Superconducting glue: are there limits on T c?

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1 Superconducting glue: are there limits on T c? Oleg V. Dolgov Max Planck Institute for Solid State Research Stuttgart Germany In collaboration with E.G. Maksimov P.N. Lebedev Physical Institute RAS Moscow Russia

2 V.L. Ginzburg Nauka Publishing Moscow 977 we have to point out however that the above estimate is based on a standard metal and can not be applied to all hypothetical situations

3 Outline. Introduction.. Electron-phonon interaction. 3. Causality and stability. 4. Restrictions from Eliashberg euations. 5. Phonon instability. 6. Nonphonon mechanisms. 7. Conclusions. Briefly:. Pnictides. Quasiparticle renormalization effects in the optical properties of iron pnictides with A.V. Boris

4 Kelvin Hg BaKBiO 3. Cs 3 C YNi B C 4. Li x HfNCl 5. p-doped p C60 6. MgB 7. C-60/CHBrC 3 Pb Nb Hg-3 P3 KBar NbCN La-4 Hg-3 Tl-3 Y-3 Nb 3 Ge Celcius

5 BCS type behavior M.Matsui et al. PRL δ δ i E v i E u G + + k k k k k k k k E u ε + k k k E v ε

6 Electrons join to form Cooper Pairs usually A Magnetic Attraction? Spin attraction? The lattice after all? Something else?

7 Electrons join to form Cooper Pairs usually A Magnetic Attraction? Spin attraction? The lattice after all?

8 Electrons join to form Cooper Pairs usually A Magnetic Attraction? Spin attraction? The lattice after all? Excitons LittleGinzburg

9 Phonon mediated superconductivity attraction: N0V v F μ * Coulomb repulsion: μ + μ log ε * > 0 then pairing / F Ω D BCS model: << and constant for < D Eliashberg formalism: l general and strong coupling effects

10 How can two electron attract?. Repulsive Coulomb interaction:. Screening by other electrons and ions Overscreening by phonons ] 4 [ 4 4 χ π π ε π tot tot e e e V + 4 ~ TF ph C e V V V χ π ~ TF C e V χ π + 4 TF C e V χ π +

11 T c.4 V av exp[ T c problem N0 V 4 ' 0 3 πe < V k k > FS d ε ~ V V C + V ] ph tot ; 0 T c.4 D exp λ μ

12 λ N0 d μ N0 d 3 3 V ph ~ V C 0 0 μ μ ε + μln F D εtot 0 λ μ

13 + λ T c.4 ϖ exp[ λ μ + μ log ε / ϖ F ];

14 + λ T c.4 ϖ exp[ λ μ + μ log ε / ϖ F ]; λ>μ ε0<0 T c /ε F λ<μ ε0> ϖ/ε F

15 Superconductivity in d- and f-band Metals AIP Conf. Proc. p.7 97!!!

16 + λ T c.4 ϖ exp[ λ μ + μ log ε / ϖ F ]; λ>μ ε0<0 T c /ε F λ<μ ε0> ϖ/ε F

17 max T c ε F exp 3 ; λ λ opt μ ; Stoner instability ε F 7 ev

18 max T c ε F exp 3 ; λ λ opt μ ; ε F 7 ev Stoner instability T max c 0K We need 0 0 ε!

19 Response functions A R х I

20 Kramers-Kronig relations Response functions A R х I causality reuirements R R + π 0 E de iδ Im R E

21 A R х I Response functions Kramers-Kronig relations Im 0 Im 0 0 E R R R E R R R E de i E de + + π δ π static case causality reuirements

22 Electromagnetic response functions δ ε δ δ ε δ D E E D or 4 ext div πδρ δ D 4 tot div πδρ δ E

23 0 Im 00 Im/ 0 / 0 0 E E E de E de + + ε ε ε ε π π arbitrary 0

24 / ε 0 + ε 00 + π 0 de E π 0 de E reuirements of stability Im ε 0 or Im/ ε E arbitrary Imε 0 E 0 Im / ε 0 for all

25 / ε 0 + ε 00 + π 0 de E π 0 de E reuirements of stability Im ε 0 or Im/ ε E arbitrary Imε 0 E 0 Im / ε 0 for all / ε 0 ε 0 ε 0 0 ε 0 0 Rev. Mod. Phys

26 Local field effects Lorentz-Lorenz formula ε + 4πn α / 4π /3nα General expression ε 4π / + 4π / Π eff G Π eff > 0 α local field corrections Π eff < 0

27 Wigner crystal Dielectric function ε ε 0 pl λ Negative for all λ e λ λ λ pl ne 0 λ ε 0 < 0 λ ne λ λ λ sum rule pl

28 Dielectric functions for real systems ε 0 normal metals : K Al Pb hypothetical metallic H classical charge fluid

29 The argument of Cohen and Anderson postulates that stability reuires the static dielectric function of a material to be positive which leads to an upper bound on Tcof approximately 0 K. This bound and stability reuirement are subseuently dismissed in the paper because of the neglect of local fields and umklapp processes and further work 4 has clarified that stability only reuires a positive static dielectric function at long wavelengths.

30 Parameters which determine Тс T c + λ exp[ ] ln λ μ large energies of intermediate bosons phonons excitons spinfluctuations etc. large coupling constants ln ~ M λ dωα Ω F Ω Ω

31 α F from tunneling conductance - planar junctions Bi Sr CaCu O GaAs and Au - break-junctions from Bi 8 Sr CaCu O 8

32 BCS McMillan Eliashberg Z0 + λ - mass renormalization freuency dependence of Mass renormalization increases DOS; why does it reduce the coupling? T c exp λ μ.4 ph * λ λ + λ.4 /.

33 Strong coupling [ ] ; / exp 3. 4 / ln / ln ; π θ π θ γ θ θ ξ π λ λ θ π λ θ π θ λ θ π ξ λ D c D D D c c T D c D c c D D c n T n c T T T e T T d T >> << + + BCS or λ>> or λ<<

34 Strong coupling [ ] ; / exp 3. 4 / ln / ln ; π θ π θ γ θ θ ξ π λ λ θ π λ θ π θ λ θ π ξ λ D c D D D c c T D c D c c D D c n T n c T T T e T T d T >> << + + BCS or λ>> or λ<< λ Z

35 Superstrong coupling λ>> 0.5 T c / ph λ ph / Upper Bound Lower Bound McMillan Euation λ

36 Metallic Hydrogen E.G.MaksimovD.Savrasov SSC λ7.33 Tc 600 K!

37 Superconductivity at 39K in MgB Akimitsu et al. Nature London

38 Something unusual is going on The uasi-d bands couple to the optical B-B bond-stretching modes which are softened by the e-ph coupling and are strongly anharmonic. Kong OVD Jepsen Andersen PRB R 00

39 Coupling of the E g phonon mode to the electronic structure

40 Journal of Superconductivity and Novel Magnetism Vol. 9 Nos. 3 5 July 006 C 006

41 Journal of Superconductivity and Novel Magnetism Vol. 9 Nos. 3 5 July 006

42 W.E. Pickett: Тс430K!!! λ.5 Problems: - lattice stability? - pair-breaking effect by low-energy phonons Dolgov&Golubov PRB

43 λ Q g δ ε δ ε MN0 k k+ Q k k+ Q Q k W.E. Pickett

44 0 Q k k k Q k k Q Q + + ε δ ε δ λ g MN 0 Q Q Q k k k Q k k Q Γ ε δ ε δ λ g MN O.V.D. O.K. Andersen I.I. Mazin PRB 008 W.E. Pickett

45 Phys. Rev. B Hypothetical BC boron-doped diamond λ3.6 T c K

46 Anisotropy vanishes for strong coupling OVD A.A. Golubov PRB

47 Phonon instability ] [ δ ξ ξ θ δ ξ ξ θ ε ε ξ ε δ i i M g n n M g bare d Σ + + k k k k k k k A A bare A M g N M g N λ λ λ λ λ 0 ; 0

49 Excitonic mechanisms Negative Electronic Dielectric Function ε el 0 < 0 Problems with the stability of phonons ph ε el Ω pl 0 0; i Ω 4πZ e pl M i N i

50 Interaction via spin-waves

51 Spin fluctuations How exactly are spin fluctuations different from phonons? Phonon induced superconductivity is much better understood than spin-fluctuation induced despite comparable history Berk-Schrieffer 66 Fay-Appel Opposite effect of on Z and SF on in singlet pairing: SF Spin fluctuations increase the mass but decrease the net pairing strength

52 Spin resonance B.Keimer00 Fig.

53 Magnetic neutron scattering and NMR against SFI I Q limim χ Q / 0 Tc Tc 9 K 9.5 K pair Im χ Q λ ~ sf gsfi d - big change of χ Q but small change of T! c

54 Spin fluctuations ~ 3.% n s λ sp ZU t 0.

56 n n n n n c n n i V T i i Z Ω Δ Δ π n.ph n.ph k k. / n ep n i Z Γ + Non-phonon ep ep T d-wave

57 n n n n n c n n i V T i i Z Ω Δ Δ π n.ph n.ph k k. / ep i Z Γ + Damping due to phonons Non-phonon ep ep T T c T c0 e ep. d-wave

58 n n n n n c n n i V T i i Z Ω Δ Δ π n.ph n.ph k k. / ep i Z Γ + Damping due to phonons Non-phonon ep ep T T c T c0 e ep. T c K!!! For λ ph ~- and T c ~60 K bare d-wave

59 n n n n n c n n i V T i i Z Ω Δ Δ π n.ph n.ph k k. / ep i Z Γ + Damping due to phonons Non-phonon ep ep T T c T c0 e ep. T c K!!! For λ ph ~- and T c ~60 K bare d-wave

60 Conclusions There are NO formal restrictions on T c. There are some problems with phonon instabilities for all mechanisms. The ROOM-TEMPERATURE superconductivity is not the myth but the object for investigations.

Replacing La with other Rare-Earths increases Tc up to 55 K Sm.

61 LaOFeAs a not-so-simple superconductor 008: LaO -x F x FeAsTc max 6 K at x0. Tetragonal layers of La-O + Fe-As F replaces O and dopes electrons into the system. Replacing La with other Rare-Earths increases Tc up to 55 K Sm. EXP: small coherence length T-dependent Hall coefficient no jump in specific heat at Tc specific heat + point contact: nodes in the gap?

LaOFeAs Electron-phonon coupling λ 0. 06K T log ME c 0.5K N0.st / ev L. Boeri OVD A.A. Golubov PRL 0 06403 008 E-ph interaction: λ~0. is too small to account for T c Doping can only decrease λ.

62 LaOFeAs Electron-phonon coupling λ 0. 06K T log ME c 0.5K N0.st / ev L. Boeri OVD A.A. Golubov PRL E-ph interaction: λ~0. is too small to account for T c Doping can only decrease λ. N0 is large λ is small because of small e-ph matrix elements. The coupling is uniform over phonon modes: the only directed bands sit far from E F. Possible two-gap scenario with large repulsive interband interaction

63 0. λ T c 0.8 K α F N e 0/N h 04/3 e-e h-h e-h h-e total mev

64 0.3 LaNiAsO 0.9 F 0. λ0.7 LaFeAsO 0.9 F 0. λ0. 0. α F mev

65 LaNiAsO 0.9 F 0. Z. Li et al. Phys. Rev. B R LaNiAsO 0.9 F 0. 0 T c 3.8 K μ*0. ΔCT c /γ N 0T c.67>.43bcs α F λ0.7 ΔC/T mj/molk γ mj/molk exp mev T/T c L.Boeri OVD A.A. Golubov the special issue of Physica C 009

66 The specific heat of the single crystal Ba -x K x Fe As P. Popovich R. Kremer A. Boris OVD

67 ln ~5-40 mev; ph ln~5 mev /T c

68 Probing SC gap from IR spectroscopy Photon energy mev Ba -x K x Fe As σ Ω cm ~6 kt c T c 38.5 K 500 ~3.5 kt c Τ c 38.5Κ ε K 34 K 5 K Wavenumber cm-

69 Probing SC gap from IR spectroscopy Photon energy mev single SC 8-9 mev strong coupling SC T c σ Ω cm Δ SC Ba -x K x Fe As Δ SC +Ω clean limit ~0 cm - s± model with intermediateboson function: ε Τ c 38.5Κ 40 K 34 K 5 K B Wavenumber cm cm mev cm -

70 Probing SC gap from IR spectroscopy O.V. Dolgov: σ Ω cm Δ SC Photon energy mev Ba -x K x Fe As Δ SC +Ω 4πRe σ/ pl clean γ intra 0 cm cm - T40 K T5 K intermediate-boson function ε Τ c 38.5Κ 40 K 34 K 5 K B cm Wavenumber cm cm -

72 Charge carrier optical self-energy or Why I am worry about /tw representation in Fe pnictides. 4 σ π ε ε ε ε i i σ π ε ε Drude i + 4 Re ] Im[ ε ε ε ε πσ τ + Σ pl Drude pl Σ

73 Charge carrier optical self-energy Sw Im[ Σ ] τ Re 4πσ pl Drude pl ε ε + ε ε /τ ev Y3 a-axis T c 9.5 K T 00 K ε inf ε inf 5 cuprates: ε 5-6 lowest inter-band transitions at ev 0. ε inf Wave number cm -

74 Charge carrier optical self-energy Sw Im[ Σ ] τ Re 4πσ pl Drude pl ε ε + ε ε /τ ev Y3 a-axis T c 9.5 K T 00 K ε inf ε inf 5 ε inf Wave number cm - cuprates: ε 5-6 lowest inter-band transitions at ev pnictides: ε - 5!! lowest inter-band transitions at ev!! An incorrect account of the interband transitions!

75 Conclusions II Pnictides except LaNiAsO 0.9 F 0. cannot be described by electron-phonon interaction. Optical properties in the N- and SC- states can be described by spin fluctuations. The linear freuency dependence of the optical scattering rate /τ is an artifact of the incorrect account of interband transitions.

76 Possible connection with other exotic superconductors S.-L. Drechsler MgB uasi-d Multibands gaps borocarbides FeAs based SC Heavy uasiparticles Unconventional pairing Heavy Fermions Cuprates Vicinity of AFM phases B-As-similarities

Can superconductivity emerge out of a non Fermi liquid.

Can superconductivity emerge out of a non Fermi liquid. Andrey Chubukov University of Wisconsin Washington University, January 29, 2003 Superconductivity Kamerling Onnes, 1911 Ideal diamagnetism High Tc