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
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
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
Kelvin 50 00 50 00 50 0 Hg 90 940 960 980 000. BaKBiO 3. Cs 3 C 60 3. 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 90 940 960 980 000 3 7 5 4 0-50 -00-50 -00 6-50 Celcius
BCS type behavior M.Matsui et al. PRL90700003 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
Electrons join to form Cooper Pairs usually A Magnetic Attraction? Spin attraction? The lattice after all? Something else?
Electrons join to form Cooper Pairs usually A Magnetic Attraction? Spin attraction? The lattice after all?
Electrons join to form Cooper Pairs usually A Magnetic Attraction? Spin attraction? The lattice after all? Excitons LittleGinzburg
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
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 + + + 4 ~ TF C e V χ π + 4 TF C e V χ π +
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
λ N0 d μ N0 d 3 3 V ph ~ V C 0 0 μ μ ε + μln F D εtot 0 λ μ
+ λ T c.4 ϖ exp[ λ μ + μ log ε / ϖ F ];
+ λ T c.4 ϖ exp[ λ μ + μ log ε / ϖ F ]; λ>μ ε0<0 T c /ε F λ<μ ε0> 0.0 0.5.0 ϖ/ε F
Superconductivity in d- and f-band Metals AIP Conf. Proc. p.7 97!!!
+ λ T c.4 ϖ exp[ λ μ + μ log ε / ϖ F ]; λ>μ ε0<0 T c /ε F λ<μ ε0> 0.0 0.5.0 ϖ/ε F
max T c ε F exp 3 ; λ λ opt μ ; Stoner instability ε F 7 ev
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!
Response functions A R х I
Kramers-Kronig relations Response functions A R х I causality reuirements R R + π 0 E de iδ Im R E
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
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
0 Im 00 Im/ 0 / 0 0 E E E de E de + + ε ε ε ε π π arbitrary 0
/ 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 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. 53 898
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
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
Dielectric functions for real systems ε 0 normal metals : K Al Pb hypothetical metallic H classical charge fluid
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.
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
α F from tunneling conductance - planar junctions Bi Sr CaCu O GaAs and Au - break-junctions from Bi 8 Sr CaCu O 8
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 /.
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<<
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
Superstrong coupling λ>> 0.5 T c / ph 0.4 0.3 0. 0.83 λ ph / Upper Bound Lower Bound McMillan Euation 0. 0 0 3 4 5 λ
Metallic Hydrogen E.G.MaksimovD.Savrasov SSC.9569 00 λ7.33 Tc 600 K!
Superconductivity at 39K in MgB Akimitsu et al. Nature London 40 63 00
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 64 0050R 00
Coupling of the E g phonon mode to the electronic structure
Journal of Superconductivity and Novel Magnetism Vol. 9 Nos. 3 5 July 006 C 006
Journal of Superconductivity and Novel Magnetism Vol. 9 Nos. 3 5 July 006
W.E. Pickett: Тс430K!!! λ.5 Problems: - lattice stability? - pair-breaking effect by low-energy phonons Dolgov&Golubov PRB 77 456008
λ Q g δ ε δ ε MN0 k k+ Q k k+ Q Q k W.E. Pickett
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
Phys. Rev. B 7409450 006 Hypothetical BC boron-doped diamond λ3.6 T c 40 60 K
Anisotropy vanishes for strong coupling OVD A.A. Golubov PRB 77 456 008
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
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
Interaction via spin-waves
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 77-80 Opposite effect of on Z and SF on in singlet pairing: SF Spin fluctuations increase the mass but decrease the net pairing strength
Spin resonance B.Keimer00 Fig.
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
Spin fluctuations ~ 3.% n s λ sp ZU t 0.
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
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
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 c0 400 00 K!!! For λ ph ~- and T c ~60 K bare d-wave
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 c0 400 00 K!!! For λ ph ~- and T c ~60 K bare d-wave
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.
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. 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
0. λ 0.4 0.093 0.083 T c 0.8 K α F 0.5 0.0 0.05 N e 0/N h 04/3 e-e h-h e-h h-e total 0.00 0 0 40 60 80 mev
0.3 LaNiAsO 0.9 F 0. λ0.7 LaFeAsO 0.9 F 0. λ0. 0. α F 0. 0.0 0 0 0 30 40 50 60 70 mev
LaNiAsO 0.9 F 0. Z. Li et al. Phys. Rev. B78 060504 R 008 0.3 LaNiAsO 0.9 F 0. 0 T c 3.8 K μ*0. ΔCT c /γ N 0T c.67>.43bcs α F 0. 0. λ0.7 ΔC/T mj/molk 5 0-5 γ 0 3.86 mj/molk exp 0.0 0 0 0 30 40 50 60 70 mev -0 0.0 0.5.0 T/T c L.Boeri OVD A.A. Golubov the special issue of Physica C 009
The specific heat of the single crystal Ba -x K x Fe As P. Popovich R. Kremer A. Boris OVD
ln ~5-40 mev; ph ln~5 mev /T c
Probing SC gap from IR spectroscopy Photon energy mev 0 0 0 30 40 50 60 70 3000 500 Ba -x K x Fe As σ Ω cm 000 500 000 ~6 kt c T c 38.5 K 500 ~3.5 kt c 0-000 -000 Τ c 38.5Κ ε -3000-4000 40 K 34 K 5 K -5000 0 80 60 40 30 400 480 560 Wavenumber cm-
Probing SC gap from IR spectroscopy Photon energy mev 0 0 0 30 40 50 60 70 3000 single SC 8-9 mev strong coupling SC 5.5-6.5T c σ Ω cm 500 000 500 000 500 Δ SC Ba -x K x Fe As Δ SC +Ω clean limit ~0 cm - s± model with intermediateboson function: 0 0.4 ε -000-000 -3000-4000 Τ c 38.5Κ 40 K 34 K 5 K -5000 0 80 60 40 30 400 480 560 B Wavenumber cm- 0 00 400 600 cm - 0.3 0. 0. 0.0 5 mev cm -
Probing SC gap from IR spectroscopy O.V. Dolgov: σ Ω cm 0 0 0 30 40 50 60 70 3000 500 000 500 000 500 0 Δ SC Photon energy mev Ba -x K x Fe As Δ SC +Ω 4πRe σ/ pl 0.4 0.004 0.003 0.00 0.00 0.000 clean γ intra 0 cm - 0 00 00 300 400 500 cm - T40 K T5 K intermediate-boson function ε -000-000 -3000-4000 Τ c 38.5Κ 40 K 34 K 5 K B 0.3 0. 0. cm - -5000 0 80 60 40 30 400 480 560 Wavenumber cm- 0.0 0 00 400 600 cm -
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 + + 4 σ π ε ε Drude i + 4 Re ] Im[ ε ε ε ε πσ τ + Σ pl Drude pl Σ
Charge carrier optical self-energy Sw Im[ Σ ] τ Re 4πσ pl Drude pl ε ε + ε ε /τ ev 0.5 0.4 0.3 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.8 -.0 ev 0. ε inf 8 0. 000 000 3000 4000 Wave number cm -
Charge carrier optical self-energy Sw Im[ Σ ] τ Re 4πσ pl Drude pl ε ε + ε ε /τ ev 0.5 0.4 0.3 0. 0. Y3 a-axis T c 9.5 K T 00 K ε inf ε inf 5 ε inf 8 000 000 3000 4000 Wave number cm - cuprates: ε 5-6 lowest inter-band transitions at.8 -.0 ev pnictides: ε - 5!! lowest inter-band transitions at 0. - 0.5 ev!! An incorrect account of the interband transitions!
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.
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