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Determining the exact pairing symmetry of the superconducting order parameterin candidate unconventional superconductors remains an important challenge.Recently a new method, based on phase sensitive quasiparticle interferencemeasurements, was developed to identify gap sign changes in isotropic multibandsystems. Here we extend this approach to the single-band and multiband nodal$d$-wave superconducting cases relevant, respectively, for the cuprates andlikely for the infinite-layer nickelate superconductors. Combining analyticaland numerical calculations, we show that the antisymmetrized correction to thetunneling density of states due to nonmagnetic impurities in the Born andintermediate-scattering limits shows characteristic features for sign-changingand sign-preserving scattering wavevectors, as well as for themomentum-integrated quantity. Furthermore, using a realistic approachaccounting for the Wannier orbitals, we model scanning tunneling microscopydata of $\text{Bi}_2\text{Sr}_2\text{CaCu}_2\text{O}_{8+\delta}$, which shouldallow the comparison of our theory with experimental data.

Phase-sensitive determination of nodal $\mathbf{d}$-wave order parameter in single-band and multiband superconductors