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$_\text{c}$ cuprate superconductors

Phys. Rev. B 93, 144501 (2016) We investigate the electronic dispersion of the high-T$_{\mathrm{c}}$ cuprate superconductors using the fully self-consistent version of the phenomenological model, where charge planar quasiparticles are coupled to spin fluctuations. The inputs we use ---the underlying (bare) band structure and the spin susceptibility $\chi$--- are extracted from fits of angle resolved photoemission and inelastic neutron scattering data of underdoped YBa$_{2}$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 the input parameters, determined by the upper branch of the hour-glass of $\chi$. We demonstrate that the properties of the kink depend qualitatively on the strength of the charge-spin coupling. (ii) The effect of the resonance mode of $\chi$ on the electronic dispersion strongly depends on its kurtosis in the quasimomentum space. A low (high) kurtosis implies a negligible (considerable) effect of the mode on the dispersion in the near-nodal region. (iii) The energy of the kink decreases as a function of the angle $\theta$ between the Fermi surface cut and the nodal direction, in qualitative agreement with recent experimental observations. We clarify the trend and make a specific prediction concerning the angular dependence of the kink energy in underdoped YBa$_{2}$Cu$_{3}$O$_{6.6}$.