Screened superexchange mechanism for superconductivity applied to cuprates

TL;DR

This paper addresses the high-temperature superconductivity puzzle in cuprates by applying a Kohn–Luttinger–style dynamical screening concept to a three-band CuO2 model. Through a Schrieffer–Wolff transformation and Hartree–Fock–Bogoliubov mean-field analysis, it derives an effective attractive interaction in the $d$-wave channel and predicts a temperature–doping phase diagram that includes superconductivity, pseudogap, strange metal, and antiferromagnetism, with a BCS-like energy spectrum featuring nodal gaps. Key contributions include the identification of density- and screening-dependent parameters $n$ and $n_{ar{oldsymbol{ abla}}}$ that govern pairing, the derivation of a $t$–$J$–like AF regime, and semi-quantitative agreement with observed cuprate phenomenology. The work suggests that strong screening of superexchange could enable higher $T_c$ and even room-temperature superconductivity under favorable conditions, providing a unified framework that links microscopic orbital physics to macroscopic phases.

Abstract

In 1965, Kohn and Luttinger published a note revealing that dynamical screening of the repulsive Coulomb interaction leads under certain conditions to an effective attraction necessary for the formation of Cooper pairs. We propose such a formalism adapted to the cuprates where the screening arises from the superexchange dynamics of virtual holes in the oxygen orbitals of the $Cu O_2$ plane. Using an adequate Schrieffer-Wolff transformation, the basic Hartree-Fock-Bogoliubov (HFB) method and the {\it ab initio} data on orbitals (energy, hopping, interaction), we derive some predictions for the temperature-doping phase diagram (pseudo-gap, strange metal, antiferromagnetism, superconducting and normal states) and for the doping dependant band energy spectrum in semi-quantitative agreement with observations.

Figures (5)

• Figure 1: Schematic explanation of pairing: (a) Four independant triads consisting each of two $d$ sites interacting via a $p$ site. Comparison between the energy of two single holes $u_1 +u_{1'}$ and the energy of no hole and pairing of energy $u_0+u_2$. (b) Schematic energy graph of $u_\nu$ for various occupation $\nu$. The repulsive potential $U_{pd}$ is crucial for pairing. Its screening role reduces the delocalisation of any hole on the $p$ orbital and increases the energy. Such a "thin" hole contrasts with a "fat" hole with a more delocalized state on the $p$ orbital. SC pairing becomes favorable with one additional hole where $u_\nu$ takes a convex form caused by the perturbative term $-t_{pd}^2/(\epsilon_p + \nu U_{pd})$. Similarly, $u_\nu$ is also convex for two additional holes but concave in absence of any hole leading to the PG phase.
• Figure 2: First graph of the hopping factor $t$ in red and potential $U$ in blue vs. the doping $n$. The dash line on the x axis is a guide for the eye. Second graph of the critical superconducting (SC) temperature vs. the doping $n$ for the parameter values $\epsilon_p=2$, $U_{pd}=0.53$, $U_d=7.925$ and $t_{pp}=0$ expressed in unit of $t_{pd}$.
• Figure 3: Same as in Fig.\ref{['fig:1']} but for $\epsilon_p=0.4$, $U_{pd}=1.55$, $U_d=6.6$ and $t_{pp}=0$.
• Figure 4: Same as in Fig.\ref{['fig:1']} but for $\epsilon_p=0.4$, $U_{pd}=1.55$, $U_d=6.6$ and $t^{eff}_{pp}=0.038$ and with the transition line for the pseudogap (PG) the strange metal (SM) and the Fermi liquid (FL) phases in the second graph.
• Figure 5: First graph: canonical free energy $f_{CN}$ vs. doping $n$ at zero temperature for the HF state for positive and negative $n_\epsilon$ and for the pseudogap expressed with respect to the free energy reference $f^{0}_{CN}$ without hopping (see Eq.(\ref{['f0']})). Second graph: pseudogap potential vs. the doping $n$. We use the parameters of Fig.\ref{['fig:3']}.