Systematic electron-phonon interaction
strength measurements in hightemperature superconductors with
femtosecond spectroscopy
Christoph Gadermaier
Department of Complex Matter
Jožef Štefan Insitute
Ljubljana, Slovenia
Conventional superconductivity
Electron-phonon interaction
BCS:
 1  
k B T c    exp  

 

Isotope effect:
Image courtesy of B. Valenzuela
What is the role of EPI in high-Tc?
Determine electron phonon interaction from electron energy
relaxation
n (arb. units)
1.0
0.8
0.6
0.4
0.2
0.0
-100
-50
0
E-EF (arb. units)
Image courtesy of G. Cerullo
50
100
The two-temperature model
excitation
hot
nonthermal
electrons
hot
thermal
electrons
cold
thermal
electrons
EPI
 
2

cold
phonons
dissipation
warm
thermal
electrons
e-e collisions
cold
phonons
EPI
cold
phonons
cold
thermal
electrons
dissipation
warm
phonons
cold
phonons
 k B Te
3   e  ph
P.B. Allen, Phys. Rev. Lett. 59, 1460 (1987).
Validity of the TTM
C. Kittel, p. 296:
Ashcroft & Mermin, p. 348:
P.B. Allen, Phys. Rev. Lett. 59, 1460 (1987):
The non-equilibrium model
excitation
hot
nonthermal
electrons
EPI+e-e
warm
nonthermal
electrons
cold
thermal
electrons
EPI
cold
phonons
 
2

2 k B Tl
3   e  ph
cold
phonons
dissipation
cold
thermal
electrons
dissipation
warm
phonons
cold
phonons
V.V Kabanov and A. S.
Alexandrov, Phys. Rev. B. 78,
174514 (2008).
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+d
Exact distribution (t=
Fermi-Dirac distribution
n()
1
0.1
a)
0.01
-5
0
5
10
15
/kBT
L. Perfetti et al., Phys. Rev. Lett. 99, 197001 (2007).
Compare predictions of TTM and NEM
TTM
 
2

NEM
 k B Te
 
3   e  ph
2

2 k B Tl
3   e  ph
all
fluences
low
fluence
high
fluence
Te  T L
Te  T L
 e  ph  c p T L
 e  ph  c p T L
 e  ph  c p T L
 e  ph   e  ph  I 
 e  ph   e  ph  I 
 e  ph   e  ph  I 
Te undefined
Temperature dependent relaxation time
T. Mertelj et al., Phys. Rev. B 81,
224504 (2010).
We need to measure well above the pseudogap temperature
Intensity independent dynamics in La1.85Sr0.15CuO4
1.4
1.2
R/R (%)
R/R (arb. units)
1.0
0.8
0.6
1.0
0.8
0.6
0.4
0.2
0.0
0
100 200 300 400 500 600
2
pump intensity (  J/cm )
0.4
2
70 J/cm
2
130 J/cm
2
270 J/cm
2
540 J/cm
0.2
0.0
-100
0
100
200
300
400
delay (fs)
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
620 nm
580 nm
540 nm
T/T (arb. units)
1.0
0.8
 a  45 fs
 b  600 fs
0.6
0.4
 a   e  ph 
0.2
2 k B Tl
3  
2
0.0
-0.2
-100
0
100
200
300
400
 
2
 800 meV
delay (fs)
C. Gadermaier et al., Phys. Rev. Lett. 105, 257001 (2010).
2
• Determination of EPI strength in YBa2Cu3O6.5
520 nm
560 nm
600 nm
T/T (arb. units)
1.0
0.8
0.6
 a  100 fs
 b  450 fs
0.4
 a   e  ph 
0.2
0.0
2 k B Tl
3  
2
-0.2
-100
0
100
200
300
400
 
2
 400 meV
delay (fs)
C. Gadermaier et al., Phys. Rev. Lett. 105, 257001 (2010).
2
The role of e-ph interaction in high-Tc
Unpublished material removed.
Please contact
christoph.gadermaier@ijs.si
Electron correlation
D
E
T. Nakano et al., J.
Phys. Soc. Jap. 67,
2622 (1998).
Tc/Tc,max
1.0
0.5
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
x/xopt
J.-H. Chu, Phys. Rev. B. 79, 014506 (2009).
Collaborative electron-electron and electronphonon
Unpublished material removed.
Please contact
christoph.gadermaier@ijs.si
Bipolarons
140
BaFe2As2
YBCO
HBCO
BiSCO
LaSCO
120
100
Tc (K)
80
60
40
20
0
0
1
2
3
4
5
TL/e-ph (K/fs)
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
6
7
8
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 nonequilibrium 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