Electronic Spectra and Their Relation to the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>(</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>)</mml:mo></mml:math>Collective Mode in High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Superconductors

Abstract

The photoemission line shape near $(\ensuremath{\pi},0)$ in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ 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 $(\ensuremath{\pi},\ensuremath{\pi})$. The inferred mode energy and its doping dependence agree well with a magnetic resonance observed by neutron scattering.