Revealing sign-reversal $s^{+-}$-wave pairing by quasiparticle interference in the heavy-fermion superconductor CeCu$_2$Si$_2$

Recent observations of two nodeless gaps in superconducting CeCu$_2$Si$_2$ have raised intensive debates as to its exact gap structure of either sign-reversal ($s^{+-}$) or sign-preserving ($s^{++}$) pairing. Here we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between $s^{+-}$ and $s^{++}$ pairing states, which include the intragap impurity resonance and a significant energy-dependence difference between two gap energies. Our predictions provide a guide for phase-sensitive QPI measurements to uncover decisively the true pairing symmetry in the heavy-fermion superconductor CeCu$_2$Si$_2$.