Unconventional properties of superconducting cuprates

We present an explanation of the unusual peak/dip/hump features observed in photoemission experiments on Bi2212 at $T\ll T_c$. We argue that these features arise from the interaction of the fermionic quasi-particles with overdamped spin fluctuations. We show that the strong spin-fermion interaction combined with the feedback effect on the spin damping due to superconductivity yields a Fermi-liquid form of the fermionic spectral function for $\omega < 2 \Delta$where$\Delta$ is the maximum value of the superconducting gap, and a non-Fermi-liquid form for $\omega >2\mathrm{\Delta }$. In the Fermi-liquid regime, the spectral function $A({\mathbf{k}}_F,\omega )$ displays a quasiparticle peak at $\omega =\mathrm{\Delta }$; in the non-Fermi-liquid regime it possesses a broad maximum (hump) at $\omega \gg \mathrm{\Delta }$. In between the two regimes, the spectral function has a dip at $\omega \sim 2\mathrm{\Delta }$. We argue that our theory also explains the tunneling data for the superconducting density of states.