Effects of a Collective Spin Resonance Mode on the STM Spectra of D-Wave Superconductors

A high-energy spin resonance mode is known to exist in many high-temperature superconductors. Motivated by recent scanning tunneling microscopy (STM) experiments in superconducting Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$, we study the effects of this resonance mode on the local density of states (LDOS). The coupling between the electrons in a d-wave superconductor and the resonance mode produces high-energy peaks in the LDOS, which displays a two-unit-cell periodic modulation around a nonmagnetic impurity. This suggests a new means to not only detect the dynamical spin collective mode but also study its coupling to electronic excitations.