Collective modes and quasiparticle interference on the local density of states of cuprate superconductors

The energy, momentum and temperature dependence of the quasiparticle local density of states (LDOS) of a two-dimensional $d_{x^2-y^2}$-wave superconductor with random disorder is investigated using the first-order T-matrix approximation. The results suggest that collective modes such as spin/charge density waves are relevant low-energy excitations of the cuprates that contribute to the observed LDOS modulations in recent scanning tunneling microscopy studies of $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{\mathrm{x}}$.