t-J model on the effective brick-wall lattice for newly discovered high temperature superconducting Ba\(_2\)CuO\(_{3+\delta}\)

Abstract

Layered copper oxides have highest superconducting transition temperatures at ambient pressure. Its mechanism remains a grand challenge in condensed matter physics. The essential physics lying in 2-dimensional copper-oxygen layers is well described by a single band Hubbard model or its strong coupling limit t-J model in 2-dimensional square lattice. Recently discovered high temperature superconductor Ba\(_2\)CuO\(_{3+\delta}\) with \(\delta \sim 0.2\) has different crystal structure with large portion of in-plane oxygen vacancies. We observe that an oxygen vacancy breaks the bond of its two neighboring copper atoms, and propose ordered vacancies in Ba\(_2\)CuO\(_{3+\delta}\) lead to extended t-J model on an effective brick-wall lattice. For the nearest neighbor hopping, the brick-wall model can be mapped onto t-J model on honeycomb lattice. Our theory explains the superconductivity of the new compound at high charge carrier density, and predict a time reversal symmetry broken pairing state.