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 T_N decreases with increasing pressure P and becomes zero at the critical pressure P_c : T_N → 0 for P → P_c. 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 P_c ≃ 2.4 GPa, revealing the first-order phase transition, together with a divergent tendency of the cyclotron mass at P_c. 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.