Superconductor of Heavy Fermion System

1. Superconductor ofHeavy Fermion System Kitaoka Lab Katsuyoshi Uematsu M1colloquium

2. Contents • Introduction • - What is Superconductivity？ • - History of Superconductivity • Heavy Fermion System • - What does “Heavy” mean？ • - Interactions between 4fand conduction electrons • (RKKY interaction and Kondo effect) • - Phase diagram of HF system • Summary

3. What is Superconductivity？ ・disappearance of electric resistance ・Meissner effect (perfect diamagnetism) 電気抵抗 (Ω) Resistance(Ω) 温度 (K) T> Tc T < Tc Tc ： superconducting transition temperature Temperature(K) Kamerlingh Onnes(1911)

4. 1900 1920 1940 1960 1980 2000 2020 Year History of Superconductivity Discovery of superconducting phenomenon 200 metal 1911 150 100 Transition temperature (K) BCS theory proposed 50 MgB2 Nb Ge Nb Pb NbN Hg NbC 0

5. BCS theory Cooper pair

6. 1900 1920 1940 1960 1980 2000 2020 Year History of Superconductivity Discovery of superconducting phenomenon 200 metal 1911 heavy fermion system high-Tc cuprate 163 Hg-Ba-Ca-Cu-O iron-based system under high pressure （ ） 150 Hg-Ba-Ca-Cu-O Heavy fermion superconductor Tl-Ba-Ca-Cu-O 1986 1979 Bi-Sr-Ca-Cu-O 100 Transition temperature (K) Y-Ba-Cu-O 77 High-Tc cuprate superconductor SmO F FeAs 50 0.9 0.11 MgB2 La-Ba-Cu-O LaO F FeAs PuCoGa5 2006 Nb Ge 0.11 0.89 Nb Pb CeCu2Si2 NbN LaOFeP Hg NbC Iron-based high-Tc superconductor 0

7. Example of Heavy Fermion System Example of heavy fermion superconductor compounds CeCu2Si2 CePd2Si2CeRh2Si2CeIn3CeRhIn5 UPt3UPd2Al3 PrOs4Sb12 PuCoGa5etc

8. 4f closed shell 5p 5d n(r) 6s r 4f 4f 4f 4f 4f 4f c-fhybridization Property of f electron Normal metal Ce3+:･･･5s25p64f 1 ＋ ＋ ＋ ＋ ＋ ＋ Heavy Fermion system ＋ ＋ ＋ Conduction electron ＋ ＋ ＋

9. D(εF) is the electronic density of states at the Fermi energy εF . m*kF e = ∝m* (effective mass) D ( ) F p 2 2 2 h What does “Heavy” mean？ “Heavy” ⇒ The effective mass is large Specific heat : C =gT [g = (2/3)p2kB2D(eF)] Susceptibility: c = c0 [c0=2mB 2D(eF)] Resistivity : r = r0 + AT n [A ∝ ∝g2] γheavy /γnormal＝ 100~ 1000

10. Two types of interactions RKKY interaction Kondo effect (RKKY:Rudermann-Kittel-Kasuya-Yoshida) Conduction electron Conduction electron Jcf Polarization Jcf Jcf 4f electron (Ce) 4felectron (Ce) Magnetic Order Fermi Liquid

11. Phase Diagram of HF system TK ∝ W exp(-1/Jcf D(εF)) TRKKY∝ D(εF) Jcf2 As Jcf increases, ⇒AFMdisappears and SC appears (near QCP) Quantum instability of AFM ⇒ SC appears AFM : antiferromagnetism(反強磁性) HF: heavy fermion(重い電子状態) QCP : quantum critical point(量子臨界点)

12. Typical Phase Diagram in HF system CePd2Si2 AFM SC N. D. Mather et al., Nature 394, 39 (1988)

13. Two Superconducting Phases S. Kawasaki et al., PRL 96, 147001 (2006) G.-q. Zheng et al., PRL 86, 4664 (2001) T. Muramatsu et al., Physica (Amsterdam) 388C–389C, 539 (2003) Crystal structure of CeMIn5

14. Summary • There are two types of the interactions between conduction and f electrons . • Superconductivity often appears around QCP. • The other superconductivity appears away from QCP • in CeIrIn5 . My Research