Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

Scanning tunneling spectroscopy (STS) is a useful probe for studying the cuprates in the superconducting and pseudogap states. Here we present a theoretical study of the Z map, defined as the ratio of the local density of states at positive and negative bias energies, which frequently is used to analyze STS data. We show how the evolution of the quasiparticle interference peaks in the Fourier transform Z map can be understood by considering different types of impurity scatterers, as well as particle-hole asymmetry in the underlying band structure. We also explore the effects of density wave orders and show that the Fourier transform Z map may be used to both detect and distinguish between them.