We study spin and charge susceptibilities in the $d$-wave superconducting state whose underlying electronic dispersion is anisotropic due to the formation of electronic nematic order. We show that the amplitude of the incommensurate peaks in the spin susceptibility near $(\pi ,\pi )$ reveals a pronounced anisotropy in momentum space. The relevance of our findings to the magnetic scattering pattern observed in recent neutron scattering measurements on untwinned $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ is discussed. In the charge channel, we identify a well-defined collective mode at small momentum transfer with strong anisotropic amplitude depending on the direction of the momentum transfer, which is associated with the broken symmetry due to nematic ordering.

• Received 14 December 2004

DOI:https://doi.org/10.1103/PhysRevB.72.024502