Bernhard Keimer, Alexey V. Pan, Chengtian Lin, Helmuth Berger, J. Geck, Bernd Büchner, Seiki Komiya, M. Knupfer, Sergey Borisenko, V. B. Zabolotnyy, J. Fink, A. A. Kordyuk, and Yoichi Ando
Applying the Kramers-Kronig consistent procedure, developed earlier, we investigate in detail the formation of the quasiparticle spectrum along the nodal direction of high-Tc cuprates. The heavily discussed ‘‘70 meV kink’’ on the renormalized dispersion exhibits a strong temperature and doping dependence when purified from structural effects such as bilayer splitting, diffraction replicas, etc. This dependence is well understood in terms of fermionic and bosonic constituents of the self-energy. The latter follows the evolution of the spin-fluctuation spectrum, emerging below some doping dependent temperature and sharpening below Tc, and is mainly responsible for the formation of the kink in question. The nodal direction is thought to be the simplest place in the Brillouin zone of high-Tc cuprates where electron renormalization effects can be most easily understood. However, since the discovery of an energy scale in the experimental dispersion [1–3], the so-called ‘‘70 meV kink’’, its origin remains a matter of extensive debate [4 – 14], which now has converged into a vital dilemma: phonon versus spin fluctuations [15]. Historically, the kink has been associated with a coupling to the magnetic resonance mode because of its energy and doping dependence [2], its seemingly smooth evolution into a spectral dip when moving to the antinodal region [3,4], and its temperature dependence (emerging below Tc )[ 5]. At the same time, the persistence of the effect above Tc reported by another group [2] was taken as an argument against the resonance mode scenario. Moreover, a visual ‘‘ubiquity’’ of the kink for a number of families of cuprates in a wide range of doping and temperature [6] and recently found similarity between a fine structure seen in dispersion to an expected phonon spectrum [8] have made a strong claim in favor of phonon scenario. However, we have also recently reported a careful investigation of the scattering rate kink [10], which is a simple consequence of the Kramers-Kronig (KK) relation between the real and imaginary parts of the electron self-energy [12]. The observed strong dependence of this kink on doping and temperature (xT dependence) questions seriously the phonon scenario. Moreover, the odd parity [13] and strong dependence on Zn impurities [14] of the nodal scattering form solid arguments for the magnetic scenario. Thus, from a number of arguments from both sides, it seems that studies on the nature of the nodal kink have brought us to a stalemate, and an evident way to resolve it is to turn from a qualitative consideration of the kink effect to its quantitative analysis to derive the parameters of the bosonic spectrum that will enable unambiguous identification of its origin. Recently we have developed a KK-consistent procedure [12] which allows extraction of both the self-energy and the underlying bare dispersion from the photoemission data, and, thus, to place the kink problem into a quantitative domain. Subsequently, we have applied this self