Analysis of the elementary excitations in high-T_c cuprates: explanation of the new energy scale observed by ARPES

Using the Hubbard Hamiltonian we analyze the energy- and momentum-dependence of the elementary excitations in high-T$_c$ superconductors resulting from the coupling to spin fluctuations. As a result of the energy dependence of the self-energy $\Sigma ({\bf k}, \omega)$, characteristic features occur in the spectral density explaining the 'kink' in recent ARPES experiments. We present results for the spectral density $A({\bf k}, \omega)$ resulting from the crossover from Im $\Sigma ({\bf k}, \omega)\propto \omega$ to Im $\Sigma ({\bf k}, \omega)\propto \omega^2$, for the feedback of superconductivity on the excitations, and for the superconducting order parameter $\Delta({\bf k}, \omega)$. These results relate also to inelastic neutron scattering and tunneling experiments and shed important light on the essential ingredients a theory of the elementary excitations in the cuprates must contain.