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

TL;DR

This study uses high-resolution laser ARPES to analyze the self-energy and fluctuation spectrum in underdoped Bi2212 superconductors, revealing two distinct peaks in the Eliashberg function that evolve with temperature and momentum.

Contribution

It introduces a method to directly extract angle-resolved self-energy and Eliashberg functions from ARPES data in the superconducting state, revealing detailed spectral features.

Findings

Identification of two peaks in the Eliashberg function at 0.05 eV and 0.015 eV.

The 0.015 eV peak emerges only below the critical temperature $T_c$.

Both peaks are enhanced as temperature decreases or momentum moves away from the nodal direction.

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 $\alpha^2 F^{(+)}(\th,\w)$ 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 $\th$ moves away from the nodal direction. The implication of these findings are discussed.