Quasiparticle scattering and local density of states in the d-density wave phase

We study the effects of single-impurity scattering on the local density of states in the high-$T_c$ cuprates. We compare the quasiparticle interference patterns in three different ordered states: d-wave superconductor (DSC), d-density wave (DDW), and coexisting DSC and DDW (DSC-DDW). In the coexisting state, at energies below the DSC gap, the patterns are almost identical to those in the pure DSC state with the same DSC gap. However, they are significantly different for energies greater than or equal to the DSC gap. This transition at an energy around the DSC gap can be used to test the nature of the superconducting state of the underdoped cuprates by scanning tunneling microscopy. Furthermore, we note that in the DDW state the effect of the coherence factors is stronger than in the DSC state. The new features arising due to DDW ordering are discussed.