Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model

Bickers, N. E.; Scalapino, D. J.; White, Steven R.

doi:10.1103/physrevlett.62.961

Cited by 922 publications

(719 citation statements)

References 16 publications

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“…The early suggestion that high temperature superconductors might exhibit unconventional, d-wave pairing, [24,11,154,8] has lead to a wide variety of new experimental probes with sensitivity sufficient to test this hypothesis. The pioneering work of Hardy and coworkers demonstrated that high resolution measurements of the London penetration depth could detect the presence of nodal quasiparticles characteristic of a d-wave pairing state [87].…”

Section: Introductionmentioning

confidence: 99%

Magnetic penetration depth in unconventional superconductors

Prozorov

Giannetta

2006

Supercond. Sci. Technol.

417

438

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Abstract. This topical review summarizes various features of magnetic penetration depth in unconventional superconductors. Precise measurements of the penetration depth as a function of temperature, magnetic field and crystal orientation can provide detailed information about the pairing state. Examples are given of unconventional pairing in hole-and electron-doped cuprates, organic and heavy fermion superconductors. The ability to apply an external magnetic field adds a new dimension to penetration depth measurements. We discuss how field dependent measurements can be used to study surface Andreev bound states, nonlinear Meissner effects, magnetic impurities, magnetic ordering, proximity effects and vortex motion. We also discuss how penetration depth measurements as a function of orientation can be used to explore superconductors with more than one gap and with anisotropic gaps. Details relevant to the analysis of penetration depth data in anisotropic samples are also discussed.Keywords: penetration depth, unconventional superconductivity, pairing symmetry IntroductionThe early suggestion that high temperature superconductors might exhibit unconventional, d-wave pairing, [24,11,154,8] has lead to a wide variety of new experimental probes with sensitivity sufficient to test this hypothesis. The pioneering work of Hardy and coworkers demonstrated that high resolution measurements of the London penetration depth could detect the presence of nodal quasiparticles characteristic of a d-wave pairing state [87]. Since that time, a large number of new superconductors have been discovered, many of which exhibit nontrivial departures from BCS behavior. As we show in this review, penetration depth measurements can be used to examine not only nodal quasiparticles but two-gap superconductivity, anisotropy of the energy gap, Andreev surface states, nonlinear Meissner effect, interplane transport, proximity coupled diamagnetism, vortex matter and the coexistence of magnetism and superconductivity, to name several problems of current interest.

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Section: Introductionmentioning

confidence: 99%

Magnetic penetration depth in unconventional superconductors

Prozorov

Giannetta

2006

Supercond. Sci. Technol.

417

438

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“…We want to study the doped antiferromagnet since there are strong indications that the Fermi liquid is unstable towards pairing near half filling; they come from diagrammatic approaches [15], renormalization group techniques [16], [17] and also cluster diagonalizations [32]. Therefore exact results on the half filled Hubbard Model may be relevant to antiferromagnetism and to the mechanism of the superconducting instability as well.…”

Section: The Doped Hubbard Antiferromagnetmentioning

confidence: 99%

“…At weak coupling, we can ignore the effect of the renormalizations in Eq. (15). Furthermore, we can discard the inter-shell interactions.…”

Section: Pairing In the Cuo 4 Clustermentioning

confidence: 99%

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W= 0 pairing in Hubbard and related models of low-dimensional superconductors

Balzarotti

Cini

Perfetto

et al. 2004

J. Phys.: Condens. Matter

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Abstract. Lattice Hamiltonians with on-site interaction W have W = 0 solutions, that is, many-body singlet eigenstates without double occupation. In particular, W = 0 pairs give a clue to understand the pairing force in repulsive Hubbard models. These eigenstates are found in systems with high enough symmetry, like the square, hexagonal or triangular lattices. By a general theorem, we propose a systematic way to construct all the W = 0 pairs of a given Hamiltonian. We also introduce a canonical transformation to calculate the effective interaction between the particles of such pairs. In geometries appropriate for the CuO 2 planes of cuprate superconductors, armchair Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound state in a physically relevant range of parameters. We also show that W = 0 pairs quantize the magnetic flux like superconducting pairs do. The pairing mechanism breaks down in the presence of strong distortions. The W = 0 pairs are also the building blocks for the antiferromagnetic ground state of the half-filled Hubbard model at weak coupling. Our analytical results for the 4 × 4 Hubbard square lattice, compared to available numerical data, demonstrate that the method, besides providing intuitive grasp on pairing, also has quantitative predictive power. We also consider including phonon effects in this scenario. Preliminary calculations with small clusters indicate that vector phonons hinder pairing while half-breathing modes are synergic with the W = 0 pairing mechanism both at weak coupling and in the polaronic regime.

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“…For the square lattice, where the spin fluctuations develop near Q = (π, π ), we have to change the sign of the gap between the wavevectors ∼(π, 0) and ∼(0, π ) in order to have a finite as a solution for the gap equation, which results in a d-wave gap as shown in figure 2. By applying fluctuation exchange (FLEX) approximation to this system, which is a kind of self-consistent perturbation theory that collects random phase approximation type diagrams, we can obtain the Green's function and the spin susceptibility [19]. These can be plugged into the Eliashberg equation, whose solution gives d-wave superconductivity with T c of the order 0.01t, where t is the nearest-neighbor hopping integral (if t ∼1 eV, T c is of the order of 100 K).…”

Section: Square Latticementioning

confidence: 99%

Unconventional pairing in doped band insulators on a honeycomb lattice: the role of the disconnected Fermi surface and a possible application to superconducting β-MNCl (M=Hf, Zr)

Kuroki¹

2008

Science and Technology of Advanced Materials

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We investigate the possibility of realizing unconventional superconductivity in doped band insulators on the square and honeycomb lattices. The latter lattice is found to be a good candidate due to the disconnectivity of the Fermi surface. We propose applying the theory to the superconductivity in doped layered nitride β-MNCl (M = Hf, Zr). Finally, we compare two groups of superconductors with disconnected Fermi surface, β-MNCl and the iron pnictides, which have high critical temperature T c , despite some faults against superconductivity are present.

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Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model

Cited by 922 publications

References 16 publications

Magnetic penetration depth in unconventional superconductors

Magnetic penetration depth in unconventional superconductors

W= 0 pairing in Hubbard and related models of low-dimensional superconductors

Unconventional pairing in doped band insulators on a honeycomb lattice: the role of the disconnected Fermi surface and a possible application to superconducting β-MNCl (M=Hf, Zr)

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