Quasiparticle Scattering Interference in High Temperature Superconductors

By performing explicit T-matrix calculations we show that scattering by impurities can produce quasiparticle interference patterns recently observed by high resolution scan tunnelling microscopy image of the local density of states in $Bi_2Sr_2CaCu_2O_{8+\delta}$ [hoff2]. This result clarifies the extent by which real-space STM images can extract quasiparticle dispersion in the momentum space.