Role of the upper branch of the hour-glass magnetic spectrum in the formation of the main kink in the electronic dispersion of high-T$_ ext{c}$ cuprate superconductors

摘要

We investigate the electronic dispersion of the high-T$_{\mathrm{c}}$ cupratesuperconductors using the fully self-consistent version of the phenomenologicalmodel, where charge planar quasiparticles are coupled to spin fluctuations. Theinputs we use ---the underlying (bare) band structure and the spinsusceptibility $\chi$--- are extracted from fits of angle resolvedphotoemission and inelastic neutron scattering data of underdopedYBa$_{2}$Cu$_{3}$O$_{6.6}$ by T. Dahm and coworkers (T. Dahm et al., Nat. Phys.5, 217 (2009)). Our main results are: (i) We have confirmed the finding by T.Dahm and coworkers that the main nodal kink is, for the present values of theinput parameters, determined by the upper branch of the hour-glass of $\chi$.We demonstrate that the properties of the kink depend qualitatively on thestrength of the charge-spin coupling. (ii) The effect of the resonance mode of$\chi$ on the electronic dispersion strongly depends on its kurtosis in thequasimomentum space. A low (high) kurtosis implies a negligible (considerable)effect of the mode on the dispersion in the near-nodal region. (iii) The energyof the kink decreases as a function of the angle $\theta$ between the Fermisurface cut and the nodal direction, in qualitative agreement with recentexperimental observations. We clarify the trend and make a specific predictionconcerning the angular dependence of the kink energy in underdopedYBa$_{2}$Cu$_{3}$O$_{6.6}$.