Wave-vector power spectrum of the local tunneling density of states: Ripples in ad-wave sea

A weak scattering potential imposed on a CuO₂ layer of a cuprate superconductor modulates the local density of states N(x,ω). In recently reported experimental studies, scanning-tunneling maps of N(x,ω) have been Fourier transformed to obtain a wave-vector power spectrum. Here, for the case of a weak scattering potential, we discuss the structure of this power spectrum and its relationship to the quasiparticle spectrum and the structure factor of the scattering potential. Examples of quasiparticle interferences in normal metals and s- and d-wave superconductors are discussed.