Analysis of Laser ARPES from Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ in superconductive state: angle resolved self-energy and fluctuation spectrum

Abstract

We analyze the ultra high resolution laser angle resolved photo-emission spectroscopy (ARPES) intensity from the slightly underdoped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ in the superconductive (SC) state. The momentum distribution curves (MDC) were fitted at each energy $\w$ employing the SC Green's function along several cuts perpendicular to the Fermi surface with the tilt angle $\theta$ with respect to the nodal cut. The clear observation of particle-hole mixing was utilized such that the complex self-energy as a function of $\omega$ is directly obtained from the fitting. The obtained angle resolved self-energy is then used to deduce the Eliashberg function $α^2 F^{(+)}(þ,\w)$ in the diagonal channel by inverting the d-wave Eliashberg equation using the maximum entropy method. Besides a broad featureless spectrum up to the cutoff energy ${\omega }_c$, the deduced ${\alpha }^{2}F$ exhibits two peaks around 0.05 eV and 0.015 eV. The former and the broad feature are already present in the normal state, while the latter emerges only below $T_c$. Both peaks become enhanced as $T$ is lowered or the angle $þ$ moves away from the nodal direction. The implication of these findings are discussed.

7 pages, 5 figures, summited to PRB