Spin-Triplet Pairing Induced by Near-Neighbor Attraction in the Cuprate Chain

In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, mediated by phonons, has been unveiled in one-dimensional copper-oxide chain Ba$_{2-x}$Sr$_x$CuO$_{3+\delta}$. Yet, it is unclear how this strong near-neighbor attraction $V$ influences the superconductivity pairing in the compound. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion $U>0$ and attraction $V<0$ that well describes the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase -- besides the spin density wave and various phase separation phases -- that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened in the parameter space and extends to larger $U$, offering a feasible mechanism to realize $p$-wave superconductivity in realistic cuprate chains.