Quasiparticle scattering interference in cuprate superconductors

The quasiparticle scattering interference (QSI) is intimately related to the nature of the quasiparticle and of its interplay with a variety of electronic orders and superconductivity. Here, starting from the microscopic octet scattering model, the nature of QSI in cuprate superconductors is studied in the $T$-matrix approach. In particular, a method of the inversion of matrix is developed to accurately derive the $T$ matrix for various kinds of impurities, and then the obtained $T$ matrix is employed to calculate the local density of states (LDOS). It is shown that the overall features of the LDOS modulation can be described qualitatively by taking into account the quasiparticle scattering from a single impurity on the kinetic-energy-driven homogeneous superconducting state, where the QSI scattering wave vectors ${\mathbf{q}}_{i}$ and the related QSI peak dispersions are internally consistent within the octet scattering model. However, the pronounced QSI peaks in the momentum-space LDOS modulation pattern for a single impurity are smeared heavily in the case for multiple impurities, and then the momentum-space LDOS modulation for multiple impurities exhibits a speckle pattern. Moreover, the momentum-space LDOS modulation for Gaussian random distribution of on-site impurity at a relatively large deviation displays a similar behavior of the LDOS modulation for multiple impurities. The theory also indicates that the impurity weight linearly increases with the increase of the impurity scattering strength for the weak scattering strength and tends to saturate in the strong scattering strength, while it decreases with the increase of the impurity-scattering screening length for the short screening length and saturates in the long screening length.