The exact Richardson solution of the reduced BCS Hamiltonian is used to study the BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media. Based on the exact eigenstate we will discuss the Cooper-pair concept proposing a scenario for the BCS-to-BEC crossover in which a mixture of quasifree fermions and pair resonances (BCS) evolves to a system of weakly bound molecules (BEC). In this single unified scenario the Cooper-pair wavefunction has a unique functional form. We propose a new definition of the condensate fraction which, within the limits of the BCS model, gives a qualitative description of recent experiments in ultracold atomic Fermi gases. Finally, we will introduce a new integrable model for asymmetric superfluid systems able to describe different homogeneous and inhomogeneous competing phases such as, breached superconductivity, deformed Fermi superfluidity, and the elusive Larkin-Ovchinnikov-Flde-Ferrell (LOFF) state.The exact Richardson solution of the reduced BCS Hamiltonian is used to study the BCS-to-BEC crossover, as well as the nature of Cooper pairs, in superconducting and Fermi superfluid media. Based on the exact eigenstate we will discuss the Cooper-pair concept proposing a scenario for the BCS-to-BEC crossover in which a mixture of quasifree fermions and pair resonances (BCS) evolves to a system of weakly bound molecules (BEC). In this single unified scenario the Cooper-pair wavefunction has a unique functional form. We propose a new definition of the condensate fraction which, within the limits of the BCS model, gives a qualitative description of recent experiments in ultracold atomic Fermi gases. Finally, we will introduce a new integrable model for asymmetric superfluid systems able to describe different homogeneous and inhomogeneous competing phases such as, breached superconductivity, deformed Fermi superfluidity, and the elusive Larkin-Ovchinnikov-Flde-Ferrell (LOFF) state.

International Journal of Modern Physics BDec 15, 20061 citation

Pseudogap formation in organic superconductors

Shusaku Imajo, Takuya Kobayashi, Y. Matsumura +4 more

The condensation of paired fermions into superfluid states changes progressively depending on the coupling strength. At the midpoint of the crossover between Bardeen-Cooper-Schrieffer (BCS) weak-coupling and Bose-Einstein condensate (BEC) strong-coupling limits, paired fermions condensate most robustly, thereby leading to the emergence of a pseudogap due to enhanced pairing fluctuations. In the case of electrons in solids, excessively strong interactions often induce competing electronic orders instead of strong-coupling superconductivity, and experimental comprehension of the pseudogap remains incomplete. In this study, we provide experimental evidence demonstrating the opening of a pseudogap, marking the incipient stage of the BCS-BEC crossover in the organic system $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}X$. By controlling electron correlations, we investigate the thermodynamic properties of the BCS-BEC crossover and pseudogap phase. Since the superconductivity of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}X$ arises from a simple Fermi liquid that does not exhibit any other electronic orders, our study sheds light on the inherent nature of the BCS-BEC crossover.The condensation of paired fermions into superfluid states changes progressively depending on the coupling strength. At the midpoint of the crossover between Bardeen-Cooper-Schrieffer (BCS) weak-coupling and Bose-Einstein condensate (BEC) strong-coupling limits, paired fermions condensate most robustly, thereby leading to the emergence of a pseudogap due to enhanced pairing fluctuations. In the case of electrons in solids, excessively strong interactions often induce competing electronic orders instead of strong-coupling superconductivity, and experimental comprehension of the pseudogap remains incomplete. In this study, we provide experimental evidence demonstrating the opening of a pseudogap, marking the incipient stage of the BCS-BEC crossover in the organic system $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}X$. By controlling electron correlations, we investigate the thermodynamic properties of the BCS-BEC crossover and pseudogap phase. Since the superconductivity of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}X$ arises from a simple Fermi liquid that does not exhibit any other electronic orders, our study sheds light on the inherent nature of the BCS-BEC crossover.

arXiv:2312.04034Physical Review MaterialsDec 26, 20239 citations

General pairing mechanisms in the BCS-theory of superconductivity

Christian Hainzl, Michael Loss

arXiv:1603.07659The European Physical Journal BApr 28, 20177 citations

Relativistic BCS-BEC crossover at finite temperature and its application to color superconductivity

Lianyi He, Pengfei Zhuang

The nonrelativistic ${G}_{0}G$ formalism of BCS-BEC crossover at finite temperature is extended to relativistic fermion systems. The uncondensed pairs contribute a pseudogap to the fermion excitations. The theory recovers the BCS mean field approximation at zero temperature and the nonrelativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superfluid to the nonrelativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.The nonrelativistic ${G}_{0}G$ formalism of BCS-BEC crossover at finite temperature is extended to relativistic fermion systems. The uncondensed pairs contribute a pseudogap to the fermion excitations. The theory recovers the BCS mean field approximation at zero temperature and the nonrelativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superfluid to the nonrelativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.

arXiv:0705.1634Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsSep 12, 200733 citations

The nonrelativistic

{G}_{0}G

formalism of BCS-BEC crossover at finite temperature is extended to relativistic fermion systems. The uncondensed pairs contribute a pseudogap to the fermion excitations. The theory recovers the BCS mean field approximation at zero temperature and the nonrelativistic results in a proper limit. For massive fermions, when the coupling strength increases, there exist two crossovers from the weak coupling BCS superfluid to the nonrelativistic BEC state and then to the relativistic BEC state. For color superconductivity at moderate baryon density, the matter is in the BCS-BEC crossover region, and the behavior of the pseudogap is quite similar to that found in high temperature superconductors.