Evolution from BCS superconductivity to Bose-Einstein condensation: Current correlation function in the broken-symmetry phase

Andrenacci, Natascia; Pieri, P.; Strinati, G. C.

doi:10.1103/physrevb.68.144507

Cited by 51 publications

(100 citation statements)

References 38 publications

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“…Following Refs. [24] and [27], we approximate this term by the series of ladder diagrams in the broken-symmetry phase which are depicted in Fig.3(a). Here, the interaction potential is taken to be of the short-range (contact) type and the lines represent the BCS single-particle Green's functions in Nambu notation:…”

Section: Inclusion Of Pairing Fluctuations Below T Cmentioning

confidence: 99%

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Temperature dependence of the pair coherence and healing lengths for a fermionic superfluid throughout the BCS-BEC crossover

Palestini

Strinati

2014

Phys. Rev. B

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We calculate the pair correlation function and the order parameter correlation function, which probe, respectively, the intra-pair and inter-pair correlations of a Fermi gas with attractive interparticle interaction, in terms of a diagrammatic approach as a function of coupling throughout the BCS-BEC crossover and of temperature, both in the superfluid and normal phase across the critical temperature Tc. Several physical quantities are obtained from this calculation, including the pair coherence and healing lengths, the Tan's contact, the crossover temperature T * below which interpair correlations begin to build up in the normal phase, and the signature for the disappearance of the underlying Fermi surface which tends to survive in spite of pairing correlations. A connection is also made with recent experimental data on the temperature dependence of the normal coherence length as extracted from the proximity effect measured in high-temperature (cuprate) superconductors.

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Section: Inclusion Of Pairing Fluctuations Below T Cmentioning

confidence: 99%

“…Quite generally, the two-particle Green's function G 2 in Eq. (3) can be represented in terms of the single-particle Green's function G and the many-particle T-matrix T , in the form [24]:…”

Section: A General Formalismmentioning

confidence: 99%

Temperature dependence of the pair coherence and healing lengths for a fermionic superfluid throughout the BCS-BEC crossover

Palestini

Strinati

2014

Phys. Rev. B

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“…In Ref. [28], the authors propose "good candidates" for the response function Feynman diagrams. Here we emphasize that the WTI provides a direct procedure to determine not just good candidates but the exact full vertex, given in Eq.…”

Section: Particle-only T-matrixmentioning

confidence: 99%

“…A third and final model was introduced by Strinati and co-workers using a generalized t-matrix [26][27][28]. In this model the self-energy is obtained from Eq.…”

Section: Particle-only T-matrixmentioning

confidence: 99%

“…Models of this sort are associated with the work of Yang, Rice, and Zhang [3], and also with the work of Refs. [26][27][28], who address BCS-BEC crossover effects via a t-matrix. Also belonging to this class is an alternate t-matrix theory of BCS-BEC crossover [6,25], which, in contrast to the work of Ref.…”

Section: Correlation Effects Beyond Bcs Theory: Ward-takahashi Idmentioning

confidence: 99%

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Gauge-invariant theories of linear response for strongly correlated superconductors

Boyack

Anderson

et al. 2016

Phys. Rev. B

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We present a general diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. The general treatment of correlations beyond BCS theory requires a new theoretical formalism not contained in the current literature. Among concrete examples are a rather extensive class of theoretical models which incorporate BCS-BEC crossover as applied to the ultra cold Fermi gases, along with theories specifically associated with the high-Tc cuprates. The challenge is to maintain gauge invariance, while simultaneously incorporating additional self-energy terms arising from strong correlation effects. Central to our approach is the application of the Ward-Takahashi identity, which introduces collective mode contributions in the response functions and guarantees that the f -sum rule is satisfied. We outline a powerful and very general method to determine these collective modes in a manner compatible with gauge invariance. Finally, as an alternative approach, we contrast with the path integral formalism. Here, the calculation of gauge invariant response appears more straightforward. However, the collective modes introduced are essentially those of strict BCS theory, with no modification from correlation effects. Since the path integral scheme simultaneously addresses electrodynamics and thermodynamics, we emphasize that it should be subjected to a consistency test beyond gauge invariance, namely that of the compressibility sum-rule. We show how this sum-rule fails in the conventional path integral approach.

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Pairing Fluctuations Approach to the BCS–BEC Crossover

Strinati

2011

Lecture Notes in Physics

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The problem of the theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in what would today be referred to as the (extreme) BCS (weak-coupling) limit of the BCS-BEC crossover. The point made in this context by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc obtained when neglecting screening effects. Subsequent work on this topic, that was aimed at extending the original GMB argument away from the BCS limit with diagrammatic methods, has tout court kept this disentangling between pairing and screening throughout the BCS-BEC crossover, without realising that the conditions for it to be valid are soon violated away from the BCS limit. Here, we reconsider this problem from a more general perspective and argue that pairing and screening are intrinsically entangled with each other along the whole BCS-BEC crossover but for the BCS limit considered by GMB, with the particle-hole excitations soon transmuting into particle-particle excitations away from this limit. We substantiate our argument by performing a detailed numerical calculation of the GMB diagrammatic contribution suitably extended to the whole BCS-BEC crossover, where the full wave-vector and frequency dependence occurring in the repeated in-medium two-particle scattering is duly taken into account for the first time. Our numerical calculations are tested against analytic results available in both the BCS and BEC limits, and the contribution of the GMB diagrammatic term to the scattering length of composite bosons in the BEC limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find that it agrees quite well with Quantum Monte Carlo calculations and experimental data available in the unitarity regime.

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Evolution from BCS superconductivity to Bose-Einstein condensation: Current correlation function in the broken-symmetry phase

Cited by 51 publications

References 38 publications

Temperature dependence of the pair coherence and healing lengths for a fermionic superfluid throughout the BCS-BEC crossover

Temperature dependence of the pair coherence and healing lengths for a fermionic superfluid throughout the BCS-BEC crossover

Gauge-invariant theories of linear response for strongly correlated superconductors

Pairing Fluctuations Approach to the BCS–BEC Crossover

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