Deduction of the self-energy and bosonic spectrum of Bi2212 from ARPES experiments

We analyzed the ARPES intensity of slightly underdoped ($T_{c}$=89K)and overdoped ($T_{c}$=82K) Bi2212 superconductors. The diagonal and off-diagonal self-energy, $\Sigma$ and $\phi$, were extracted by performing MDC (momentum distribution curve) fitting using superconducting Green's function at the tilt angle $\theta$ with respect to the nodal direction. Using the extracted self-energy as input, the Eliashberg function $\alpha^{2}F^{(+)}$ and $\alpha^{2}F^{(-)}$ corresponding to $\Sigma$ and $\phi$ were deduced by inverting the d-wave Eliashberg equation. Our main results are follows: (1) The deduced Eliashberg functions are similar for slightly underdoped and overdoped Bi2212. (2) The Eliashberg function $\alpha^{2}F^{(+)}$ has two peaks at ~15meV and ~50meV. Both peaks were enhanced as the tilt angle increases or temperature decreases. The Eliashberg function $\alpha^{2}F^{(-)}$ has one peak at ~15meV. Its energy scale is almost the same as the energy scale of the low energy peak of $\alpha^{2}F^{(+)}$. Then, we will compare our results with other experiments and modal calculations.