Momentum dependence of the single-particle self-energy and fluctuation spectrum of slightly underdoped Bi2Sr2CaCu2O8+δ from high-resolution laser angle-resolved photoemission

We deduce the normal-state angle-resolved single-particle self-energy Sigma(theta,omega) and the Eliashberg function (i.e., the product of the fluctuation spectrum and its coupling to fermions alpha F-2(theta,omega) for the high-temperature superconductor Bi2Sr2CaCu2O8+delta from the ultrahigh-resolution laser angle-resolved photoemission spectroscopy (ARPES). The self-energy Sigma(theta,omega) at energy omega along several cuts normal to the Fermi surface at the tilt angles theta with respect to the nodal direction in a slightly underdoped Bi2Sr2CaCu2O8+delta were extracted by fitting the ARPES momentum distribution curves. Then, using the extracted self-energy as the experimental input, the alpha F-2(theta,omega) is deduced by inverting the Eliashberg equation employing the adaptive maximum entropy method. Our principal result is that the Eliashberg functions alpha F-2(theta,omega) collapse for all theta onto a single function of omega up to the upper cut-off energy despite the theta dependence of the self-energy. The in-plane momentum anisotropy is therefore predominantly due to the anisotropic band-dispersion effects. The obtained Eliashberg function has a small peak at omega approximate to 0.05 eV and flattens out above 0.1 eV up to the angle-dependent cutoff. It takes the intrinsic cutoff of about 0.4 eV or the energy of the bottom of the band with respect to the Fermi energy in the direction theta, whichever is lower. The angle independence of the alpha F-2(theta,omega) is consistent only with the fluctuation spectra which have the short correlation length on the scale of the lattice constant. This implies among others that the antiferromagnetic fluctuations may not be the underlying physics of the deduced fluctuation spectrum.