Antiferromagnetism and superconductivity in cerium based heavy-fermion compounds

The study of competing ground states is a central issue in condensed matter physics. In this article we will discuss the interplay of antiferromagnetic order and unconventional superconductivity in Ce based heavy-fermion compounds. In all examples discussed superconductivity appears at the border of magnetic order. Special focus is given on the pressure–temperature–magnetic field phase diagram of CeRhIn 5 and CeCoIn 5 which allows one 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.