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In exotic superconductors including high-$T_c$ copper-oxides, theinteractions mediating electron Cooper-pairing are widely considered to have amagnetic rather than the conventional electron-phonon origin. Interest in suchexotic pairing was initiated by the 1979 discovery of heavy-fermionsuperconductivity in CeCu$_2$Si$_2$, which exhibits strong antiferromagneticfluctuations. A hallmark of unconventional pairing by anisotropic repulsiveinteractions is that the superconducting energy gap changes sign as a functionof the electron momentum, often leading to nodes where the gap goes to zero.Here, we report low-temperature specific heat, thermal conductivity andmagnetic penetration depth measurements in CeCu$_2$Si$_2$, demonstrating theabsence of gap nodes at any point on the Fermi surface. Moreover,electron-irradiation experiments reveal that the superconductivity surviveseven when the electron mean free path becomes substantially shorter than thesuperconducting coherence length. This indicates that superconductivity isrobust against impurities, implying that there is no sign change in the gapfunction. These results show that, contrary to long-standing belief, heavyelectrons with extremely strong Coulomb repulsions can condense into afully-gapped s-wave superconducting state, which has an on-site attractivepairing interaction.

Fully gapped superconductivity with no sign change in the prototypical heavy-fermion CeCu2Si2