1. Superconductivity and non-Fermi-liquid behavior of Ce 2 PdIn 8 V. H. Tran et al., PHYSICAL REVIEW B 83, 064504 (2011) Kitaoka Lab. M1 Ryuji Michizoe

2. Contents ・ Introduction - History of Superconductivity - Heavy fermion system ・ Results ・ Summary

3. under high pressure 0 50 100 150 200 SmO 0.9 F 0.11 FeAs LaO 0.89 F 0.11 FeAs LaOFeP Hg-Ba-Ca-Cu-O （） Tl-Ba-Ca-Cu-O Bi-Sr-Ca-Cu-O Y-Ba-Cu-O MgB 2 NbGe NbN NbC Nb Pb high-T c cuprate metal iron-based system SC transition temperature-T c (K) 1900192019401960198020002020 Year Hg La-Ba-Cu-O Discovery of superconducting phenomenon 1911 1986 High-T c cuprate superconductor 2006 Iron-based high-T c superconductor 77 163 History of Superconductivity(SC) 1979 Heavy fermion superconductor CeCu 2 Si 2 heavy fermion system PuCoGa 5

4. UPt 3 UPd 2 Al 3 CeCu 2 Si 2 CePd 2 Si 2 CeRh 2 Si 2 CeIn 3 CeRhIn 5 PrOs 4 Sb 12 PuCoGa 5 etc f electrons Heavy fermion compounds n(r)n(r) r 4f4f 5p5p 5d5d 6s6s

5. ＋＋ ff ＋ f ＋＋ ff ＋ f Heavy fermion state Normal metal ＋＋＋ ＋＋＋ Heavy fermion state c-f hybridization conduction electron

6. J cf Polarization The interplay between two 4f electrons mediated by conduction electrons Heavy fermion system Heavy fermion system RKKY interaction Conduction electron 4f electron Magnetic Order

7. Heavy fermion system Heavy fermion system 4f and conduction electrons form a spin-singlet state Kondo effect J cf Conduction electron 4f electron Fermi Liquid

8. T K ∝ W exp(-1/J cf D(ε F )) T RKKY ∝ D(ε F ) J cf 2 Phase Diagram of HF system AFM : antiferromagnetism HF : heavy fermion state QCP : quantum critical point

9. Kondo effect 4f electron Kondo effect Conduction electron

10. P dependence of T max Above T max Incoherent Kondo scattering Below T max Coherent Kondo scattering

11. T max shifts to high T P dependence of T max T max ∝ T K

12. Resistivity of Ce 2 PdIn 8 P decreases T c 1 bar T c ~ 0.7 K

13. The P dependence of T C P suppresses SC P ~ 21 kbar SC disappears

14. Non-Fermi-liquid behavior Fermi-liquid ρ(T ) = ρ 0 + AT 2 ρ(T ) = ρ 0 + AT n (n < 2) n = 1 : 2D antiferromagnetic spin fluctuation n = 1.5 : 3D antiferromagnetic spin fluctuation n = 2 : Fermi-liquid Non-Fermi-liquid

15. P dependent values of n, A, ρ 0 ρ(T ) = ρ 0 + AT n n = 1 : 2D antiferromagnetic spin fluctuation n = 1.5 : 3D antiferromagnetic spin fluctuation n = 2 : Fermi-liquid A ∝ T K -2

16. P dependent values of n, A, ρ 0 ρ(T ) = ρ 0 + AT n n = 1 : 2D antiferromagnetic spin fluctuation n = 1.5 : 3D antiferromagnetic spin fluctuation n = 2 : Fermi-liquid AF spin fluctuation is supressed by increasing P V. A. Sidorov et al., PRL 89.157004 (2002)

17. SC may be associated with AF spin fluctuation The relationship between SC and AF spin fluctuation

18. non-Fermi-liquid Fermi-liquid T FL : Fermi-liquid temperature Field dependence of resistivity Below H c2 = 2.5 T ρ(T ) ∝ AT Above H c2 = 2.5 T ρ(T ) ∝ AT 2 n = 1 : 2D antiferromagnetic spin fluctuation n = 1.5 : 3D antiferromagnetic spin fluctuation n = 2 : Fermi-liquid

19. T FL increases with rising field Fermi-liquid is recovered at strong magnetic fields Field dependence of resistivity

20. Field dependent values of n, A, ρ 0 near H c2 n : jump to n = 2 A : maximum ρ 0 : minimum AF spin fluctuations associated with a QCP Fermi-liquid ρ(T ) = ρ 0 + AT n H c2 n = 1 : 2D antiferromagnetic spin fluctuation n = 1.5 : 3D antiferromagnetic spin fluctuation n = 2 : Fermi-liquid

21. Summary H c2 n = 1 : 2D antiferromagnetic spin fluctuation n = 1.5 : 3D antiferromagnetic spin fluctuation n = 2 : Fermi-liquid SC in Ce 2 PdIn 8 may be mediated by the AF spin fluctuations

22. END

24. H. Fukazawa et al., PHYSICAL REVIEW B 86, 094508 (2012) Ce 2 PdIn 8

25. Heavy fermion system Heavy fermion system (RKKY:Rudermann-Kittel-Kasuya- Yoshida) Magnetic OrderFermi Liquid Conduction electron 4f electron RKKY interaction The interplay between two 4f electrons mediated by conduction electrons 4f electron Kondo effect 4f and conduction electrons form a spin- singlet state. Conduction electron heavy fermion system : 重い電子系

26. field dependence of the resistivity at 1 bar μ 0 H < 3 T T max ⇒ no change μ 0 H > 3 T T max ⇒ toward lower temperature suppress spin fluctuation

27. Kondo interaction strength(C K ) C K decreases with P C k : Kondo interaction strength

28. C K ~ J 3 N(E F ) 2 J : hybridization N(E F ) : density of states at Fermi level P enhances J N(E F ) strongly diminishes C K decreases P dependence of C K C K decreases with P but