Heavy fermion state and quantum criticality

The heavy fermion state in the f-electron systems is due to competition between the RKKY interaction and the Kondo effect. The typical compound is CeCu6. To understand the electronic state, we studied the Fermi surface properties via the de Haas-van Alphen (dHvA) experiments and energy band calculations for CeSn3, CeRu2Si2, UPt3, and nowadays, transuranium compounds of NpGe3 and PuIn3, together with YbCu2Si2. Pressure is also an important technique to control the electronic state. For example, the Néel temperature TNTN decreases with increasing pressure P   and becomes zero at the critical pressure Pc:TN→0Pc:TN→0 for P→PcP→Pc. The typical compound is an antiferromagnet CeRhIn5, which we studied from the dHvA experiment under pressure. A change of the 4f  -electronic state from localized to itinerant is realized at Pc≃2.4GPa, revealing the first-order phase transition, together with a divergent tendency of the cyclotron mass at Pc. It is stressed that appearance of superconductivity in CeRhIn5 is closely related to the heavy-fermion state. It is also noted that the parity-mixed novel superconducting state might be realized in a pressure-induced superconductor CeIrSi3 without inversion symmetry in the crystal structure.