Signatures of the Superconducting Mechanism in the Far Infrared F. - - PowerPoint PPT Presentation

• F. Marsiglio

Dept of Physics, University of Alberta, Edmonton, AB, CANADA and DPMC, Universite de Geneve, CH

Signatures of the Superconducting Mechanism in the Far Infrared

How do we learn about mechanism ?

• Kinetic vs. potential (sum rules)
• `attractive’ vs. repulsive
• dynamics → retardation effects (temporal)
• symmetry → structure of constituents in

momentum space (spatial)

• inhomogeneities: how does order react to

duress ?

The traditional spectroscopy: single electron tunneling Rowell and McMillan, and many more since. Another possibility --- optical conductivity: Joyce and Richards (1970), Allen (1971), Farnsworth and Timusk (1974), Marsiglio et al. (1998), Carbotte et al. (2001), Choi et al. (2000,2003) Photoelectron Spectroscopy: Arnold et al. (1991), Valla et al. (1999), LaShell et al. (2000), Lanzara et al. (2001), Eschrig and Norman (2002), Verga et al. (2002), Shi et al. (2003), Reinert et al. (2003).

BCS formalism vs. Pairing Mechanism

Tc equation (useless)

Universality

Universality is wonderful Universality is a curse!

Al BCS

B.L. Blackford and R.H. March, Can. J. Phys. 46, 141 (1968)

I V

Eliashberg Theory

• Extension of BCS formalism to include

dynamical electron-phonon interaction

• builds on Migdal theory in the normal state
• loosely modeled in BCS theory

ω ωD ωD ω

Eliashberg Theory

A functional of the interaction Question: Can we invert the theory to extract the potential uniquely from a knowledge of ∆(k,ω) ?

• I. Giaever, H.R. Hart, Jr., and K. Megerle, PRB 126, 941 (1962)

d I ~ N(ε) dV

Pb

ω(meV)

F(ω): density of phonon states from neutron scattering

• Z. Zhang, C.-C. Chen, and C.M. Lieber,

Science, 254, 1619 (1991)

15 K 10 K 4.2 K

K3C60

Optical Measurements

incident E1 reflected E2

free space metal z

E0 transmitted and absorbed

• experiment measures reflectance = R(ω) = |E2/E1|2
• require reflectivity = E2/E1 = R1/2(ω)eiθ(ω) = r (ω)
• need Kramers-Kronig to get θ(ω) from R(ω)
• complex conductivity r = (N-1)/(N+1), ε = ε∞ + 4πiσ/ω = N2

Optical Conductivity

Fermi sea Infrared light cannot be absorbed by electron-hole pair creation Solution A) Impurity-assisted absorption

• impurities are a source of elastic scattering for electrons

B) Phonon-assisted absorption

• phonons are a source of inelastic scattering for electrons

X k,E e- k’,E k,E k’,E’ q,ωq

photon, hν

∆k ∆ω

e-

Absorption processes are identified in the frequency and temperature dependence of the real part of the conductivity

A) Impurity Scattering B) Phonon Scattering

1/τ = electron-impurity scattering rate

interband transitions temperature independent !

1/τi = effective electron-impurity scattering rate at temperature Ti Extra absorption from “phonon-assisted” process

Reflectance: elastic vs. inelastic

Drude Drude +Pb

interband transitions Hagen-Rubens plasma edge more significant decrease in phonon region more rounded plasma edge

entirely Holstein process at low temperature

no Drude absorption at low temperature

clean limit

Drude absorption Holstein absorption

Holstein process is not as evident, when elastic impurity scattering is present

Ba1-xKxBiO3

Tc ~ 28 K isotope effect has β~0.2 - 0.4 ? Electron-phonon mechanism ? λ~ 0.2 !!

K3C60

• Tc ~ 30 K
• isotope effect has β ~0.4 ?
• Electron-phonon mechanism ?

Phonon modes extend out to 200 meV Use an optical inversion technique (Allen, 1971)

100 meV 1 eV 10 eV

• Phys. Lett. A 245, 172 (1998)

normal state !

Pb (actual, and numerically inverted --- these are indistinguishable

approximate (from (A) )

(A)

K3C60

• L. Pintschovius,
• Rep. Prog. Phys.

57, 473 (1996) Tc = 19 K

another example: Carbotte et al. Nature, 40, 354 (1999): YBCO = W(ν)

MgB2

• Tc ~ 39 K
• isotope effect has β~0.3
• Electron-phonon mechanism ?

Isotope effect: inconclusive Calculations:

• verwhelming YES

Experiments:

• ptical: no, but….

180 meV 2000 K 45 THz

Impact of inelastic scattering (example)

MgB2: real part of conductivity

increased inelastic scattering

MgB2 Reflectance: Theory vs Experiment Reflectance frequency

increased inelastic scattering

PRL 87, 247001 (2001)

PRB 64, 020501 (2001)

PRL 87, 247001 (2001)

MgB2 Scattering Rate: Theory vs Experiment

PRL 87, 247001 (2001)

Han-Yong Choi and Tae-Hyoung Gimm, Int. J. Mod. Phys. B 17, 3524 (2003)

500 meV

Two band model ?

• Can a two band model allow the data to

accommodate a stronger electron phonon interaction ?

• Ref. 3: F.M. PRL, 87, 247001 (2001)
• Ref. 1: E.G. Maksimov et al. PRL 89, 129703 (2002)

Data from Tu et al. PRL, 87, 277001 (2001)

Optical Sum Rule

Closely related to kinetic energy

What do you expect in the conventional BCS theory ? recall: k T = 0 !! superconducting state

Ek = 2 Σεkvk2

Back to “single band” sum rule…

van der Marel et al. cond-mat/0302169

why is there temperature dependence in the normal state ?

Answer: 1) nk ---> fk (Fermi-Dirac) 2) interactions

Note: Absolute value of kinetic energy decreases in the superconducting state. This is conventional behaviour

Ekin = 2 Σεknk

But….

M.V. Klein and G. Blumberg, Science 283, 42 (1999)

Al Ah

Explanations 1) novel superconductivity --- kinetic energy gain ! Electrons are more mobile in the superconducting state Hirsch and FM Anderson + others 2) change in interactions at the superconducting transition Norman and Pepin PRB 66, 100506 (2004) Knigavko, Carbotte and FM PRB 70, 224501 (2004) Dahm et al. cond-mat/0507723 Motivation ? Neutron scattering resonance peak See Benfatto and Sharapov, cond-mat/0508695

εk

temperature

superconductivity

e-ph interaction

elastic scattering

momentum distributions

εk εk

Elastic scattering on its own, does ‘nothing’ conventional BCS behaviour but…

Suppose the scattering rate collapses below Tc ?

(1999)

collapse of scattering rate as temperature is lowered

Nuss et al. PRL, 66, 3305 (1991)

use 1/τ = 1/ τ0 (T/Tc)4 below Tc

Now also observed in photoemission (Johnson et al. this conference)

Anomalous sum rule change at Tc

Kinetic energy vs. Sum rule change r = t’/t

K = kinetic energy T = sum rule

Summary

• Optical spectroscopy is becoming a powerful tool

for indicating mechanism

• Ba1-xKxBiO3 is NOT a conventional electron

phonon superconductor

• K3C60 probably is a conventional e-ph

superconductor

Need to see k and ω dependence of superconducting order parameter -- need angle resolution as well --- Neutron Scattering and photoemission sum rule is telling us that electrons are more free in the superconducting state than in the normal state (lifetime vs. quasiparticle residue) Acknowledgements: Carbotte, Schachinger, Timusk, Hirsch, Knigavko Funding: NSERC, CIAR, ICORE