$η$-pairing in the model with two-particle hybridization of conduction and localized electrons

TL;DR

The paper investigates a model in which conduction electrons acquire an effective two-particle attraction via a two-particle on-site hybridization with localized electrons. This attraction is realized when the two-particle localized level energy satisfies $ε_2 > 0$, and is strongest for η-pair states that form bound conduction electron pairs. Through a Schrieffer–Wolff transformation, an effective Hamiltonian $H_{\text{eff}} = H_0 + H_1 + H_2$ is derived, where $H_2$ provides a two-particle scattering term $2 c(k_1,k_2) = v^2 / (ε(k_1) + ε(k_2) - ε_2)$. The authors construct η-pair states $|Ψ_N\rangle = η^N |vac\rangle$, show off-diagonal long-range order with $\langle Ψ_N| η_{j_1} η^ abla_{j_2} |Ψ_N\rangle \sim (N/L)(1 - N/L)$, and derive the bound-pair energy $\mathcal{E} = \tfrac{1}{2}( ε_2 \pm \sqrt{ε_2^2 + 4 v^2})$, including the large- $ε_2$ limit $\mathcal{E} \approx -\frac{v^2}{ε_2}$. The work generalizes η-pairing to this two-particle hybridization model and suggests a mechanism for η-based superconductivity in real high-temperature superconductors.

Abstract

Within the framework of a model, that takes into account two-particle hybridization of conduction and localized electrons, the effective interaction between conduction electrons is calculated. It is shown that this interaction is attractive when the energy of the localized electron corresponding to the two-particle state lies in the conduction band above the Fermi energy. The magnitude of the attractive interaction is minimal for $η$-paired states of conduction electrons. We generalize the original $η$-pairing construction for the proposed model and show that the superconducting state can indeed be realized.

Figures (2)

• Figure 1: The one-particle energies of conduction $\epsilon (k)=-2\cos k$ (blue line) and localized electrons (red lines) as a function of the wave vector, $\epsilon_2=2\varepsilon_g +U$.
• Figure 2: $\delta c(k_1,k_2)/v^2=-\frac{1}{\epsilon_2}-\frac{1}{\epsilon (k_1)+\epsilon(k_2)-\epsilon_2}$ as a function of the wave vectors of scattered electrons $k_1$ and $k_2$ calculated for $\epsilon_2=1$, $\epsilon (k)=-2\cos k$.