Energy-Dependent LDOS Modulation in Cuprate Superconductors

Motivated by the recent scanning tunneling microscopy (STM) experiment [J. E. Hoffman, {\it et al.}, Science {\bf 297}, 1148 (2002)], we investigate the energy-dependent modulation induced by a weak and extended defect in a d-wave superconductor. The Fourier component of the local density of states (LDOS) is calculated up to the first order in the defect parameters. Our numerically obtained image maps together with the energy-dependent charge modulation wave vectors at different dopings exhibit the essential features as those measured by the experiment. We also predict new modulation wave vectors in the first Brillouin zone. Hopefully, they could be verified by future STM experiments.