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AIP conference proceedings

Theory of the photoemission spectral function in high T[sub c] cuprates

Takami Tohyama, Susumu Nagai, Yasumasa Shibata, Sadamichi Maekawa

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.59612

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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.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on La1.28Nd0.6Sr0.12CuO4.{\mathrm{La}}_{1.28}{\mathrm{Nd}}_{0.6}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}.La1.28​Nd0.6​Sr0.12​CuO4​.
By comparing single-particle spectral functions of t-J and Hubbard models with recent angle-resolved photoemission (ARPES) results for LSCO and Nd-LSCO, we can decide where holes go as a function of doping, and more specifically, which type of stripe (bond-, site-centered) is present in these materials at a given doping. For dopings greater than about 12% our calculation shows furthermore that the holes prefer to proliferate out of the metallic stripes into the neighboring antiferromagnetic domains. The spectra were calculated by a cluster perturbation technique, for which we present an alternative formulation. Implications for the theory for high-Tc superconductivity are discussed.
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.
The 2D t-J model with and without t' and t'' hopping-terms is studied by exact diagonalization on a 5 x 4 cluster, which realizes a hole stripe in y-direction in a dimerized singlet background. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle-peaks in the single-particle spectrum is in good agreement with a simple bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of t' and t''. The resulting spectral weight distribution and Fermi surface agree well with experimental ARPES spectra on La_1.28 Nd_0.6 Sr_0.12 Cu O_4.
It is shown that spectral functions within the extended t-J model, evaluated using the finite-temperature diagonalization of small clusters, exhibit the high-energy kink in single-particle dispersion consistent with recent angle-resolved photoemission results on hole-doped cuprates. The kink and waterfall-like features persist up to large doping and to temperatures beyond J; hence, the origin can be generally attributed to strong correlations and incoherent hole propagation at large binding energies. In contrast, our analysis predicts that electron-doped cuprates do not exhibit these phenomena in photoemission.
Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated antiferromagnets (AFMs). But, describing them theoretically, even in simplified toy models, remains a challenge. Here, we study ARPES spectra of a single mobile hole in the $t\ensuremath{-}J$ model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the undoped parent AFM. We thoroughly test this hypothesis for a single hole doped into a two-dimensional Heisenberg AFM by comparing our semianalytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state calculations of the spectral function. Our conclusion is supported by a microscopic trial wave function describing spinon-chargon bound states, which captures the momentum and t/Jt/Jt/J dependence of the quasiparticle residue. From our conjecture we speculate that ARPES measurements in the pseudogap phase of cuprates may directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wave function provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the crossover from two to one dimension, where spinons and chargons are confined and deconfined, respectively.