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Abstract

The heavy-fermion metal CeCu2Si2 was the first discovered unconventional, non-phonon-mediated superconductor and, for a long time, was believed to exhibit single-band d-wave superconductivity, as inferred from various measurements hinting at a nodal gap structure. More recently, however, measurements using a range of techniques at low temperatures (T < 0.1 K) provided evidence for a fully gapped superconducting order parameter. In this Colloquium, after a historical overview the apparently conflicting results of numerous experimental studies on this compound are surveyed. The different theoretical scenarios that have been applied to understanding the particular gap structure are then addressed, including both isotropic (sign-preserving) and anisotropic two-band s-wave superconductivity, as well as an effective two-band d-wave model, where the latter can explain the currently available experimental data on CeCu2Si2. The lessons from CeCu2Si2 are expected to help uncover the Cooper-pair states in other unconventional, fully gapped superconductors with strongly correlated carriers, and, in particular, highlight the rich variety of such states enabled by orbital degrees of freedom.