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

Signatures of the Superconducting Mechanism in the Far Infrared F. Marsiglio Dept of Physics, University of Alberta, Edmonton, AB, CANADA and DPMC, Universite de Geneve, CH

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!

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

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 ω D ω ω D

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

Z. Zhang, C.-C. Chen, and C.M. Lieber, Science, 254, 1619 (1991) 15 K K 3 C 60 10 K 4.2 K

Optical Measurements free space metal reflected E 2 E 0 transmitted and absorbed z incident E 1 • experiment measures reflectance = R( ω ) = |E 2 /E 1 | 2 • require reflectivity = E 2 /E 1 = R 1/2 ( ω )e i θ ( ω ) = r ( ω ) • need Kramers-Kronig to get θ ( ω ) from R( ω ) • complex conductivity r = (N-1)/(N+1), ε = ε ∞ + 4 π i σ / ω = N 2

Optical Conductivity photon, h ν Fermi sea ∆ω ∆ k Infrared light cannot be absorbed by electron-hole pair creation Solution X k’,E e - k,E A) Impurity-assisted absorption • impurities are a source of elastic scattering for electrons q, ω q k,E e - B) Phonon-assisted absorption k’,E’ • phonons are a source of inelastic scattering for electrons

Absorption processes are identified in the frequency and temperature dependence of the real part of the conductivity A) Impurity Scattering 1/ τ = electron-impurity scattering rate temperature independent ! interband transitions B) Phonon Scattering 1/ τ i = effective electron-impurity scattering rate at temperature T i Extra absorption from “phonon-assisted” process

Reflectance : elastic vs. inelastic more significant Hagen-Rubens decrease in phonon region more rounded plasma edge Drude Drude +Pb interband plasma edge transitions

clean limit no Drude absorption at low temperature entirely Holstein process at low temperature

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

Ba 1-x K x BiO 3 T c ~ 28 K isotope effect has β ~0.2 - 0.4 ? Electron-phonon mechanism ? λ ~ 0.2 !!

K 3 C 60 • T c ~ 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)

1 eV 10 eV 100 meV

normal state ! Phys. Lett. A 245 , 172 (1998)

(A) Pb (actual, and numerically inverted --- these are indistinguishable approximate (from (A) )

L. Pintschovius, K 3 C 60 Rep. Prog. Phys. 57, 473 (1996) T c = 19 K

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

MgB 2 • T c ~ 39 K • isotope effect has β ~0.3 • Electron-phonon mechanism ? Isotope effect: inconclusive Calculations: overwhelming YES Experiments: optical: no, but….

180 meV 2000 K 45 THz

Impact of inelastic scattering (example)

MgB 2 : real part of conductivity increased inelastic scattering

MgB 2 Reflectance: Theory vs Experiment increased inelastic Reflectance scattering frequency PRL 87 , 247001 (2001)

PRB 64 , 020501 (2001) PRL 87 , 247001 (2001)

MgB 2 Scattering Rate: Theory vs Experiment PRL 87 , 247001 (2001)

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

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

Back to “single band” sum rule… What do you expect in the conventional BCS theory ? recall: superconducting state T = 0 !! E k = 2 Σε k v k2 k

why is there temperature dependence in the normal state ? Answer: 1) n k ---> f k (Fermi-Dirac) 2) interactions E kin = 2 Σ ε k n k Note: Absolute value of kinetic energy decreases in the superconducting state. This is conventional behaviour van der Marel et al. cond-mat/0302169

But….

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

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

momentum distributions e-ph interaction temperature ε k ε k elastic scattering superconductivity ε k

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

Suppose the scattering rate collapses below T c ? (1999) collapse of scattering rate as temperature is lowered Nuss et al. PRL, 66, 3305 (1991)

use 1/ τ = 1/ τ 0 (T/T c ) 4 below T c Now also observed in photoemission (Johnson et al. this conference)

Anomalous sum rule change at Tc

Kinetic energy vs. Sum rule change K = kinetic energy T = sum rule r = t’/t

Summary • Optical spectroscopy is becoming a powerful tool for indicating mechanism • Ba 1-x K x BiO 3 is NOT a conventional electron phonon superconductor • K 3 C 60 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