Motivated by the recent scanning tunneling microscopy (STM) experiments [J. E. Hoffman et al., Science 297, 1148 (2002); K. McElroy et al., Nature (London) 422, 592 (2003)], we investigate the real-space local density of states (LDOS) induced by weak disorder in a d-wave superconductor. We first present the energy- dependent LDOS images around a single weak defect at several energies, and then point out that the experimentally observed checkerboard patterns in the LDOS could be understood as a result of quasiparticle interference by randomly distributed defects. It is also shown that the checkerboard pattern oriented along $45°$ to the Cu-O bonds at low energies would transform to that oriented parallel to the Cu-O bonds at higher energies. This result is consistent with the experiments.

• Received 8 October 2003

DOI:https://doi.org/10.1103/PhysRevB.69.012501