuremathμ\ensuremath{\mu}\ensuremathμ), which we call a resonant pair scattering. By elucidating the dependence of the effective interactions and gap functions on \ensuremathμ\ensuremath{\mu}\ensuremathμ, we can draw an analogy between the resonant pair scattering and the Feshbach resonance.
We show that in two-band sss-wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband sss-wave interactions, in sharp contrast to single-band sss-wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: (I) BCS pairing in both bands (BCS-BCS), (II) BCS pairing in one band and BEC pairing in the other (BCS-BEC), and (III) Bose pairing in both bands (BEC-BEC). Furthermore, we show that by fine tuning the interband interactions to zero one can induce QPTs in the ground state between three distinct superfluid phases. There are two phases where only one band is superfluid (S1S_1S1​ or S2S_2S2​), and one phase where both bands are superfluid (S1+S2)(S_1 + S_2)(S1​+S2​), a situation which is absent in one-band sss-wave systems. Lastly, we suggest that these crossovers and QPTs may be observed in 173^{173}173Yb and 87^{87}87Sr.
We study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozi\`eres-Schmitt-Rink approach to a two-band system. In comparison with the single-band case, we find a strong enhancement of the critical temperature, a significant reduction of the preformed pair region where pseudogap effects are expected, and the entanglement of two kinds of composite bosons in the strong-coupling BEC regime.
Abstract We show that in two-band s -wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband s -wave interactions, in sharp contrast to single-band s -wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: I) BCS pairing in both bands (BCS-BCS), II) BCS pairing in one band and BEC pairing in the other (BCS-BEC), and III) Bose pairing in both bands (BEC-BEC). Furthermore, we show that by fine tuning the interband interactions to zero one can induce QPTs in the ground state between three distinct superfluid phases. There are two phases where only one band is superfluid ( S 1 or S 2 ), and one phase where both bands are superfluid , a situation which is absent in one-band s -wave systems. Lastly, we suggest that these crossovers and QPTs may be observed in multi-component systems such as 6 Li, 40 K, 87 Sr, and 173 Yb.
We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling.
We examine theoretically a continuity between atomic and molecular Fermi superfluids in a Bose-Fermi mixture near the Feshbach resonance. Considering a two-channel model with Fermi atoms fff, Bose atoms bbb, and the closed-channel molecules FFF, we construct a mean-field framework based on the perturbative expansion of the $b\text{\ensuremath{-}}f\text{\ensuremath{-}}F$ Feshbach coupling. The resulting effective Hamiltonian not only exhibits the continuity between atom-atom to molecule-molecule Cooper pairings but also becomes equivalent to the two-band-superconductor model with Suhl-Matthias-Walker--type pair-exchange coupling. We demonstrate how these atomic and molecular Fermi superfluids coexist within the two-band-like superfluid theory. The pair-exchange coupling $ff\ensuremath{\leftrightarrow}FF$ and resulting superfluid gaps $\ensuremath{\langle}ff\ensuremath{\rangle}$ and $\ensuremath{\langle}FF\ensuremath{\rangle}$ are found to be strongly enhanced near the Feshbach resonance due to the interplay between the infrared singularity of Bogoliubov phonons and their Landau damping arising from the coupling with fermions. The pair-exchange coupling can be probed via the observation of the intrinsic Josephson effect between atomic and molecular superfluids.
We extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover by changing the sss-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and sss-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and preformed molecules to the total condensate density along the two crossovers.