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 CeRhIn5 and CeCoIn5 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.