High-Energy Kink in the Single-Particle Spectra of the Two-Dimensional Hubbard Model

Abstract

Employing dynamical cluster quantum Monte Carlo calculations we show that the single particle spectral weight A(k, ω) of the one-band two-dimensional Hubbard model displays a high energy kink in the quasiparticle dispersion followed by a steep dispersion of a broad peak similar to recent ARPES results reported for the cuprates. Based on the agreement between the Monte Carlo results and a simple calculation which couples the quasiparticle to spin fluctuations, we conclude that the kink and the broad spectral feature in the Hubbard model spectra is due to scattering with damped high energy spin fluctuations. Introduction.Angle-resolved photoemission spectroscopy (ARPES) has revealed much about the cuprates, including the energy scales associated with the d-wave gap[1] and a low energy kink presumably associated with strong electron-phonon coupling [2]. Recent ARPES experiments have revealed a high-energy (HE) kink and a waterfall structure [3,4,5,6,7,8], in which the band dispersion broadens and falls abruptly at binding energies below ≈ 0.35 eV. The origin of this kink has been attributed to a crossover from the quasiparticle (QP) to the Mott-Hubbard band[4, 9] the settlement of spincharge separation [3], or interaction of the quasiparticles (QP) with spin fluctuation excitations [5,10,11,12,13].In this Letter, we study the single particle spectral weight A(k, ω) of the one-band 2D Hubbard model with near-neighbor hopping t and Coulomb interaction U in the regime where U is comparable to the bandwidth W = 8t and in the doping range relevant for cuprate superconductors. The single-band Hubbard model is believed to describe the low-energy physics of the cuprates down to energies of ≈ 2t below Fermi surface (FS). Surprisingly, the calculated spectra of the single band model are remarkably similar to the experimental ones down to binding energies of ≈ 4t − 5t. They reveal a sharp QP feature down to a kink energy E kink , followed by a steep dispersion of a broad waterfall structure. We find that these features are accurately captured by a renormalized second order (RSO) approximation to the self-energy in which the QP couple only to spin fluctuations. A careful inspection of the different contributions to the RSO self energy shows that the HE kink and the waterfall structure is due to the coupling to damped high energy spin excitations.

Anisotropic softening of magnetic excitations along the nodal direction in superconducting cuprates

“…These two approaches can be seen as approximations of the Hubbard model, which probably contains the relevant physics, including superconductivity 10 , and could form the basis of a comprehensive theory that bridges the gap between these two limits. Indeed, numerical calculations on clusters of finite size have shown to be consistent with experimentally measured electronic and magnetic excitation spectra 11,12 . However, a generally valid solution to the Hubbard model remains out of reach.…”

Calculated Momentum Dependence of Zhang-Rice States in Transition Metal Oxides

“…Here, all spectral weight gets transferred to the Hubbard bands located at the scale of U and also to the oxygen band. While we are unable to account for the effect of the imaginary self-energy in the exact diagonalization for small clusters, recent DCA simulations of the Hubbard model [23] have shown very asymmetric k-dependent spectral functions resembling the waterfall. On top of that a lot of other states are present below −1 eV, as shown in Fig.1 (bottom panel).…”

“…A hot discussion has appeared in the literature around most recent ARPES experiments which have shown that the ZR band vanishes as the wave vector approaches the Γ point, with the spectral weight seemingly transferring to higher-energies as the "waterfall" [14]. While it could be simple photoemission matrix element effect, most recent dynamical cluster approximation (DCA) based simulations of the 2D Hubbard model show [23] large imaginary part of the self-energy, resulting in asymmetric spectral functions resembling the waterfall. As we generally see, the HTSCs still represent a challenge for the theory, particularly for modern electronic structure calculations, which try to incorporate all hopping integrals accurately and use realistic values of the Coulomb interaction parameters.…”

High-Energy Anomaly in the Angle-Resolved Photoemission Spectra ofNd2−xCexCuO4:

“…This difference was interpreted in terms of a shift of the chemical potential [14]. The experimental studies were accompanied by numerous theoretical papers [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

“…For the phenomenon of the HEA, a number of explanations have been suggested including Mott-Hubbard models with a transition from the coherent quasi-particle dispersion to the incoherent lower Hubbard band [5,18,21,26,32], a disintegration of the low-energy branch into a holon and spinon band due to a spin charge separation [2], a coupling to spin fluctuations [9,17,19,29,33], a coupling to phonons [7], string excitations of spinpolarons [32], a bifurcation of the quasi-particle band due to an excitation of a bosonic mode of charge 2e [22], and a coupling to plasmons [16]. These are all intrinsic interpretations in terms of many-body interactions leading to a change of the spectral function.…”