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We deduce the normal state angle-resolved single-particle self-energy$\Sigma(\theta, \omega)$ and the Eliashberg function (i.e., the product of thefluctuation spectrum and its coupling to fermions) $\alpha^2 F(\theta,\omega)$for the high temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ fromthe ultra high resolution laser angle-resolved photoemission spectroscopy(ARPES). The self-energy $\Sigma(\theta, \omega)$ at energy $\omega$ alongseveral cuts normal to the Fermi surface at the tilt angles $\theta$ withrespect to the nodal direction in a slightly underdopedBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ were extracted by fitting the ARPES momentumdistribution curves. Then, using the extracted self-energy as the experimentalinput, the $\alpha^2 F(\theta,\omega)$ is deduced by inverting the Eliashbergequation employing the adaptive maximum entropy method. Our principal newresult is that the Eliashberg function $\alpha^2F(\theta,\omega)$ collapse forall $\theta$ onto a single function of $\omega$ up to the upper cut-off energydespite the $\theta$ dependence of the self-energy. The in-plane momentumanisotropy is therefore predominantly due to the anisotropic band dispersioneffects. The obtained Eliashberg function has a small peak at$\omega\approx0.05$ eV and flattens out above 0.1 eV up to the angle-dependentcut-off. It takes the intrinsic cut-off of about 0.4 eV or the energy of thebottom of the band with respect to the Fermi energy in the direction $\theta$,whichever is lower. The angle independence of the $\alpha^2 F(\theta,\omega)$is consistent only with the fluctuation spectra which have the shortcorrelation length on the scale the lattice constant. This implies among othersthat the antiferromagnetic fluctuations may not be underlying physics of thededuced fluctuation spectrum.

physical review. b, condensed matter and materials physics

Momentum Dependence of the Single-Particle Self-Energy and Fluctuation  Spectrum of Slightly Underdoped Bi_2 Sr_2 CaCu_2 O_{8+\delta} from High  Resolution Laser ARPES