Quasiparticle scattering interference in high-temperature superconductors

We propose that the energy-dependent spatial modulation of the local density of states seen by Hoffman [Science 297, 1148 (2002)] is due to the scattering interference of quasiparticles. In this paper we present the general theoretical basis for such an interpretation and lay out the underlying assumptions. As an example, we perform an exact T-matrix calculation for the scattering due to a single impurity. The results of this calculation is used to check the assumptions, and to demonstrate that quasiparticle scattering interference can indeed produce patterns similar to those observed by Hoffman et al.