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Multiband superconductivity with dominant two-gap features are recentlyproposed to challenge the earlier accepted nodal $d$-wave pairing in the firstunconventional superconductor CeCu$_{2}$Si$_{2}$. Here we obtain multibandFermi-surface topology of CeCu$_{2}$Si$_{2}$ via first-principles calculations,and study the problem within an effective two hybridization band modelincluding detailed band-structure. Within T-matrix approximation, ourcalculations reveal that different pairing candidates could yield qualitativelydistinct features characterised by impurity-induced bound states. Except forthe nodeless $s^{\pm}$-wave, both loop-nodal $s$-wave and $d$-wave pairings cangive rise to intra-gap impurity bound states. In particular, the intra-gapstates for the $d_{x^2-y^2}$-wave and loop-nodal $s$-wave are distinguishableand locate either near or far away from the Fermi energy, respectively. Thesefeatures can be readily verified by high-resolution scanning tunnelingmicroscopy/spectroscopy and provide an unambiguous justification for theongoing debate about the superconducting gap symmetry of CeCu$_{2}$Si$_{2}$ atambient pressure.

Impurity-induced bound states as a signature of pairing symmetry in multiband superconducting CeCu$_{2}$Si$_{2}$