Superconductivity in Alcaline-Earth-Substituted La
                    <sub>2</sub>
                    CuO
                    <sub>4</sub>
                    : A Theoretical Model

Labbé, J.; Bok, J.

doi:10.1209/0295-5075/3/11/012

Cited by 362 publications

(122 citation statements)

References 15 publications

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“…This result has been obtained by several other authors [3][4][5][6][7][8][9].We will use this approximation below.…”

supporting

confidence: 66%

“…This is not the spirit in the conventional theory. Nevertheless, several authors [3,[5][6][7][8]10], based on the way in which they look at the approximate account of the available experimental results that they get from their generalization, rise a conclusion for or against BCS as if one could pretend that it is an exact theory. There is also an undeclared trend to associate it with the electron-phonon interaction although actually no specification about the mechanism is really necessary.…”

mentioning

confidence: 99%

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BCS-universal ratios within the Van Hove scenario

Baquero¹,

Quesada²,

Trallero‐Giner³

1996

Physica C: Superconductivity

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Within conventional superconductivity, BCS theory represents a well defined weakcoupling limit. The central result are the Universal Ratios which do not depend on physical parameters of the particular superconductor under study. Several attempts have been made to introduce the van Hove Scenario within BCS theory but in none of them the Universal Ratios of conventional superconductivity appear to be a number independent of parameters.This fact prevents the precise definition of a deviation from the BCS value for a particular superconductor. This concept is at the basis of several applications of BCS theory in characterizing conventional superconductors. We define a system that constitutes a weak coupling limit that retains the essential features of the high-Tc oxides and which does not differ in any essential way from other models widely used in generalizations of BCS theory to high-Tc superconductors. The difference is that we found a natural way of dealing with the mathematics of the problem so as to get Universal Ratios in the same sense as in conventional superconductivity. This formulation could play an analogous role as the original BCS theory played in conventional superconductivity. A central result of this theory are the Universal Ratios (UR). These relate thermodynamic quantities among themselves in a universal way, i. e. they are equal to the same number for every possible superconductor.When compared to experiment, BCS turns out not to be an exact theory of CS. Deviations from it are frequent in all but some of the weak coupling CSr as Al, In, and Sn.Since it is a precisely established limit, the deviations from it do have a well defined physical meaning. This theory is useful as a point of reference and as a tool to study different, more complicated physical situations in a transparent and easy way from which trends can be established. It is important to recall that, in the spirit of the theoretical treatment of CS, the deviations from BCS theory characterize the particular superconductor, not the theory. The validity of BCS theory itself is based on its approximate description of the most important experimental trends and on its characterization as a well-defined weak coupling limit. This is a very important point for this letter. The precise many-body theory of the electron-phonon (e-ph) CS is described through the so called Eliashberg gap Equations [2]

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“…This result has been obtained by several other authors [3][4][5][6][7][8][9].We will use this approximation below.…”

supporting

confidence: 66%

mentioning

confidence: 99%

BCS-universal ratios within the Van Hove scenario

Baquero¹,

Quesada²,

Trallero‐Giner³

1996

Physica C: Superconductivity

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show abstract

“…[1][2][3][4] These flat regions in the energy dispersion are directly observed in ARPES experiments on various cuprate compounds. [5][6][7][8][9] Recently, it was also observed in the tunneling spectra of Bi-2201.…”

mentioning

confidence: 70%

Role of the van Hove singularity in the quantum criticality of the Hubbard model

et al. 2011

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A quantum critical point is found in the phase diagram of the two-dimensional Hubbard model [Vidhyadhiraja et al., Phys. Rev. Lett. 102, 206407 (2009)]. It is due to the vanishing of the critical temperature associated with a phase separation transition, and it separates the non-Fermi liquid region from the Fermi liquid. Near the quantum critical point, the pairing is enhanced since the real part of the bare d-wave pairing susceptibility exhibits an algebraic divergence with decreasing temperature, replacing the logarithmic divergence found in a Fermi liquid [Yang et al., Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore the single-particle and transport properties near the quantum critical point using high quality estimates of the self energy obtained by direct analytic continuation of the self energy from Continuous-Time Quantum Monte Carlo. We focus mainly on a van Hove singularity coming from the relatively flat dispersion that crosses the Fermi level near the quantum critical filling. The flat part of the dispersion orthogonal to the antinodal direction remains pinned near the Fermi level for a range of doping that increases when we include a negative next-near-neighbor hopping t ′ in the model. For comparison, we calculate the bare d-wave pairing susceptibility for non-interacting models with the usual two-dimensional tight binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare d-wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A negative next-near-neighbor hopping t ′ increases the doping region with marginal Fermi liquid character. Both T and negative t ′ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.

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“…[31][32][33][34][35][36][37][38] The curvature of the FS has important implications in the properties of the system, and the inflexion points, which separate regions where the curvature has opposite signs, may induce anomalous effects. 39,40 The crucial role that the FS geometry plays on the unusual physics of 2D systems makes desirable a deeper insight in the interplay between it and measurable parameters.…”

Section: A Self-energy Corrections To the Fermi Surface Near Hot Spotsmentioning

confidence: 99%

Self-energy corrections to anisotropic Fermi surfaces

et al. 2006

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The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper-oxide superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is nontrivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.

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Superconductivity in Alcaline-Earth-Substituted La ₂ CuO ₄ : A Theoretical Model

Cited by 362 publications

References 15 publications

BCS-universal ratios within the Van Hove scenario

BCS-universal ratios within the Van Hove scenario

Role of the van Hove singularity in the quantum criticality of the Hubbard model

Self-energy corrections to anisotropic Fermi surfaces

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Superconductivity in Alcaline-Earth-Substituted La 2 CuO 4 : A Theoretical Model

Cited by 362 publications

References 15 publications

BCS-universal ratios within the Van Hove scenario

BCS-universal ratios within the Van Hove scenario

Role of the van Hove singularity in the quantum criticality of the Hubbard model

Self-energy corrections to anisotropic Fermi surfaces

Contact Info

Product

Resources

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Superconductivity in Alcaline-Earth-Substituted La ₂ CuO ₄ : A Theoretical Model