Anomalous isotope effect and Van Hove singularity in superconducting Cu oxides

Tsuei, C. C.; Newns, D. M.; C., C.; Pattnaik, Pratap

doi:10.1103/physrevlett.65.2724

Cited by 276 publications

(120 citation statements)

References 27 publications

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“…The van Hove scenario is also argued [12][13][14] to be responsible for the marginal Fermi liquid behavior 15 in which the lifetime broadening of the quasiparticles is of the order of its energy. Thus the van Hove scenario is argued to account for the linear-T resistivity, 13,14,16 T -independent thermopower, 13 anomalous isotope effect, 14 etc.…”

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confidence: 99%

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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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confidence: 99%

“…Thus the van Hove scenario is argued to account for the linear-T resistivity, 13,14,16 T -independent thermopower, 13 anomalous isotope effect, 14 etc.…”

mentioning

confidence: 99%

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

et al. 2011

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“…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.…”

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confidence: 99%

“…Several authors [3][4][5][6][7][8][9][10] have attempted to extend BCS theory to describe the HTCS. Essentially the efforts were directed to include the vHS in the DOS into the otherwise standard BCS theory.…”

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confidence: 99%

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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“…[4] In this context, the quasiparticle dispersion is sometimes extracted from angle-resolved photoemission (ARPES) experiments or band structure calculations, a vertex interaction is proposed (usually invoking electronphonon or excitonic mechanisms), and predictions for superconductivity are made using standard techniques. The strong point of this approach is the natural existence of an optimal doping which occurs when the chemical potential reaches the vH singularity.…”

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Antiferromagnetic and van Hove Scenarios for the cuprates: Taking the best of both worlds

1995

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The purpose of this paper is to describe a microscopically-based theory of the cuprates that combines the strong features of the above described antiferromagnetic and van Hove scenarios. The first step in the construction of such a theory is the observation that the ARPES quasiparticle dispersion may be caused by holes moving in a local antiferromagnetic environment, rather than by band structure effects. This idea is motivated by the existence of universal flat bands [5][6][7] near k = (π, 0), (0, π) in the spectrum of hole-doped cuprates (2D square lattice language), which are difficult to understand unless caused by correlation effects in the CuO 2 planes. Recently, [8,9] it has been shown that models of correlated electrons can account for such flat bands, and here we further elaborate on this idea showing that the agreement with ARPES is quantitative.Using the well-known two dimensional (2D) t − J model defined by the Hamiltonian,2 in the standard notation, the dispersion of one hole in an antiferromagnet can be calculated accurately [8] with numerical or analytical techniques. At small J/t, it was found that the hole dispersion iswhich was calculated using a Green's Function Monte Carlo method.[8] J = 0.125eV is the actual scale of the problem, and Eq. (2) shows that holes move within the same sublattice to avoid distorting the AF background. To improve the quantitative agreement with experiments described below, here a small hopping amplitude along the plaquette diagonals t ′ = 0.05t has been included in the Hamiltonian to produce the dispersion Eq.(2), but the qualitative physics presented in this paper is the same as long as |t ′ /t| is small. Now, let us assume a rigid band picture for the quasiparticles.[8] The dispersion is plotted in Fig.1a against momentum with the Fermi level at the flat band which corresponds to a hole density of x = 0.15 (in Fig.1a and 1c below, ǫ k is inverted i.e. the electron language is used rather than the hole language to facilitate the comparison with experiments). ǫ k contains a saddle-point located close to k = (π, 0), (0, π), which induces a large DOS in the spectrum.In addition, ǫ k is nearly degenerate along the cosk (Fig.1b). The most important detail to consider at a small but finite hole density is that the quasiparticle weight is smaller for the bands centered at momentum (π, π) than those at (0, 0) (as represented pictorially in Fig.1a-b, with dashed lines). These are the "shadow bands" which were discussed before in the spin-bag approach.[11] Another argument in favor of using our hole dispersion at a finite 3 density also comes from experiments. In Fig.1c we compare ǫ k along the k = (0, 0) − (π, 0) direction against ARPES results by the Argonne group [5,12] for YBCO. The agreement is excellent. It is worth emphasizing that the theoretical curve of Fig.1c is derived from a microscopic Hamiltonian, and it is not a fit of ARPES data. This is a major difference between the present approach and previous vH scenario calculations.To further elaborate on whether our...

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Anomalous isotope effect and Van Hove singularity in superconducting Cu oxides

Cited by 276 publications

References 27 publications

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

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

BCS-universal ratios within the Van Hove scenario

Antiferromagnetic and van Hove Scenarios for the cuprates: Taking the best of both worlds

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