Two impurities in a d-wave superconductor: Local density of states

We study the problem of two local potential scatterers in a d-wave superconductor, and show how quasiparticle bound-state wave functions interfere. Each single-impurity electron and hole resonance energy is in general split in the presence of a second impurity into two, corresponding to one even parity and one odd parity state. We calculate the local density of states (LDOS), and argue that scanning tunneling microscopy (STM) measurements of two-impurity configurations should provide more robust information about the superconducting state than one-impurity LDOS patterns. In some configurations highly localized, long-lived states are predicted. We discuss the effects of realistic band structures, and how two-impurity STM measurements could help distinguish between current explanations of LDOS impurity spectra in the BSCCO-2212 system.