Interplay between heavy-fermion quantum criticality and unconventional superconductivity
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1 Interplay between heavy-fermion quantum criticality and unconventional superconductivity F. Steglich Max Planck Institute for Chemical Physics of Solids, Dresden, Germany Center for Correlated Matter, Zhejiang University, Hangzhou, China Institute of Physics, Chinese Academy of Sciences, Beijing, China
2 Emergence of superconductivity in the canonical heavy-electron metal YbRh 2 Si 2 Science 351, 485 (2016) Erwin Schuberth (WMI) ultra-low T measurements Marc Tippmann (WMI) (T min = 0.4 mk) Lucia Steinke (BNL) Stefan Lausberg (MPI CPfS) design of new χ ac set-up Alexander Steppke (MPI CPfS) Manuel Brando (MPI CPfS) Cornelius Krellner (U. Frankfurt) high-quality YbRh 2 Si 2 single crystals Christoph Geibel (MPI CPfS) Rong Yu (Renmin U.) 3-component GL theory Qimiao Si (Rice U.) F S (MPI CPfS, CCM, IOP)
3 Doniach phase diagram of Kondo lattice (HF metal) [S. Doniach, Physica B+C 91, 231 (1977)] Conventional (SDW) QCP e.g., CeCu 2 Si 2 Unconventional (Kondo breakdown) QCP e.g., YbRh 2 Si 2
4 S eff = 1/2 YbRh 2 Si 2 : T B phase diagram [J. Custers et al., Nature 424, 524 (2003); T. Westerkamp, Dissertation, TU Dresden (2008)]
5 NFL effects in YbRh 2 Si 2 : C el (T)/T & ρ(t); No sign of superconductivity at T 10 mk P. Gegenwart et al., Nature Phys. 4, 186 (2008) P. Wölfle & E. Abrahams, PRB 84, (2011) H = 0 data fit: ρ = T 3/4 RRR 150
6 Fermi surface collapse [S. Friedemann et al., PNAS 107, (2010)] T (K) Crossover position T*(B) T N FWHM(T) T LFL cross- single- magnetofield field resistivity YbRh 2 Si 2 R H (B 2 ) R ~ H (B 1 ) ρ(b 2 ) sample 1 sample B 2 (T) T*(B) agrees with data from ρ, λ, M (P. Gegenwart et al., Science 315, 969 (2007)) FWHM (T) (R H -R H )/(RH 0 -RH ) Crossover width cross- single- magnetofield field resistivity ~ YbRh 2 Si 2 R H (B 2 ) R H (B 1 ) ρ(b 2 ) sample 1 sample T (K) FWHM ~ T T 0 T B/B 0
7 Heavy-Fermion Superconductors T c (K) CeCu 2 Si ('79 K) [p = 2.9 GPa: 2.3 ('84 GE/GR)] CeNi 2 Ge ('97 DA, '98 CA/GR) CeIrIn ('00 LANL) CeCoIn ('00 LANL) Ce 2 CoIn ('02 NA) Ce 2 PdIn ('09 WR) CePt 3 Si 0.7 ('03 VI) CeCu 2 Ge 2 p > ('92 GE) CePd 2 Si ('98 CA) CeRh 2 Si ('95 LANL) CeCu ('97 GE/KA) CeIn ('98 CA) CeRhIn ('00 LANL) Ce 2 RhIn ('03 LANL) CeRhSi ('05 SE) CeIrSi ('06 OS) CeCoGe ('06 OS) Ce 2 Ni 3 Ge ('06 OS) CeNiGe ('06 OS) CePd 5 Al ( 08 OS) CeRhGe ('09 OS) CePt 2 In ( 10 LANL) CeIrGe ( 10 OS) CeAu 2 Si ( 14 GE) T c (K) Ce 3 PdIn (`15 PR) Ce 3 PtIn (`15 PR) PrOs4Sb ('01 UCSD) PrIr 2 Zn ('10 HI) PrTi 2 Zn ('12 TO) β-ybalb ('08 TO/IR) YbRh 2 Si ('14 M/DD) Eu metal p > ('09 SL/OS) UBe ('83 Z/LANL) UPt ('84 LANL) URu 2 Si ('84 K/DA) U 2 PtC ( 84 LANL) UNi 2 Al ('91 DA) UPd 2 Al ('91 DA) URhGe 0.3 ('01 GR) UCoGe 3.0 ('07 AM/KA) UGe 2 p > ('00 CA/GR) UIr 0.14 ('04 OS NpPd 5 Al ('07 OS) PuCoGa ('02 LANL) PuRhGa ('03 KA) PuCoIn ( 11 LANL) PuRhIn ( 12 LANL) Am metal p > ('05 KA) YFe 2 Ge (`14 CA) CrAs p > (`14 BEI/TO)
8 Heavy-fermion superconductivity in the vicinity of an antiferromagnetic quantum critical point N.D. Mathur et al., Nature 394, 39 (1998) QCP at p = p c 28 kbar CePd 2 Si 2 T BUT: no SC in YbRh 2 Si 2 (YRS) at T 10 mk p YRS: QCP at B = B N 60 mt ( c), THUS: SC (even HF SC) with T c < 10 mk impossible at this field
9 Erwin Schuberth: PrNi 5 nuclear demag (T min = 0.4 mk)
10 Field - cooled (fc) DC magnetization at T 1.4 mk M/B (10-6 m 3 /mol) T c T B T AF YbRh 2 Si 2 M/B (10-6 m 3 /mol) B c (mt) B B c 6 20 A T (mk) T AF = 70 mk: primary electronic AF order T c 2 mk: peak in M(T); visible above T = 1 mk up to B = 23 mt T B 10 mk: shoulder; M(T) increases below T B
11 Superconductivity: zfc - M DC (T) & χ AC (T) M/B (a.u.) 3 2 T B B c (mt) C T (mk) χ ac (SI) T c D B = T (mk) T c = 2 mk M/B (arbitrary units) B c YbRh 2 Si 2 B (mt) T (mk) T < T c : large sc shielding T < T B : partial sc shielding Primary electronic AF order is apparently detrimental to SC! BUT: what is the reason for its weakening below T T B?
12 field - cooled (fc) M DC (T): Meissner effect 4 3 M/B (a.u.) 2 T B B c (mt) C χ ac (SI) T (mk) peak in fc - M(T) at T c 2 mk T < T c : flux expulsion ( Meissner effect ) Meissner volume 3%: strong pinning!
13 Determination of heat capacity C*(T) using M(T) of YbRh 2 Si 2 as internal thermometer - via heat - pulse (C* = ΔQ/ΔT) and relaxation (τ = R C*) method
14 Nuclear specific heat C(T) & entropy S I (T) A T A YbRh 2 Si 2 C(T, B) = C Q (T) + C Z (T, μ el (B)) C/T (J/K 2 mol) C/T (J/K 2 mol) T A µ Yb /µ B B (mt) B c T (mk) S I / S I,tot A. Steppke et al., Phys. Stat. Sol. B 247, 737 (2010) ΔC (T) = C(T, B = 2.4 mt) C(T, 0) T 10 mk: S I (T) = S I,tot S I,tot 1.8 Rln 2 0 B B = 2.4 mt T (mk) 0.8 C T (mk) 171 Yb (I = 1/2, 14.3%) 173 Yb (I = 5/2, 16.1%)
15 Superconductivity along with Nuclear Kondo Effect, in the absence of Nuclear Order? Kondo temperature T K = D exp(-d/j K ) Nuclear Kondo temperature T K,nucl = T F,eff exp(-t F,eff / T hf ) T hf 25 mk, T F,eff T K 25 K: T K,nucl = T K exp(-1000) ( T K /1000) Mass enhancement: m*/m el D/k B (10 4 K)/T K,nucl = 400/exp(-1000) ( superheavy fermions) For heavy-fermion superconductivity: T K 10 T c T K,nucl 10 T c Even if T K,nucl 25 mk ( T K /1000) m*/m el ! Conclusion: nuclear Kondo effect requires m*/m el This can be compared with experimental value derived from B c2 (T)!
16 Field-cooled DC magnetization at very low fields M vs. 1/T M (arbitrary units) 0-20 A YbRh 2 Si 2 T (mk) M (arbitrary units) 1 B T L T H T A 0-1 T c T (mk) 2 M vs. T -40 B c B = 0.09 mt /T (1/mK) 1 C B (mt) B 3 mt: - T A > T c - db c2 /dt Tc = B c2 25 T/K from Meissner effect (cf. CeCu 2 Si 2 ) heavy-fermion SC with m*/m el several 100
17 Field-cooled DC magnetization at B = 10.1 mt μ sat = 1.24 μ B Ø J (2%) μ B Below T c : ΔM μ B 2/3 due to Meissner effect, SC likely to persist B > 3 mt
18 First-order nature of superconducting transition T T c : increase in χ (T) superconducting transition: 1 st order 10 8 B c YbRh 2 Si 2 (10-6 m 3 /mol) χ ac, χ ac 6 B = 28 mt, 2.5 µt ac B = 0 (earth), 2.5 µt ac 4 B = 0 (earth), 2.5 µt ac B = 0 (earth), 10 µt ac from T. Westerkamp et al T (mk)
19 New T B phase diagram of YbRh 2 Si 2 B c2 25 T/K from shielding effect g eff (~T A /B A ) hybrid A phase: (dominating) nuclear AF order
20 Three - component GL theory by R. Yu & Q. Si A B T T T I A AF hf T T T hyb AF T T AF = 70 mk: Φ AF with Q AF T T hyb = T A = 2.3 mk: Φ J, Φ I with Q 1 Q AF (- λφ J Φ I ) SC m AF λ (~ A hf = 100T/μ B ) 25 mk T hyb T AF Below T A : hybrid order competes with primary order system approaches QCP superconductivity develops, driven by quantum critical fluctuations T
21 Qutlook: Interplay between unconventional superconductivity and quantum criticality Heavy - fermion superconductivity robust at any AF QCP Conventional (3D - SDW) QCP, CeCu 2 Si 2 presumably also: CePd 2 Si 2, CeIn 3, UBe 13,. Unconventional (Kondo destroying) QCP, CeRhIn 5 (H. Shishido et al. '05; T. Park et al. '06, G. Knebel et al. `08) new example: YbRh 2 Si 2 Kondo breakdown QCP: (T=0) 4f-orbital selective Mott transition Link to doped Mott insulators e.g., cuprates, organic charge transfer salts
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