Pseudogap in the Eliashberg approach based on electron‐phonon and electron‐electron‐phonon interaction

Abstract

The properties of the superconducting and the anomalous normal state were described by using the Eliashberg method. The pairing mechanism was reproduced with the help of the Hamiltonian, which models the electron-phonon and the electron-electron-phonon interaction (EEPh). The set of the Eliashberg equations, which determines the order parameter function (ϕ), the wave function renormalization factor (Z), and the energy shift function (χ ), was derived. It was proven that for the sufficiently large values of the EEPh potential, the doping dependence of the order parameter (ϕ/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 χ -the contribution from ϕ is negligible. The electron density of states possesses the characteristic asymmetric form and the pseudogap is observed above the critical temperature.

Superconducting Properties of 3D Low-Density Translation-Invariant Bipolaron Gas

“…Surprisingly, it was found that, in oxide ceramics, the correlation length is some orders of magnitude less than that in traditional metal superconductors while the ratio of the energy gap to the temperature of superconducting transition is much greater [3]. The current status of research can be found in books and reviews [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Diagram of the Critical Temperature—Nernst Temperature for the Superconductivity Induced by Modified Electron-Phonon Interaction

“…Above T C , the values of ϕ (T ) are declining much faster, while for T = 183.5 K, we observe the first order phase transition instead of the second order phase transition. Note that the change in the nature of the phase transition is induced by the applied approximations-the correct type of the phase transition is predicted on the Eliashberg equations level [36]. Interestingly, the value of the temperature, at which the transition occurs, is well defined and can be properly interpreted physically as will be discussed in the next section.…”

“…In the presented paper, we will show that beginning from the Eliashberg equations, presented in [36], one can get the generalized mean-field model. Next, we will derive the analytical formulas for the most important thermodynamic parameters of the superconducting state.…”

“…Recently, the EPh and EEPh interactions were analyzed beyond the mean-field approximation in the framework of the Eliashberg formalism [36]. It was shown that for the relevantly large values of the EEPh potential the dependence of the order parameter on the doping has the analogous course like in cuprates (visible is even the characteristic plateau [3]), the electron density of states is asymmetric which also agrees qualitatively with the experimental data [37], and above the critical temperature exists the pseudogap, which turns out to be induced by the many-body and strong-coupling effects.…”

The Symmetry of Pairing and the Electromagnetic Properties of a Superconductor with a Four-Fermion Attraction at Zero Temperature

“…We suspect that the four-electron term would appear in the second order of this expansion. One needs to mention that the problem of the four-fermion interaction in superconductors was investigated in a series of papers by Szczȩśniak et al [14][15][16]. In some of them, the Eliashberg formalism was applied in order to deal with cuprates as systems with strong coupling of electrons to phonons.…”