Evolution of the bosonic spectral density of the high-temperature superconductor Bi2Sr2CaCu2O8+δ

We demonstrate that an Eliashberg inversion of the optical self-energy, based on maximum-entropy considerations, can be used to extract in numerical form the bosonic excitation spectra of high-transition-temperature superconductors. In Bi2Sr2CaCu2O8+delta we explicitly show that the bosonic mode that dominates the self-energy at low temperatures and small energies directly evolves out of a balanced transfer of spectral weight to the mode from the continuum just above it. This redistribution starts already at 200 K in optimally doped materials but is much weaker in overdoped samples. This finding presents a challenge to theories of the spin susceptibility and to neutron scattering experiments in high-temperature superconductors.