Antiferromagnetism and Superconductivity in Cerium based Heavy Fermion Compounds

The study of competing ground states is a central issue in condensed matter physic. In this article we will discuss the interplay of antiferromagnetic order and unconventional superconductivity in Ce based heavy-fermion compounds. In all discussed examples superconductivity appears at the border of magnetic order. Special focus is given on the pressure-temperature-magnetic field phase diagram of CeRhIn5 and CeCoIn5 which allows to discuss microscopic coexistence of magnetic order and superconductivity in detail. A striking point is the similarity of the phase diagram of different classes of strongly correlated systems which is discussed briefly. The recently discovered non-centrosymmetric superconductors will open a new access with the possible mixing of odd and even parity pairing.