1 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 ) Field induced confinement in quasi-one dimensional organic conductors S. H., N. Belmechri, S. Charfi-Kaddour and M. Héritier et al. PRB 78, (2008).

2 Low dimensional system are quite interesting New physics: Quantum effects Strong correlations Important effect of disorder FQHE (Nobel prize 1998) Giant magnetoresistance (Nobel prize 2007) Hard disk

3 Needle like Bechgaard salts (TMTSF) 2 X TMTSF X a b c TMTSF=tétraméthyl-tétraséléna-fulvalène X= anion: Br -, PF 6 - ; ClO 4 - …

4 t c « t b « t c  c «  b «  a quasi-1D conductors a b c Organic chains of TMTSF molecules Conducting planes tbtb tata Key parameters of (TMTSF) 2 X tctc Highly anisotropic materials

5 1D LL 3D FL Phase diagram of Bechgaard salts 2D FL? NFL ? Different energy scales 1D ----> 2D 2D ----> 3D

6 2D system 1D system Fermi liquid Confined system 3D system Luttinger liquid The wondrous world of quasi-one organic conductors ( after, W. Kang’s idea)

7 Transport properties: Temperature and field dependent inplane electron-electron scattering rate H b c I a Field induced confinement Field induced confinement: Theoretical approach Quantum calculations: Outline Field induced confinement: a brief review Theory vs. experiments Conclusion and what should be next

8 Field induced confinement: semiclassical picture a b c H a Free of bird flu ! b

9 metal insulator Danner et al Field induced confinement: experiments H b c I a (TMTSF) 2 ClO 4

10 Joo et al metal (TMTSF) 2 ClO 4 insulator Field induced confinement: experiments

11 Lee et al (TMTSF) 2 PF 6 Field induced confinement: experiments

12 Hussey et al Hussey et al Hawthorn et al YBa 2 Cu 4 O 8 La 2-x Sr x CuO 4+  High-Tc superconductors

13 H a b c I FISDW (Behnia et al. PRL 74, 5272 (1995)) H a b c I R xx (arb.units) insulator metal BUT, No localization in R zz Field induced confinement: existing theories Localization scenario magnetic field charge gap Metal-insulator transition Metal-insulator transition expected in BOTH R xx and R zz

14 Field induced confinement: existing theories Semi-classical approaches BUT ! H a b c Danner et al. PRL 78, 983 (1997) Sugawara et al. J. P.S.J. 75, (2006)  electron-electron scattering time depends only on temperature ! I Conductivity in Boltzmann theory Explains the minima in R zz Magnetic energy

15 Saturation behavior of R zz as a function of the magnetic field Semi-classical approaches cannot explain… Lee et al saturation (TMTSF) 2 PF 6 Semi-classical results

16 Hussey et al Change of R zz field dependence from B 2 to a linear behavior Semi-classical approaches cannot explain…  zz is independent of field orientation in the conducting plane (except for range around a axis) T=1.5 K H=14 T Kang et al (TMTSF) 2 ClO 4

17 Quantum models for field induced confinement Index layer Probability in transverse direction Lebed, PRL (2005) But, does not explain the temperature and field resistance behavior !

18 Our proposed model: The electron-electron inplane scattering time  depends on Green function method Quantum mechanical approach: temperature and magnetic field ! Field induced confinement: theoretical approach c H

19 3 D system Coherent interplane hopping 2 D system Incoherent interplane tunneling Field induced confinement Inplane electron scattering  =1/  should increase with magnetic field electron c H

20 Lebed, PRL 1989 ∞ Field independent scattering rate !!! BUT No cutoff limit

21  c : magnetic energy Temperature T, magnetic energy  c and the interplane hopping t c Three competing energy scales: Temperature dependent cutoff E d (T) (different energy scales of the phase diagram)

22 Low temperature (T<t c ) Intermediate temperature (T~t c ) high temperature (T> t c ) Saturation at high temperature Fermi liquid behavior FL? NFL?

23 Low Temperature, three regimes for the field dependent behavior of the scattering rate: low field: slow increase with increasing field H 1 < H< H2 : large enhancement H > H 2 : the increase is slowed down Scattering rate (arb. units) H1H1 H2H2 H2H2 3D-2D crossover (  c > tc) 2D 3D c 3D-2D 2D

24 Green function

25 Green function z c

26 Conductivities aa H b c I a cc H b c I a

27 Experiment H b c I Our model Transverse resistivity (Danner et al. 1997)S. H., N. Belmechri, S. Charfi-Kaddour and M. Héritier PRB 78, (2008) (TMTSF) 2 ClO 4 a

28 Transverse magnetoresistance Experiments (Cooper et al. 86’, Korin-Hamzi ć 03) R zz (H)-R zz (0) / R zz (0) Positive magnetoresistance (TMTSF) 2 ClO 4

29 Saturation of the transverse resistivity at low temperature Danner et al Our model semi-classical model T=1.5 K H=14 T Kang et al (TMTSF) 2 ClO 4

30 H b c I a R xx (arb.units) No field induced confinement along the a axis S. Haddad et al. PRB 78, (2008) (TMTSF) 2 ClO 4 Behnia et al. 1997)

31 Concluding remarks H b c I a 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

32 If the inplane scattering rate is field independent  (T)… No field induced confinement even at H= 9T ! Experiment (TMTSF) 2 ClO 4 !? Inplane scattering rate should depend on the magnetic field !

33 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) H b c a  T=1.5 K H=14 T Kang et al (TMTSF) 2 ClO 4

34 What should be next ?  Field induced confinement in other compounds: cuprates,  phase of organic conductors References N. Matsunaga et al. J. Low Temp. Phys. 117, 1735 (1999) A.J. Greer et al. Physica C 400, 59 (2003) N. Joo et al., cond-mat/ S. K. McKernan et al., P.R.L 75, 1630 (1995) O. H. Chung et al., P.R.B 61, (2000) J. Moser, Ph. D. thesis, Orsay (France) (1999) (unpublished) C. Bourbonnais and L. G. Caron, Int. J. Mod. Phys. B, 5, 1033 (1991) J. Kishine and K. Yonemitsu, J. Phys. Soc. Jpn. 67, 1714 (1998) T. Osada et al. P.R.L. 77, 5261 (1996) S. Uji et al., P.R.B 53, (1996) H. Yoshino et al., Synth. Met , 55 (2003) H. I. Ha et al., cond-mat/ A.G. Lebed et al., P.R.L. 93, (2004) A.G. Lebed and P. Bak, P.R.B 40, R11433 (1989) T. Osada et al., P.R.L. 69, 1117 (1992) S. Haddad et al., P.R.B 72, (2005) Strong anisotropy : a=7.354Å, c=67.997Å ? Results of Papavassiliou, Murata and Brooks groups

35 Acknowledgments D. Jérome, C. Pasquier, N. Joo, T. Osada, Y. Suzumura, B. Korin-Hamzi ć and W. Kang French-Tunisian CMCU project 04/G1307