Field induced confinement in quasione dimensional organic conductors

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, Tunisia ) S. H. , N. Belmechri, S. Charfi-Kaddour and M. Héritier et al. PRB 78, 075104 (2008). 1

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) 2 Hard disk

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

Key parameters of (TMTSF)2 X Conducting planes ta tb c tc b a Organic chains of TMTSF molecules tc « tb « tc sc « sb « sa quasi-1 D conductors Highly anisotropic materials 4

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

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

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

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

Field induced confinement: experiments insulator (TMTSF)2 Cl. O 4 c metal b H I a Danner et al. 1997 9

Field induced confinement: experiments (TMTSF)2 Cl. O 4 insulator metal Joo et al. 2006 10

Field induced confinement: experiments (TMTSF)2 PF 6 Lee et al. 1997 11

High-Tc superconductors YBa 2 Cu 4 O 8 Hussey et al. 2002 Hussey et al. 1998 La 2 -x. Srx. Cu. O 4+d Hawthorn et al. 2003 12

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

Field induced confinement: existing theories Semi-classical approaches c Danner et al. PRL 78, 983 (1997) Sugawara et al. J. P. S. J. 75, 053704 (2006) I b H Conductivity in Boltzmann theory a t electron-electron scattering time depends only on temperature ! Explains the minima in Rzz Magnetic energy BUT ! 14

Semi-classical approaches cannot explain… Saturation behavior of Rzz as a function of the magnetic field (TMTSF)2 PF 6 saturation Lee et al. 1997 Semi-classical results 15

Semi-classical approaches cannot explain… T=1. 5 K H=14 T (TMTSF)2 Cl. O 4 Kang et al. 2007 szz is independent of field orientation in the conducting plane (except for range around a axis) Hussey et al. 1998 Change of Rzz field dependence from B 2 to a linear behavior 16

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

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

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

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

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 21

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

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

Green function 24

Green function z c 25

Conductivities c H b a c I a sc H b I sa 26

Transverse resistivity Our model Experiment (TMTSF)2 Cl. O 4 S. H. , N. Belmechri, S. Charfi-Kaddour and M. Héritier (Danner et al. 1997) PRB 78, 075104 (2008) c b H I 27 a

Transverse magnetoresistance Rzz(H)-Rzz(0) / Rzz(0) (TMTSF)2 Cl. O 4 Experiments (Cooper et al. 86’, Korin-Hamzić 03) Positive magnetoresistance 28

Saturation of the transverse resistivity at low temperature (TMTSF)2 Cl. O 4 Our model T=1. 5 K H=14 T Kang et al. 2007 semi-classical model Danner et al. 1997 (TMTSF)2 Cl. O 4 29

Rxx (arb. units) (TMTSF)2 Cl. O 4 S. Haddad et al. PRB 78, 075104 (2008) c (TMTSF)2 Cl. O 4 b a H I No field induced confinement along the a axis Behnia et al. 1997) 30

Concluding remarks c Transport properties of layered conductors in the presence of H// b can be understood within The field induced confinement scenario b H I a Field dependent inplane scattering rate 31

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

What should be next ? c Effect of the field induced confinement on b j Øthe angle dependence of the magnetoresistance (Kang et al. PRL 2007) Øthe critical fields of the superconducting phase H a (Shinagawa et al. PRL 2007) T=1. 5 K H=14 T (TMTSF)2 Cl. O 4 33 Kang et al. 2007

What should be next ? ØField induced confinement in other compounds: cuprates, t phase of organic conductors Strong anisotropy : a=7. 354Å, c=67. 997Å ? Results of Papavassiliou, Murata and Brooks groups 34

Acknowledgments D. Jérome, C. Pasquier, N. Joo, T. Osada, Y. Suzumura, B. Korin-Hamzić and W. Kang French-Tunisian CMCU project 04/G 1307 35