Supermodulation in the atomic structure of the superconductor Bi₂Sr₂CaCu₂O_8+x from ab initio calculations

We present results of density functional theory (DFT) calculation of the structural supermodulation in Bi₂Sr₂CaCu₂O_8+x structure, and show that the supermodulation is indeed a spontaneous symmetry breaking of the nominal crystal symmetry, rather than a phenomenon driven by interstitial O dopants. The structure obtained is in excellent quantitative agreement with recent x-ray studies, and reproduces several qualitative aspects of scanning tunneling microscopy (STM) experiments as well. The primary structural modulation affecting the CuO₂ plane is found to be a buckling wave of tilted CuO₅ half-octahedra, with maximum tilt angle near the phase of the supermodulation where recent STM experiments have discovered an enhancement of the superconducting gap. We argue that the tilting of the half-octahedra and concomitant planar buckling are directly modulating the superconducting pair interaction.