Network topology and subgap resonances observed by Fourier transform scanning tunnelling microscopy of cuprate high-temperature superconductors

Fourier transform scanning tunnelling microscopy (STM) on Bi2Sr2CaCu2O8+ δ (BSCCO) subgap resonances has deciphered an octet of ‘quasiparticle’ states that are consistent with the Fermi surface and energy gap observed by angle-resolved photoemission spectroscopy (ARPES), but the origin of the high-intensity k-space octets and the sharply defined r-space chequerboard is unexplained. The filamentary ferroelastic nanodomain model that predicted the r-space chequerboard 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 chequerboard noise.