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

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

under high pressure 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) Year Hg La-Ba-Cu-O Discovery of superconducting phenomenon High-T c cuprate superconductor 2006 Iron-based high-T c superconductor History of Superconductivity(SC) 1979 Heavy fermion superconductor CeCu 2 Si 2 heavy fermion system PuCoGa 5

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

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

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

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

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

Kondo effect 4f electron Kondo effect Conduction electron

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

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

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

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

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

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

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 (2002)

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

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

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

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

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

END

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

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

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

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

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