Eliashberg Analysis of Overdoped Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8+\delta }\) Intrinsic Tunneling Spectra

Considering that Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8+\delta }\) (Bi2212) intrinsic Josephson junctions have a body-centered tetragonal structure, and we adjusted a directional tunneling matrix element in the effective density of states. Using the d-wave Eliashberg equations, tunneling spectra of overdoped Bi2212 intrinsic Josephson junction are well reproduced in a wide temperature range below the critical temperature \(T_c\). From which we obtained the pairing glue spectral function \(\alpha ^2F(\Omega )\), which is composed of a low-energy resonance peak and a high-energy broad spectrum. These two parts have different effects on the tunneling spectra: the low-energy resonance peak controls the entire shape of the tunneling spectra, and the high-energy broad spectrum maintains a certain electron-boson coupling constant \(\lambda \). Some interesting and important rules in the fitting process are summarized. The dip of tunneling spectra gradually disappears with increasing temperature, which can be fitted using a simple Dynes’ form of density of states, where the energy gap is energy-independent. As the temperature rises to \(T_c\), the main peak position of the density of states of the sample still remains a finite value, that is, the energy gap is not closed when the superconductivity disappears, which provides an angle to investigate the pseudogap phenomenon in high-\(T_c\) superconductors.