Network Topology and Subgap Resonances Observed by Fourier Transform Scanning Tunnelling Microscopy in Cuprate High-Temperature Superconductors

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Fourier transform scanning tunneling microscopy on BSCCO subgap resonances has deciphered an octet of "quasi-particle" states that are consistent with the Fermi surface and energy gap observed by ARPES, but the origin of the high-intensity k-space octets and the sharply defined r-space checkerboard is unexplained. The filamentary ferroelastic nanodomain model that predicted the r-space checkerboard also explains the k-space octets and the origin of the apparent anisotropic surface d-wave gap by using strong electron-phonon interactions outside the CuO2 planes. The topological model identifies the factors that stabilize high-intensity k-space octets in the presence of a very high level of irregular r-space checkerboard noise.