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Unconventional superconductivity? The strange case of Ce Cu 2 Si 2

Unconventional superconductivity? The strange case of Ce Cu 2 Si 2. Collaboration Neutron scattering , STM/STS J . Arndt, O. Stockert , S . Wirth (MPI CPS, Dresden) Penetration depth , specific heat

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Unconventional superconductivity? The strange case of Ce Cu 2 Si 2

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  1. Unconventional superconductivity? The strange case of CeCu2Si2 Collaboration Neutron scattering, STM/STS J. Arndt, O. Stockert, S. Wirth (MPI CPS, Dresden) Penetration depth, specificheat G. M. Pang, M. Smidman, J. L. Zhang, L. Jiao, Z. Weng. Y. Chen, W. Jiang, Y. Zhang, W. Xie, H. Lee, H. Q. Yuan (CCM, ZJU Hangzhou) Single crystals H. S. Jeevan, P. Gegenwart (U. Augsburg): CeCu2Si2 C. Krellner (U. Frankfurt): YbRh2Si2 Theory G. Zwicknagl (TU Braunschweig) J. X. Zhu (LANL) E. M. Nica, R. Yu, Q. Si (RCQM, Rice U., Houston, TX) F. Steglich+,§,# + Max Planck Institute for Chemical Physics of Solids (MPI CPfS), Dresden, Germany § Center for Correlated Matter, Zhejiang University (CCM, ZJU), Hangzhou, China # Institute of Physics, Chinese Academy of Sciences (IOP, CAS), Beijing, China

  2. Phase diagrams of unconventional superconductors Cuprates, …… Organic charge-transfer salts, Fe-based compounds, B. Keimer et al., Nature (2015) Spin, charge, orbital, lattice excitations Heavy fermion metals separation of scales: λSO(103-104K), ΔCF(102K), TK ,TRKKY(10 K), Tc (1 K) ↷ spin - / charge - fluctuations Quantum criticalparadigm: AF QCP in clean, stoichiom. HF metal↷ unconv. SC! ExploreCeCu2Si2 & YbRh2Si2!

  3. CeCu2Si2 Homogeneity range: ~ 1% Cu/Si site exchange ΔCF ≫ kBTK∽JK≃2 meV Seff= 1/2 Pairing interactions ≤IRKKY ≃JK ↑ ← Cu deficit true stoichiometry Cu excess →

  4. Quantum criticalityin CeCu2Si2 Δρ ~ T3/2, γ= γ0 – bT1/2 [P. Gegenwart et al., PRL81, 1501 (‘98)] S-type crystal in low-T n-state χ‘‘T3/2= f (ħω/(kBT)3/2) [J. Arndt et al., PRL106, 246401 (’11)] 3D-SDW QCP B - p phase diagram [E. Lengyel et al., PRL107, 057001 (‘11) A/S-type crystal

  5. (1-band) d - wave superconductivity in CeCu2Si2 Cu NQR K. Fujiwara et al., JPSJ77,123711 (‘08) cf. also K. Ishida et al., PRL 82, 5353 (‘99) T = Tc : no Hebel-Slichterpeak T < Tc : 1/T1 ~ T3 d- wave SC, nodesofΔ(k) strong couplingd– wave SC: 2Δ0/kBTc = 5 [weakcoupling d - wave SC: 2Δ0/kBTc = 4.3]

  6. T - dependence of specific heat for CeCu2Si2 [S. Kittaka et al., PRL112, 067002 (2014)] Fully gapped as T→ 0 T. Takenaka et al., PRL 119, 077001 (2017): Tc insensitive against el-irradiation ↷ CeCu2Si2: Two-band s-wave superconductor without sign-changing Δ(k) [BCS SC]

  7. T -dependenceof superfluid densityϱs(T) in CeCu2Si2 [G. M. Pang et al., PNAS115, 5343 (2018)]

  8. Harmless disorder in CeCu2Si2 G. M. Pang et al., PNAS115, 5343 (2018) Tc ≃ 0.6 K insensitive against variations ofϱ0 : ϱ0(“S”) ≃ 4 ϱ0(“A/S”) • Cu/Si interchange < 1 % (changeofϱ0) harmless • shiftfromlatticesitesintointerstitials (el. irradiation)

  9. Atomic substitution in CeCu2Si2 [H. Spille, U. Rauchschwalbe, FS, Helv. Phys. Acta 56, 165 (1983); H. Q. Yuan, F. M. Grosche, M. Deppe et al., Science302, 2104 (2003)] sitedependence Si-site: xc: (15 – 20) at% forGe x= 0.1:lmfp> ξ; 0.25:lmfp< ξ Cu-site: xc ≃ 1 at% forMn, Pd, Rh (ΔTK ≃ + 7 mK) Ce-site (size-dependence): ΔrCe-M [Å]xc[at%] Sc + 0.28 1 Y + 0.13 6 Th + 0.06 20 La - 0.03 10 Incompatiblewiths++pairing [P. W. Anderson, Phys. Rev. Lett. 3, 325 (1959)]

  10. Nature of the AF (A) phase in CeCu2Si2[O. Stockert, G. Zwicknagl et al., PRL 92, 136401 (2004)] Long-range AF order with propagation vector QAF= (0.215 0.215 0.530) at T = 50 mKTN  0.8 Km0≲ 0.1 B Observation of AF satellite peaksin (hhl) scattering plane

  11. Nesting of large Fermi surface in CeCu2Si2 [O. Stockert, G. Zwicknagl et al., PRL 92, 136401(2004)] Fermi surface of heavy quasiparticles calculated with renormalized band method, m*  500 mewarped columns along tetragonal axis Static susceptibility in (hhl) plane Nesting for incommensurate wave vectorτ≃(0.21 0.21 0.55) ≃ QAFFermi surface unstable with respect to formation of spin-density wave

  12. Superconductivity in CeCu2Si2 near a (3D) SDW QCP [O. Stockert et al., Nature Phys. 7, 119 (2011)] k= QAF B = 2 T: quasielasticline, HWHM ↷ TK B = 0: spingapbelowpeak at 0.2 meV Propagating ‘paramagnon‘mode(not a ‘spin resonance‘)at 3.9 kBTc[< 2Δ1(T=0) ≃ 5kBTc] [J. Arndt et al., PRL106, 246401 (2011)] “slowing down“ ΔГ ~ Tα α = 1.38 ∓ 0.16 (3D SDW) α= 1.5

  13. Inelastic n-scatteringrevealssignchangeofΔ(k) [O. Stockert et al., Nature Phys. 7, 119 (2011)] Large INS intensity in sc state at k = QAF and lowħω , i.e., coherence factor {1-cos[Φ(k)]} ≃ 2, whereΦ(k) isthe phasedifference in Δ(k) betweenk & k + QAF, ↷ Φ(k) ≃ π ↷ signchangeofΔ(k) alongQAF insidedominatingHF band! ↷ Nos - wave superconductor s++: doesn‘tshowsignchange in Δ(k)! no onsite pairing of HFs: Ueff≃ kBTK! s+-: nesting wavevector different from QAF can‘texplainspinresonance! ↷ “d+d band - mixing“ Cooper pairing [E. Nica et al. ‘16] 2 - band d - wave SC withoutnodes, cf. 3He - Bphase (p - wavepairing)

  14. Band-mixing ‘d+d ‘ pairing model: explains ALL data [(E.M. Nica, R. Yu and Q. Si., npj Quantum Materials (2017) 2:24] Band basis: Intraband: ~ dx2-y2 Interband:~ dxy • Finite gap on whole Fermi surface; • Sign-change of intra-band pairing (within warped cylinders).

  15. YbRh2Si2: Emergenceof SCbynuclearAF order [Science351, 485 (2016)] a.TN≃70 mK: 4f - electr. AF order TB≃ 10 mK:increase of M(T) TA≃ 2 mK: new phase transition b.Tc ≃ 2 mK: SC [χ’’(T): 1storder!)] c.TA ≃ 2 mK: “A - phase“ d. B< 4 mT: TA> Tc

  16. TB: smallscregions, Tc: largesuperconductingshielding T< Tc= 2 mK: largesuperconductingshieldingsignal in zfc - MDC(T) and χAC(T) T < TB = 10 mK: partialscshielding– concurswith increasingfc - MDC(T) whichis illustrating decreasingprimarystaggeredmagnetization,mAF, due to competingnuclear (A-phase) short-range correlations (nuclearspinentropy!)

  17. Summary YbRh2Si2 E. Schubert et al. (2016) Bc2‘ ≃ 25 T/K from Meissner measurements (same from shielding measurements) ⦁ MDC(T), χAC(T) prove: (bulk) heavy-fermion SCat B< 4 mT ⦁ YbRh2Si2: - SC near(4f– “Mott – type“) transition (T = 0),like CeRhIn5 atp > 0 - both systems form link between (≃ 50) HFSCsand cuprates, organics, … near true Mott transition

  18. Quantum Critical Paradigm: UnconventionalSCatHFAFQCPs CePd2Si2 N. D. Mathur et al., Nature394, 39 (1998) ● YbRh2Si2: HF SC, Tc = 2 mK ● CeCu2Si2: fully gapped 2 - band d - wave superconductor ● Unconventional SC near AF QCPs: robust phenomenon Further reading: M. Smidman et al., Phil. Mag. 98, 2930 (2018)

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