Sonia Haddad

1
Field induced confinement in quasi-one
dimensional organic conductors

• Sonia Haddad
• LPMC, Département de Physique,
• Faculté des Sciences de Tunis, Tunisia
• Collaboration
• N. Belmechri, (LPS, Orsay, France)
• M. Héritier, (LPS, Orsay, France)
• S. Charfi-Kaddour, (LPMC, Tunis, Tunisia )

S. H., N. Belmechri, S. Charfi-Kaddour and M.
Héritier et al. PRB 78, 075104 (2008).
2
Low dimensional system are quite interesting
New physics Quantum effects Strong
correlations Important effect of disorder
Giant magnetoresistance (Nobel prize 2007)
FQHE (Nobel prize 1998)
Hard disk
3
Bechgaard salts (TMTSF)2X
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Key parameters of (TMTSF)2X
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Phase diagram of Bechgaard salts
Different energy scales 1D ----gt 2D 2D ----gt
3D
2D FL? NFL ?
6
The wondrous world of quasi-one organic conductors
2D system
3D system
Confined system
Fermi liquid
1D system
Luttinger liquid
(after, W. Kangs idea)
7
Field induced confinement
Outline

• Field induced confinement a brief review
• Theory vs. experiments

• Field induced confinement Theoretical approach
• Quantum calculations

• Transport properties
• Temperature and field dependent inplane
  electron-electron scattering rate

• Conclusion and what should be next

8
Field induced confinement semiclassical picture
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Field induced confinement experiments
(TMTSF)2ClO4
insulator
metal
Danner et al. 1997
10
Field induced confinement experiments
(TMTSF)2ClO4
insulator
metal
Joo et al. 2006
11
Field induced confinement experiments
(TMTSF)2PF6
Lee et al. 1997
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High-Tc superconductors
YBa2Cu4O8
Hussey et al. 2002
Hussey et al. 1998
La2-xSrxCuO4d
Hawthorn et al. 2003
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Field induced confinement existing theories
Localization scenario
(Behnia et al. PRL 74, 5272 (1995))
magnetic field charge gap
Metal-insulator transition
Metal-insulator transition expected in BOTH Rxx
and Rzz
insulator
BUT, No localization in Rzz
Rxx (arb.units)
metal
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Field induced confinement existing theories
Semi-classical approaches
c
I
Danner et al. PRL 78, 983 (1997)
H
Sugawara et al. J. P.S.J. 75, 053704 (2006)
b
Conductivity in Boltzmann theory
a
t electron-electron scattering time depends only
on temperature !
BUT !
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Semi-classical approaches cannot explain
Saturation behavior of Rzz as a function of the
magnetic field
(TMTSF)2PF6
Semi-classical results
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Semi-classical approaches cannot explain
Hussey et al. 1998
Change of Rzz field dependence from B2 to a
linear behavior
szz is independent of field orientation in the
conducting plane (except for range around a axis)
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Quantum models for field induced confinement
Probability in transverse direction
But, does not explain the temperature and field
resistance behavior !
Index layer
Lebed, PRL (2005)
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Field induced confinement theoretical approach
Our proposed model
H
The electron-electron inplane scattering time t
depends on

• temperature and magnetic field !

Quantum mechanical approach
Green function method
19
c
electron
3 D system Coherent interplane hopping
Field induced confinement
H
2 D system Incoherent interplane tunneling
Inplane electron scattering h1/t should increase
with magnetic field
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Lebed, PRL 1989
8
BUT No cutoff limit
Field independent scattering rate !!!
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Temperature dependent cutoff Ed (T) (different
energy scales of the phase diagram)
wc magnetic energy
Three competing energy scales
Temperature T , magnetic energy wc and the
interplane hopping tc
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Fermi liquid behavior
FL? NFL?
Intermediate temperature (Ttc)
Low temperature (Tlttc)
Saturation at high temperature
FL? NFL?
high temperature (Tgt tc)
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2D
3D-2D
3D

• Low Temperature, three regimes for the field
  dependent
• behavior of the scattering rate
• low field slow increase with increasing field
• H1lt Hlt H2 large enhancement
• H gt H2 the increase is slowed down

3D
3D-2D crossover (wc gt tc)
2D
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Green function
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Green function
z
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Conductivities
c
H
b
I
a
sa
sc
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Transverse resistivity
Our model
(TMTSF)2ClO4
(TMTSF)2ClO4
(Danner et al. 1997)
S. H., N. Belmechri, S. Charfi-Kaddour and M.
Héritier PRB 78, 075104 (2008)
I
c
H
b
a
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Transverse magnetoresistance
(TMTSF)2ClO4
Rzz(H)-Rzz(0) / Rzz(0)
Experiments (Cooper et al. 86, Korin-Hamzic 03)
Positive magnetoresistance
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Saturation of the transverse resistivity at low
temperature
Our model
semi-classical model
Danner et al. 1997
(TMTSF)2ClO4
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(TMTSF)2ClO4
Rxx (arb.units)
S. Haddad et al. PRB 78, 075104 (2008)
c
(TMTSF)2ClO4
H
b
I
Behnia et al. 1997)
a
No field induced confinement along the a axis
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Concluding remarks
Transport properties of layered conductors in
the presence of H// b can be understood
within The field induced confinement
scenario Field dependent inplane scattering rate
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If the inplane scattering rate is field
independent h (T)
(TMTSF)2ClO4
(TMTSF)2ClO4
!?
No field induced confinement even at H 9T !
Inplane scattering rate should depend on the
magnetic field !
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What should be next ?

• Effect of the field induced confinement on
• the angle dependence of the magnetoresistance
• (Kang et al. PRL 2007)
• the critical fields of the superconducting phase
• (Shinagawa et al. PRL 2007)

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What should be next ?

• Field induced confinement in other compounds
  cuprates, t phase of organic conductors

Strong anisotropy a7.354Å, c67.997Å
?
Results of Papavassiliou, Murata and Brooks
groups

• 
  References
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  (1999)
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  (unpublished)
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• S. Haddad et al., P.R.B 72, 085104 (2005)

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• Acknowledgments
• D. Jérome, C. Pasquier, N. Joo, T. Osada,
• Y. Suzumura, B. Korin-Hamzic and W. Kang

French-Tunisian CMCU project 04/G1307