Systematic electron-phonon interaction strength measurements in

high-temperature superconductors with femtosecond spectroscopy

Christoph GadermaierDepartment of Complex Matter

Jožef Štefan InsituteLjubljana, Slovenia

What is the role of EPI in high-Tc?

Conventional superconductivityElectron-phonon interaction

Image courtesy of B. Valenzuela

BCS:

1

expcBTk

Isotope effect:

Determine electron phonon interaction from electron energy relaxation

-100 -50 0 50 100

0.0

0.2

0.4

0.6

0.8

1.0

n (a

rb. u

nits

)E-E

F (arb. units)

Image courtesy of G. Cerullo

The two-temperature model

cold thermal

electrons

hot nonthermal electrons

cold phonons

cold phonons

cold phonons

warm phonons

cold phonons

hot thermal

electrons

warm thermal

electrons cold

thermal electrons

excitation

e-e collisions

EPI

dissipation

dissipation EPI

P.B. Allen, Phys. Rev. Lett. 59, 1460 (1987).phe

eBTk

3

2

Validity of the TTMC. Kittel, p. 296:

Ashcroft & Mermin, p. 348:

P.B. Allen, Phys. Rev. Lett. 59, 1460 (1987):

The non-equilibrium model

hot nonthermal electrons

cold thermal

electrons

cold phonons

cold phonons

warm phonons

cold phonons

warm nonthermal electrons

cold thermal

electrons

excitation

EPI+e-e

dissipation

dissipation EPI

V.V Kabanov and A. S. Alexandrov, Phys. Rev. B. 78,

174514 (2008).phe

lBTk

3

22

e-e thermalisation is not faster than e-ph energy relaxation

C. Gadermaier et al., Phys. Rev. Lett. 105, 257001 (2010).Metal data from S. D. Brorson et al., Phys. Rev. Lett. 64, 2172

(1990).

Electron distribution during relaxation in Bi2Sr2CaCu2O8+

-5 0 5 10 15

0.01

0.1

1 Exact distribution (t= Fermi-Dirac distribution

n()

/kBT

a)

L. Perfetti et al., Phys. Rev. Lett. 99, 197001 (2007).

Compare predictions of TTM and NEM

phe

eBTk

3

2

phe

lBTk

3

22

TTM NEM

low fluence

high fluence

Le TT

Lpphe Tc

Iphephe

Le TT

Lpphe Tc

Iphephe

all fluence

s

Te undefined

Lpphe Tc

Iphephe

Temperature dependent relaxation time

We need to measure well above the pseudogap temperature

T. Mertelj et al., Phys. Rev. B 81, 224504 (2010).

-100 0 100 200 300 400

0.0

0.2

0.4

0.6

0.8

1.0

0 100 200 300 400 500 6000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

R/R

(%

)

pump intensity (J/cm2)

70 J/cm2

130 J/cm2

270 J/cm2

540 J/cm2

R/R

(ar

b. u

nits

)

delay (fs)

Intensity independent dynamics in La1.85Sr0.15CuO4

400K < “Te” < 800 K

C. Gadermaier et al., Phys. Rev. Lett. 105, 257001 (2010).

Arguments for the non-equilibrium model

• textbook knowledge

• comparison of measured e-ph relaxation and estimated e-e thermalisation times

• time-dependent electron distribution from ARPES

• intensity independent dynamics

• Determination of EPI strength in La1.85Sr0.15CuO4

fsa 45

-100 0 100 200 300 400-0.2

0.0

0.2

0.4

0.6

0.8

1.0

620 nm 580 nm 540 nm

T/T

(ar

b. u

nits

)

delay (fs)

fsb 600

23

2

lB

phea

Tk

22 800meV

C. Gadermaier et al., Phys. Rev. Lett. 105, 257001 (2010).

• Determination of EPI strength in YBa2Cu3O6.5

fsa 100

fsb 450

23

2

lB

phea

Tk

22 400meV-100 0 100 200 300 400

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

520 nm 560 nm 600 nm

T/T

(ar

b. u

nits

)

delay (fs)

C. Gadermaier et al., Phys. Rev. Lett. 105, 257001 (2010).

The role of e-ph interaction in high-Tc

Unpublished material removed. Please contact

christoph.gadermaier@ijs.si

Electron correlation

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.5

1.0

D E

Tc/

Tc,

max

x/xopt

T. Nakano et al., J. Phys. Soc. Jap. 67,

2622 (1998).

J.-H. Chu, Phys. Rev. B. 79, 014506 (2009).

Collaborative electron-electron and electron-phonon

Unpublished material removed. Please contact

christoph.gadermaier@ijs.si

Bipolarons

A. S. Alexandrov, Phys. Rev. B. 38, 925 (1988).Basic theory derived already in A. S. Alexandrov, Zh. Fi.

Khim. 57, 273 (1983) before the discovery of high Tc

0 1 2 3 4 5 6 7 80

20

40

60

80

100

120

140

Tc (

K)

TL/

e-ph (K/fs)

BaFe2As2 YBCO HBCO BiSCO LaSCO

Stripes and other textures

T. Mertelj, V.V. Kabanov, and D. Mihailovic, Phys. Rev.Lett. 94, 147003 (2005).

Conclusion

• electron-phonon interaction is determined from electron energy relaxation

• electron energy relaxation is described by the non- equilibrium model, qualitatively even for non-Fermi liquids → TL/e-ph is a good measure of electron-phonon interaction

• almost universal dependence of Tc of optimally doped compounds on TL/e-ph, sharp maximum at 5 K/fs → high Tc is a collaborative effect of electron-phonon interaction and electron correlation

Acknowledgements

• Primož Kušar, Viktor Kabanov, Tomaž Mertelj, Ljupka Stojchevska, Yasunori Toda, Dragan Mihailović

• Sasha Alexandrov

• Cristian Manzoni, Daniele Brida, Dario Polli, Giulio Cerullo

• grazas pola súa atención