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A recently discovered high-Tc cuprate superconductor Ba2CuO$_{4-\delta}$exhibits exceptional Jahn-Teller distortion, wherein the CuO6 octahedrons arecompressed along the c axis. As a consequence, the O vacancies prefer to residein the CuO2 plane, but the exact structure is not known. By combiningfirst-principles total energy calculation with the automated structureinversion method, the effective cluster interactions of O vacancies are mappedout. Around $\delta$=0.8, where the 73K superconductivity was observedexperimentally, we predict that the ordered O vacancies slice the CuO2 planeinto not only 1D chains and but also two-leg ladders. A Monte Carlo simulationis performed based on the effective cluster interaction model, showing thatsuch an ordering pattern is stable up to ~900 K. Our results put forth aconcrete structural basis to discuss the underlying superconducting mechanism.

In-plane ordering of O vacancies in a high-Tc cuprate superconductor with compressed Cu-O octahedrons: a first-principles cluster expansion study