Quasiparticle Interference in a Superconducting State with a Fourfold Phase Change

Quantum interference revealed in Bi$\text{}_{2}$Sr$\text{}_{2}$Ca Cu$\text{}_{2}$O$\text{}_{8+δ}$ by Fourier transform scanning spectroscopy is primarily determined by maxima of the joint density of states which correspond to an octet of scattering wave vectors connecting points at the constant quasiparticle energy contours where the density of states is maximal. We consider a superconductor with a constant quasiparticle density of states where the interference is due to the fourfold change in the phase of the order parameter. Our results may be helpful in a discussion of the interference in a d-wave superconductor at the tunneling energy exceeding the gap magnitude.