Evidence for phonon-like charge and spin fluctuations from an analysis of angle-resolved photoemission spectra of La${}_{2\ensuremath{-}x}$Sr${}_{x}$CuO${}_{4}$ superconductors

In high temperature superconductors we provide evidence of spin and mixed phonon-charge collective modes as mediators of the effective electron-electron interaction and suggestive of a charge and spin density wave instability competing with superconductivity. Indeed, we show that the so-called kinks and waterfalls observed in angle-resolved photoemission spectra of La2-xSrxCuO4, a prototypical high-T-c superconducting cuprate, are due to the coupling of quasiparticles with two distinct nearly critical collective modes with finite characteristic wave vectors, typical of charge and spin fluctuations. The simultaneous presence of these two modes reconciles the long standing dichotomy whether kinks are due to phonons or spin waves.