Fourier Transform Scanning Tunneling Spectroscopy: A New Window on the Electronic Structure of Bi₂Sr₂CaCu₂O _8+δ

Scanning tunneling spectroscopy is used to study the dispersive wave vectors of the local-density-of-states modulations in near-optimal Bi ₂Sr₂CaCu₂O_8+δ. Atomic-resolution energy-resolved spectroscopic images are acquired in a 650 Å field of view on the BiO cleave surface of these crystals at 4.2 K. Fourier transforms are used to measure the wave vectors of spatial modulations in the local density of states. At sub-gap energies, up to 16 inequivalent sets of dispersive wave vectors are observed. When analyzed within a model of quasiparticle scattering-induced interference between a characteristic "octet" of states in momentum-space, they yield an estimate of the Fermi-surface location and the energy gap |Δ(k)| in agreement with angle-resolved photoemission spectroscopy. At energies approaching the gap-maximum, the local-density-of-states modulations become intense, commensurate with the crystal, and localized by the apparent nanoscale domains. This may indicate that the lifetimes of the k = (π/a₀, 0) quasiparticles are determined by nanoscale disorder scattering.