BCS to Bose crossover in anisotropic superconductors

Wallington, Jonathan P.; Annett, James F.

doi:10.1103/physrevb.61.1433

Cited by 25 publications

(14 citation statements)

References 44 publications

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“…19 They found that for any coupling the s wave has the lowest critical temperature, except for a small region near half filling, where the Van Hove singularity of density of states weighted with the angular factors stabilizes the d-wave phase. The presence of the hard-core repulsion allows d-wave superconductivity to appear on a much larger portion of the phase diagram.…”

Section: Discussionmentioning

confidence: 99%

Superconductivity with hard-core repulsion: BCS-Bose crossover ands−/d-wave competition

Pistolesi

Nozières

2002

Phys. Rev. B

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We consider fermions on a two-dimensional lattice interacting repulsively on the same site and attractively on the nearest-neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong-coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave function correctly vanishes when the two fermions ͑with antiparallel spin͒ sit on the same site. This fact has important consequences for the superconducting state that are somewhat unusual. In particular this implies a radial node line for the gap function. When a next-neighbor hopping tЈ is present we find that the s-wave state may develop nodes on the Fermi surface.

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Section: Discussionmentioning

confidence: 99%

Superconductivity with hard-core repulsion: BCS-Bose crossover ands−/d-wave competition

Pistolesi

Nozières

2002

Phys. Rev. B

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“…In this Section we consider the problem of d−wave pairing in 2D at zero temperature both in lattice [167][168][169][170][171] and in continuum models [172,173]. The motivation for considering this type of pairing is the experimental observation in the ARPES and other measurements [4,8,[13][14][15]] of a d x 2 −y 2 symmetry in HTSC.…”

Section: Crossover In the Models With D-wave Pairingmentioning

confidence: 99%

Phase fluctuations and pseudogap phenomena

2001

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This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temperature superconductors. In particular we compare this approach which relies on the twodimensional nature of the superconductivity to the often used T -matrix approach. Starting from simple pairing Hamiltonians we present a broad pedagogical introduction to the BCS-Bose crossover problem. The finite temperature extension of these models naturally leads to a discussion of the Berezinskii-Kosterlitz-Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impurities. We stress the differences between simple Bose-BCS crossover theories and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is welldefined. The Green's function and its associated spectral function, which explicitly show non-Fermi liquid behaviour, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle-vortex and vortex-vortex interactions for the filling of the gap above T c are considered. 5The superconducting transition as a BKT transition and the temperature scale for the opening of the pseudogap 52 5.1 Phase diagram based on the classical phase fluctuations in the absence of Coulomb repulsion 52 5.2 The peculiarities of the phase diagram for the lattice model 67 5.3 The effects of Coulomb repulsion and quantum phase fluctuations 70 5.4 The effect of non-magnetic impurities 77 6 The Green's function in modulus-phase representation and non-Fermi liquid behaviour 86 6.1 The modulus-phase representation for the fermion Green function 87 6.2 The correlation function for the phase fluctuations 88 6.3 The Fourier transform of D(r) 92 6.4 The derivation of the fermion Green's function in Matsubara representation and its analytical continuation 93 6.5 The branch cut structure of G(ω, k) and non-Fermi liquid behaviour 97 7 The spectral function in the modulus-phase representation and filling of the gap 99 7.1 Absence of gap filling for the Green's function calculated for the static phase fluctuations in the absence of spin-charge coupling 99 7.2 Gap filling by static phase fluctuations due to quasi-particle vortex interactions. The phenomenology of ARPES 103 7.3 Gap filling due to dynamical phase fluctuations without quasi-particle vortex interactions 106 8 Concluding remarks 109 A Calculation of the effective potential 111 B Another representation for the retarded Green's function 113 References 114particle weight, or equivalently a pseudogap, below T * . Until recently most ARPES measurements were performed for the photon energy range between 19 and 25eV . The most recent data [10], which was taken with a higher photon energy of 33eV , is in contradiction with the previous data. This question is now under intensive investigation [11], particularly since ohmic losses may alter the ARPES spectra [12].An explanation of the pseudogap phenomen...

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“…In what follows we consider a purely d-wave saddle point, and neglect completely a possible s-wave component. Being small at the Fermi surface near half filing, the amplitude of the s-wave order parameter is expected to be completely suppressed by the dominate d-wave component [39].…”

Section: Model and The Superconducting Saddle Pointmentioning

confidence: 99%

Quantum fluctuations, pseudogap, and theT=0superfluid density in strongly correlatedd-wave superconductors

Herbut

2004

Phys. Rev. B

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I study the effect of Coulomb interaction on superconducting order in a d-wave lattice superconductor at T = 0 by considering the superconducting saddle point in the two dimensional t-J-U model with a repulsion U . The theory of low-energy superconducting phase fluctuations around this saddle point is derived in terms of the effective hard-core bosons (representing the density of spin-up electrons and the phase of the order parameter), interacting with the fluctuating density of spin-down electrons. Whereas the saddle-point value of the superconducting gap is found to continuously increase towards half filling, the phase stiffness at T = 0 has a maximum, and then decreases with further underdoping. Right at half filling the phase stiffness vanishes for large U . This argues that the pseudogap phenomenon of the type observed in cuprates is in principle possible without a development of any competing order, purely as a result of growing correlations in the superconducting state. Implications for the finite temperature superconducting transition and the effects of static disorder are discussed qualitatively. I. INTRODUCTIONPseudogap phenomenon has become one of the hallmarks of high temperature superconductivity [1]: while the suppression of the single particle density of states is observed in many quantities at a high temperature T * , which appears to increase towards half filling, the superconducting transition temperature T c , together with the T = 0 superfluid density, at the same time continuously approaches zero [2]. Being in dramatic contrast to the well understood behavior of the standard BCS superconductors [3], this puzzling phenomenon has prompted different explanations. These may be grouped into at least two conceptually separate camps. The first group postulates development of a second order parameter in the underdoped region, which competes with superconductivity and suppresses its transition temperature [4] [17], and the Nernst effect [18] may all be understood as directly or indirectly supporting the proposed superconducting origin of the pseudogap temperature. Some of the same measurements, however, may also be understood within a competing theory, and the physics of underdoped high temperature superconductors at present still remains controversial.In this paper it is argued that the pseudogap phenomenon may in principle arise purely from strong Coulomb interactions in a d-wave superconductor and sufficiently near half filling, without any competing order. While a competing order is possible, and indeed in some materials may even be likely in the underdoped region, it seems not to be required simply by the existence of pseudogap. Furthermore, this is shown for a superconductor with only a weak attraction in the d-wave channel, so the mechanism behind the pseudogap considered here is different than in the real-space pairing approaches extensively discussed in the literature [19], [13]. Deriving from Coulomb repulsion, it is similar in spirit, although still different in detail, to the one in the R...

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BCS to Bose crossover in anisotropic superconductors

Cited by 25 publications

References 44 publications

Superconductivity with hard-core repulsion: BCS-Bose crossover ands−/d-wave competition

Superconductivity with hard-core repulsion: BCS-Bose crossover ands−/d-wave competition

Phase fluctuations and pseudogap phenomena

Quantum fluctuations, pseudogap, and theT=0superfluid density in strongly correlatedd-wave superconductors

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