Supermodulation in the atomic structure of the superconductorBi2Sr2CaCu2O8+xfromab initiocalculations

Abstract

We present results of density functional theory (DFT) calculation of the structural supermodulation in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ 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 $\mathrm{Cu}{\mathrm{O}}_{2}$ plane is found to be a buckling wave of tilted $\mathrm{Cu}{\mathrm{O}}_{5}$ 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.