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Heon-Ick Ha 1 A.G.Lebed 2 M.J. Naughton 3 1. Harvard University

Angular Magnetoresistance Experiments in (TMTSF) 2 ClO 4 : Interference Commensurate Effect and Dimensional Crossover. Heon-Ick Ha 1 A.G.Lebed 2 M.J. Naughton 3 1. Harvard University 2. University of Arizona 3. Boston College

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Heon-Ick Ha 1 A.G.Lebed 2 M.J. Naughton 3 1. Harvard University

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  1. Angular Magnetoresistance Experiments in (TMTSF)2ClO4: Interference Commensurate Effect and Dimensional Crossover Heon-Ick Ha1 A.G.Lebed2 M.J. Naughton3 1. Harvard University 2. University of Arizona 3. Boston College Research support : NSF By Jerome

  2. Q1D Organic Superconductors: Physics 100 metal 10 (TMTSF)2ClO4 TEMPERATURE Spin Peierls SDW 1 PRESSURE b’ a c* (pressure enhance inter-chain coupling tb) tb Q1D organic materials phase diagram: • In magnetic field, • What can we learn about: • normal ground state? • FL vs non-FL • How does open FS • which has no closed orbit • quantization shows various • oscillation effect? • What is the mechanism for • each AMRO? SC (TMTSF)2PF6

  3. Outline : • Introduction to AMRO in Q1D system • Theory : Interference Commensurate Effect • Experiment vs Theory • Summary

  4. Angular Magnetoresistance Oscillation: in Metallic State

  5. c* f q H 13.5T B b’ • Experimental techniques so far: • Other than transport Measurements H//b’c*-plane: • Torque measurement : Phys. Rev. Lett. 67 (1991) • Nernst Effect : Phys. Rev. Lett. 91 (2003) • Eun Sang Choi, PRL,(2005) • Transport measurement in various field direction: In-situ rotator(q) dq ~ 0.003° a Ex-situ rotator(f) df = 0.0025° 10mK-13.5T Dil-fridge

  6. MA effect DKC effect Third Angular effect c* a f b’ T. Osada, et al. : PRL. 66, 1525 (1991) for triclinic, minima at G.M.Danner, et al.. : PRL. 72, 3714 (1994) f(degree) at this special angle, electron moves will be localized in extended BZ H. Yoshino, et al.,:J.phys. Soc.Jpn 64,2307 (1995) In (DMET)2I3 I.J.Lee, et al.,:PRB 57,7423 (1998) in (TMTSF)2PF6 tanqn ~ 2ctb/n2pvF Measuretb ~ 0.012eV Experimentally Observed AMRO effects: estimate ta/tb

  7. Experimentally Observed AMRO effects: Off-angle (LN) effect in (TMTSF)2PF6 Boltzmann kinetic equation : found each minima appears at sinf = N(b*/c*)tanq I.J.Lee, et al.,:PRB 57,7423 (1998)

  8. Unresolved theoretical analysis in LN effect: • Each minima position: • Why each minima in resistivity appears at commensurate • directions of a magnetic field • sinf = N (b*/c*)tanq (N : integer) • The origin of oscillations: • What is the origin of this complicated oscillations • Analytical expression for rzz(H) for Q1D system

  9. New Analytical Theory by A.G. Lebed: Interference Commensurate Oscillations

  10. Interference Commensurate (IC) Oscillations : • Derive an analytical expression for rzz (H) • Define the position of its minima : • commensurate vs non-commensurate direction • Reveal interference nature of IC oscillations

  11. c* f q B b’ Theory: Interference Commensurate Oscillations in Q1D conductors Equations of electron motion in an inclined magnetic field: At certain direction of magnetic field (commensurate direction), e- trajectories in a reciprocal plane (py,pz) become periodic, and A.G.Lebed, et al.,:PRL 91,187003 (2003)

  12. Theory: Interference Commensurate Oscillations in Q1D conductors For interference nature : for e- motion in extended BZ where Bragg reflection occurs Summation of an infinite number of electron waves with relative phase from Brillouine zone boundaries which occur as electron moves along open orbits in the extended BZ. Phases in electron wave A.G.Lebed, et al.,:PRL 91,187003 (2003)

  13. Theory: Interference Commensurate Oscillations in Q1D conductors (TMTSF)2PF6 A.G.Lebed, et al.,:PRL 91,187003 (2003) Maxima @ “commensurate” direction (sinf = N(b*/c*)tanq)

  14. Measure LNL effect in (TMTSF)2ClO4 Magnetic field dependence at each minima & maxim Theory: Interference Commensurate Oscillations in Q1D conductors • What can we learn about IC effect: • is IC effect universal in Q1D (TMTSF)2X system? • the nature of Interference Commensurate Oscillation

  15. sinf = N (b*/c*)tanq (N : integer) Experiment: Interference Commensurate Oscillations in (TMTSF)2ClO4 q 15 12 10 7 6 5 4.5 4 3 2.5 2 1 0 q 7 6 5 4.5 4 3 2 1 0 H.I. Ha, A.G. Lebed & M.J Naughton,:cond-mat/0503649

  16. Experiment vs Theory: Interference Commensurate Oscillations in (TMTSF)2ClO4 IC effect in (TMTSF)2ClO4 : Account for the doubling of the unit cell along the b-axis due to anion ordering A.G.Lebed,H.I.Ha & M.J.Naughton.,:PRB 71,132504 (2005) Fitting parameters : ta/tb=9.75 from TAE wct=15 @10T Eg /2tb=DAO/2tb=0.1 Eg=DAO=40~50K (tb~200~250K) H.Yoshino, et al.,:Synth. Met. 133-134,55 (2003) V.M. Yakovenko, et al.,:cond-mat/0509039(2005) H.I. Ha, A.G. Lebed & M.J Naughton,:cond-mat/0503649

  17. 1D  2D Dimensional Crossover ?: Delocalization of electron wave function at commensurate direction

  18. Incommensurate direction : for electron wave functions localized on conducting x-chains, for conductivity between chains szz= 0 for Theory: 1D to 2D dimensional crossover at commensurate magnetic field direction • commensurate direction: • For electron wave functions delocalized on the planes, • szz expect to be similar to szz of free electron at B=0, • rzz =1/szz will be saturate

  19. Experiment: 1D to 2D dimensional crossover at commensurate magnetic field direction? max min max min max min H.I. Ha, A.G. Lebed & M.J Naughton,:cond-mat/0503649

  20. Experiment: 1D to 2D dimensional crossover at commensurate magnetic field direction? at minima at maxima q 12 8 7 5.5 4.5 2.5 H.I. Ha, A.G. Lebed & M.J Naughton,:cond-mat/0503649

  21. Talk : Th15 by H. Yoshino Osada, et al.,:Physica E. 18, (2003) V.M. Yakovenko, et al.,:cond-mat/0509039(2005) Experiment vs Theory : More experiment : In high magnetic field, resistivity will show saturation behavior at minima? H.I. Ha, A.G. Lebed & M.J Naughton,:cond-mat/0503649

  22. Summary • The origin of LN effect : IC effect in extended BZ • Derive an analytical expression for rzz (H) using IC effect • Define the position of its minima : • commensurate vs non-commensurate direction • Reveal interference nature of IC oscillations : • Novel qualitative magnetic field-dependent effect

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