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arXiv:1104.2631 · Physical Review Letters

Extremely Correlated Fermi-Liquid Description of Normal-State ARPES in Cuprates

G.-H. Gweon, B. Sriram Shastry, Genda D. Gu

Published Jul 29, 2011• 30 citations
arXivHTMLPDF

Abstract

The normal-state single particle spectral function of the high temperature superconducting cuprates, measured by the angle-resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand. Here, we report an unprecedented success of the new extremely correlated Fermi liquid theory by one of us [B. S. Shastry, Phys. Rev. Lett. 107, 056403 (2011)] to describe both laser and conventional synchrotron ARPES data (nodal cut at optimal doping) on Bi(2)Sr(2)CaCu(2)O(8+δ) and synchrotron data on La(1.85)Sr(0.15)CuO(4). It fits all data sets with the same physical parameter values, satisfies the particle sum rule and successfully addresses two widely discussed kink anomalies in the dispersion.

DOI
10.1103/physrevlett.107.056404

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The normal-state single particle spectral function of the high temperature superconducting cuprates, measured by the angle-resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand. Here, we report an unprecedented success of the new extremely correlated Fermi liquid theory by one of us [B. S. Shastry, Phys. Rev. Lett. 107, 056403 (2011)] to describe both laser and conventional synchrotron ARPES data (nodal cut at optimal doping) on Bi(2)Sr(2)CaCu(2)O(8+δ) and synchrotron data on La(1.85)Sr(0.15)CuO(4). It fits all data sets with the same physical parameter values, satisfies the particle sum rule and successfully addresses two widely discussed kink anomalies in the dispersion.
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We present detailed results from a recent microscopic theory of extremely correlated Fermi liquids, applied to the ttt-JJJ model in two dimensions, developed recently by Shastry [Phys. Rev. Lett. 107, 056403 (2011); Phys. Rev. B 87, 125124 (2013)]. The second-order theory in the parameter $\ensuremath{\lambda}$, related to the density, is argued to be quantitatively valid in the overdoped regime for $0\ensuremath{\le}n\ensuremath{\lesssim}0.75$, with nnn denoting the particle density. The calculation involves the self-consistent solution of equations for an auxiliary Fermi liquid Green's function and an adaptive spectral weight. We present numerical results at low as well as high TTT, at various low to intermediate densities in the normal phase, using a minimal set of band parameters relevant to the cuprate superconductors. We display the momentum space occupation function mk{m}_{k}mk​, energy dispersion curves locating the peaks of spectral functions, the optical conductivity, relaxation rates for quasiparticles, and the electronic spectral functions on an absolute scale. The line shapes have an asymmetric shape and a broad background that is also seen in experiments, and our calculations validate approximate recent versions of the theory. The results also display the experimentally noted high-energy kink and provide an in-depth understanding of its origin and dependence on band parameters.
We present our theoretical study of the single-particle spectral function in two-dimensional cuprates by using numerically exact diagonalization method on small clusters of the extended t-J model containing long-range hopping matrix elements. For a set of the parameter values, the calculated spectral function systematically explains the angle-resolved photoemission spectroscopy (ARPES) data for Bi2Sr2CaCu2O8+δ. For La2−xSrxCuO4 (LSCO), it is found that slightly smaller values of long-range hoppings are necessary for understanding an observed change of the Fermi surface topology with x. In addition, the dramatic suppression of spectral weight along (0,0)-(π,π) direction observed in under-doped LSCO is found to be explained by introducing an additional potential for holes which stabilizes vertical charge stripes.
We perform time resolved photoelectron spectroscopy measurements of optimally doped $\tn{Bi}_2\tn{Sr}_2\tn{CaCu}_2\tn{O}_{8+δ}$ (Bi-2212) and $\tn{Bi}_2\tn{Sr}_{2-x}\tn{La}_{x}\tn{Cu}\tn{O}_{6+δ}$ (Bi-2201). The electrons dynamics show that inelastic scattering by nodal quasiparticles decreases when the temperature is lowered below the critical value of the superconducting phase transition. This drop of electronic dissipation is astonishingly robust and survives to photoexcitation densities much larger than the value sustained by long-range superconductivity. The unconventional behaviour of quasiparticle scattering is ascribed to superconducting correlations extending on a length scale comparable to the inelastic path. Our measurements indicate that strongly driven superconductors enter in a regime without phase coherence but finite pairing amplitude. The latter vanishes near to the critical temperature and has no evident link with the pseudogap observed by Angle Resolved Photoelectron Spectroscopy (ARPES).
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gap-like behavior on parts of the Fermi surface, leaving a non-gapped segment known as Fermi arc around the diagonal of the Brillouin zone. Starting from the ttt-JJJ model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase in the framework of a novel renormalization scheme called PRM. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at a renormalized 'free' Hamiltonian for correlated electrons. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: We find well-defined excitation peaks around ω=0ω=0ω=0 near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small ωωω-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.
Recent photoemission spectroscopy measurements (T. J. Reber et al., arXiv:1509.01611) on cuprate superconductors have inferred that over a wide range of doping, the imaginary part of the electron self-energy scales as ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{''}}\ensuremath{\sim}{({\ensuremath{\omega}}^{2}+{\ensuremath{\pi}}^{2}{T}^{2})}^{a}$ with a=1a=1a=1 in the overdoped Fermi-liquid state and a<0.5a<0.5a<0.5 in the optimal to underdoped regime. We show that this non-Fermi-liquid scaling behavior can naturally be explained by the presence of a scale-invariant state of matter known as unparticles. We evaluate analytically the electron self-energy due to interactions with fermionic unparticles. We find that, in agreement with experiments, the imaginary part of the self-energy scales with respect to temperature and energy as ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{''}}\ensuremath{\sim}{T}^{2+2\ensuremath{\alpha}}$ and ${\ensuremath{\omega}}^{2+2\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ is the anomalous dimension of the unparticle propagator. In addition, the calculated occupancy and susceptibility of fermionic unparticles, unlike those of normal fermions, have significant spectral weights even at high energies. This unconventional behavior is attributed to the branch cut in the unparticle propagator which broadens the unparticle spectral function over a wide energy range and nontrivially alters the scattering phase space by enhancing (suppressing) the intrinsic susceptibility at low energies for negative (positive) $\ensuremath{\alpha}$. Our work presents evidence suggesting that unparticles might be important low-energy degrees of freedom in strongly coupled systems such as the cuprate superconductors.