Pseudogap in Eliashberg approach based on electron-phonon and electron-electron-phonon interaction

TL;DR

This paper models the pseudogap phenomenon in cuprate superconductors using an extended Eliashberg approach that includes electron-phonon and electron-electron-phonon interactions, reproducing key experimental features.

Contribution

It introduces a modified Eliashberg framework incorporating EEPh interactions, explaining pseudogap behavior and doping dependence consistent with experiments.

Findings

Pseudogap appears above the critical temperature.

Energy gap is mainly due to wave function renormalization and energy shift.

Doping dependence of the order parameter matches experimental trends.

Abstract

The properties of the superconducting and the anomalous normal state have been described by using the Eliashberg method. The pairing mechanism has been reproduced with help of the Hamiltonian, which models the electron-phonon and electron-electron-phonon interaction (EEPh). The set of the Eliashberg equations, which determines the order parameter function ($\varphi$), the wave function renormalization factor ($Z$), and the energy shift function ($\chi$) has been derived. It has been proven that for the sufficiently large values of EEPh potential, the doping dependence of order parameter ($\varphi/Z$) has the analogous course to that observed experimentally in cuprates. The energy gap in the electron density of states is induced by $Z$ and $\chi$ - the contribution from $\varphi$ is negligible. The electron density of states possesses the characteristic asymmetric form and the pseudogap is observed above the critical temperature.