Electronic Spectra and Their Relation to the(π,π)Collective Mode in High-TcSuperconductors

The photoemission line shape near $(\pi ,0\mathrm{})$ in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ below $T_c$ is characterized by a sharp peak, followed at higher energy by a dip and hump. We study the evolution of this line shape as a function of momentum, temperature, and doping. We find the hump scales with the peak and persists above $T_c$ in the pseudogap state. We present strong evidence that the peak-dip-hump structure arises from the interaction of electrons with a collective mode of wave vector $(\pi ,\pi )$. The inferred mode energy and its doping dependence agree well with a magnetic resonance observed by neutron scattering.