Superconductivity in the two-dimensional Hubbard model: One-particle correlation functions

Pao, C.‐H.; Bickers, N. E.

doi:10.1103/physrevb.51.16310

Cited by 57 publications

(46 citation statements)

References 7 publications

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“…1 therein. This is in the frame of numerical self-consistent FLEX calculations 7 . Further, numerically ImG R (k, ǫ) is very small compared to the band energy for small couplings, and the difference of ImΣ(k, ǫ), as seen in our numerical calculation, for small and large coupling constants is mostly quantitative rather than qualitative.…”

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confidence: 99%

Quasiparticle scattering rate in overdoped superconducting cuprates

Kastrinakis

2005

Phys. Rev. B

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We calculate the quasiparticle scattering rate in the superconducting state of the overdoped cuprates, in the context of the Eliashberg formalism for a Fermi liquid with strong van Hove singularities close to the chemical potential. For a d x 2 −y 2 superconducting gap, we demonstrate analytically that the scattering rate is linear in the maximum of temperature or energy, but with different intercepts and momentum dependence, thus extending our earlier results on the normal state. We discuss our results in view of angle-resolved photoemission experiments. We also comment on the case of a s-wave gap.The nature of the carriers in the cuprates is an important question, which has been discussed and debated extensively. The availability of relevant experimental data over the years, and in particular angle-resolved photoemission (ARPES), should be helpful in the effort towards achieving a better understanding of this question.Here, we look at a characteristic one-particle property, relevant to ARPES. We obtain analytically the scattering rate in the superconducting state for a Fermi liquid with strong density of states peaks -van-Hove singularities (vHs) in 2-D -located close to the chemical potential µ. Incidentally, this model does not apply to the underdoped cuprates, as there is no indication that a Fermi liquid description is appropriate. The qualitative nature of our results does not depend on the doping level, for as long as we remain within the realm of Fermi liquid theory. Precise numerical calculations can yield the quantitative dependence of the theory on the doping etc. A review of related work in the frame of the so-called van-Hove scenario has been given in 1 . The pinning of the vHs close to µ seems to be a plausible explanation for the common characteristics of a good many cuprates, whose van-Hove singularities are located between 10-30 meV below the Fermi surface 2 , as ARPES experiments have shown. A review of some calculations yielding the pinning of the vHs close to µ appears in 3 . The present work extends our results for the normal state, obtained in 3,4 , to the superconducting state. The analysis presented below can also be done in the frame of a weak-coupling BCS-type approach. We opt for the intermediate to strong-coupling Eliashberg approach, which is relevant for the cuprates. Qualitatively, i.e. as far as power laws etc. are concerned in terms of energy and temperature, the answers are the same for the two approaches.We consider a generic dispersion appropriate for the cuprates, of the type t, t ′ , t ′′

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confidence: 99%

Quasiparticle scattering rate in overdoped superconducting cuprates

Kastrinakis

2005

Phys. Rev. B

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“…We study have the possibility of singlet pairing. Confining ourselves here to the transition temperature T c and the normal state properties we may linearize the equations (4, 5) and (11,12) with respect to the anomalous self-energy Σ (2) (k, iω n ) or F (2) (k, iω n ). T c can be calculated as the highest temperature where the following equation for the normalized anomalous self-energy…”

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confidence: 99%

Spin fluctuation-induced superconductivity in organic compounds

Kondo

Moriya

2000

Physica B: Condensed Matter

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Spin fluctuation-induced superconductivity in two-dimensional organic compounds such as κ-(ET)2X is investigated by using a simplified dimer Hubbard model with right-angled isosceles triangular lattice (transfer matrices −τ , −τ ′ ). The dynamical susceptiblity and the self-energy are calculated self-consistently within the fluctuation exchange approximation and the value for Tc as obtained by solving the linearized Eliashberg-type equations is in good agreement with experiment. The pairing symmetry is of d x 2 −y 2 type. The calculated (U/τ )-dependence of Tc compares qualitatively well with the observed pressure dependence of Tc. Varying the value for τ ′ /τ from 0 to 1 we interpolate between the square lattice and the regular triangular lattice and find firstly that values of Tc for κ-(ET)2X and cuprates scale well and secondly that Tc tends to decrease with increasing τ ′ /τ and no superconductivity is found for τ ′ /τ = 1, the regular triangular lattice. Major topics in condensed matter physics in recent years may certainly include the unconventional superconductivity observed in high-T c cuprates, heavy electron systems and organic compounds. Among various possible mechanisms proposed so far the spin fluctuation mechanism seems to have possibilities of explaining all of these three.1) The superconductivity in heavy electron systems is believed to be almost certainly due to the spin fluctuation mechanism. Although the mechanism for cuprates is still controversial, the spin fluctuation mechanism seems to be rather unique in its ability of explaining not only the values of T c and the pairing symmetry but also various anomalous physical properties in the normal state as well as in the superconducting state in a systematic fashion at least in the optimal and overdoped concentration regimes;2) the underdoped regime still remains to be clarified.As for the two-dimensional (2D) organic superconductors the spin fluctuation mechanism seems to be the only available mechanism provided the superconducting order parameter is anisotropic, say of d-wave, as was indicated by recent investigations.3, 4, 5) Major differences of this problem from that of high-T c cuprates are that the superconductivity occurs without doping and in many cases in the metallic side of a metal-insulator Mott transition and thus the system should be in the intermediate correlation regime. For example, the t-J model should safely be excluded.We wish to discuss the spin fluctuation mechanism of superconductivity in 2D organic compounds, keeping κ-is an antiferromagnetic insulator and under increasing pressure it undergoes a insulator to superconductor transition.7) Each layer of molecules in these compounds may be regarded as consisting of dimers each of which has one hole in the antibonding dimer orbital of the highest occupied molecular orbitals (HOMO). 8, 9)There are transfer matrices −τ (τ > 0) between dimers and the additional consideration of intra-dimer electron interaction U naturally leads to the Hubbard model. For U ≫ τ we have antiferrom...

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“…[1,2,3,4,5,6,7] Following systematic studies based on the parameterized spin fluctuation theory, more quantitative studies were carried out by using the Hubbard model [8,9,10,11,12,13,14] and the d-p model [15,16,17,18] within the so-called fluctuation exchange (FLEX) approximation.…”

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confidence: 99%

Theory of Spin Fluctuation-Induced Superconductivity Based on ad-pModel. II. –Superconducting State–

Takimoto

Moriya

1998

J. Phys. Soc. Jpn.

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The superconducting state of a two-dimensional d-p model is studied from the spin fluctuation point of view by using a strong coupling theory. The fluctuation exchange (FLEX) approximatoin is employed to calculate the spin fluctuations and the superconducting gap functions self-consistently in the optimal-and over-doped regions of hole concentration. The gap function has a symmetry of d x 2 −y 2 type and develops below the transition temperature Tc more rapidly than in the BCS model. Its saturation value at the maximum is about 10kBTc. When the spin fluctuation-induced superconductivity is well stabilized at low temperatures in the optimal regime, the imaginary part of the antiferromagnetic spin susceptibility shows a very sharp resonance peak reminiscent of the 41 meV peak observed in the neutron scattering experiment on YBa2Cu3O7. The one-particle spectral density around k = (π, 0) shows sharp quasi-particle peaks followed by dip and hump structures bearing resemblance to the features observed in the angle-resolved photoemission experiment. With increasing doping concentration these features gradually disappear.

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Superconductivity in the two-dimensional Hubbard model: One-particle correlation functions

Cited by 57 publications

References 7 publications

Quasiparticle scattering rate in overdoped superconducting cuprates

Quasiparticle scattering rate in overdoped superconducting cuprates

Spin fluctuation-induced superconductivity in organic compounds

Theory of Spin Fluctuation-Induced Superconductivity Based on ad-pModel. II. –Superconducting State–

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