Coexistence of $s$- and $d$-wave gaps due to pair-hopping and exchange interactions

TL;DR

This paper models high-$T_c$ superconductivity in a three-band system, revealing coexistence of $s$- and $d$-wave gaps driven by pair-hopping and exchange interactions, with implications for understanding complex gap structures.

Contribution

It introduces a three-band $t$-$J$-$U$ model incorporating pair-hopping and exchange interactions, demonstrating coexistence of $s$- and $d$-wave gaps in high-$T_c$ superconductors.

Findings

Superconductivity arises from pair-hopping and exchange interactions via the Suhl-Kondo mechanism.

Coexistence of extended $s$- and $d_{x^2-y^2}$-wave gaps in the superconducting state.

Charge fluctuations and $d$-$p$ band hybridization are key to gap coexistence.

Abstract

I investigate the superconductivity of the three-band $t$-$J$-$U$ model derived from the three-band Hubbard model using the Schrieffer-Wolff transformation. My model is designed considering the hole-doped high-$T_{\mathrm{c}}$ superconducting cup-rate. The model does not exclude the double occupancy of Cu sites by $d$ electrons, and there is a pair-hopping interaction between the $d$ and $p$ bands together with the exchange interaction. I analyse the superconducting transition temperature, electronic state, and superconducting gap function based on strong coupling theory and find that the superconductivity emerges due to the pair-hopping and exchange interactions via the Suhl-Kondo mechanism. In the superconducting state, the extended $s$- and $d_{x^2-y^2}$-wave superconducting gaps coexist, where both charge fluctuations and $d$-$p$ band hybridization are key ingredients.