Doping induced singlet to triplet superconducting transition in Ba${}_2$CuO${}_{3+\hat{I}´}$

Abstract

In this study, we perform a numerical simulation on the recently discovered high-temperature superconductor ($T_c$= 73K) Ba${}_2$CuO${}_{3.2}$ \cite{lietal} while focusing on doping dependence of alternating CuO${}_6$ octahedra and CuO chain-like states. Employing the multiband random-phase approximation, we compute the spin-fluctuation mediated pairing interaction, subsequently determining its pairing eigenvalues and eigenfunctions relative to oxygen-doping levels. We find that, for the certain range of hole doping in Ba${}_2$CuO${}_{3+\hat{I}´}$, a singlet $d_{x^2-y^2}$-wave pairing symmetry emerges as long as we keep the doping below the critical value $x_c$. Interestingly upon hole doping, the dominant pairing symmetry undergoes a transition to a triplet (odd paring) type from the singlet state. This change in pairing is driven by the competition between the nesting vectors coming from the Fermi surface of $d_{z^2}$ and $d_{x^2-y^2}$ orbitals within the CuO${}_6$ octahedra. This triplet state is attainable through hole doping, while supressing inter-layer self-doping effects. Furthermore, we present the density of states within the superconducting phase, offering a potential comparison with tunnelling spectra in Ba${}_2$CuO${}_{3+\hat{I}´}$. Our research provides novel insights into the intricate pairing symmetries in Ba${}_2$CuO${}_{3+\hat{I}´}$ and their underlying pairing mechanisms.