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Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors

ECRYS-2011, August, 15-27, 2011 at the Institute of Scientific Studies in Cargese , Corse. Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors . Toshihiro Takahashi

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Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors

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  1. ECRYS-2011, August, 15-27, 2011 at the Institute of Scientific Studies in Cargese, Corse Charge Fluctuation, Charge Ordering and Zero-Gap State in Molecular Conductors Toshihiro Takahashi Department of Physics, Gakushuin University, Mejiro 1-5-1, Toshima-ku, Tokyo 171-8588, Japan

  2. Charge FluctuationCharge Ordering Zero-Gap State 3 keywords: “San-dai-banashi” A style of Japanese traditional comic story, “rakugo”. Three keywords are given independently by the audience. The storyteller, “rakugo-ka”, makes ad lib a consistent comic story using all the keywords. 三題噺

  3. Outline • Introduction to NMR technique to probe charge degree of freedom • Charge fluctuation and charge ordering in θ-phase BEDT-TTF salts • Charge disproportionation in the zero-gap state of α-BEDT-TTF2I3 • Coupling with the permanent electric dipolar moment of anion in TMTSF2FSO3 • Charge disproportionation in λ-type BETS salts • Summary & Remarks

  4. Outline • Introduction to NMR technique to probe charge degree of freedom • Charge fluctuation and charge ordering in θ-phase BEDT-TTF salts • Charge disproportionation in the zero-gap state of α-BEDT-TTF2I3 • Coupling with the permanent electric dipolar moment of anion in TMTSF2FSO3 • Charge disproportionation in λ-type BETS salts • Summary & Remarks

  5. Simple Picture of Charge Ordering (CO) • 1/4-filled system, D2A or DA2, without large dymerization One carrier per two molecules • Coulomb interaction, U & V, … finding a charge arrangement to minimize Coulomb energy • As includingtransfer =>rich variety of phenomena

  6. Charge Ordering vs. Charge Disproportionation • Long-range Charge Ordering (CO) vs. Charge Disproportionation (CD) • Charge Frustration • Melting of CO • Charge Fluctuation/Charge Dynamics • Various Optical/Dielectric responses

  7. How can NMR detect CO/CD? Note that; • Not detecting “charge” but “spin”density • Not detecting Long Range CO but just the distribution of local charge (spin) • What we observed in CO/CD systems in common were anomalous broadening of NMR spectrum. How can CO/CD affect NMR spectrum and other NMR parameters?

  8. Brief introduction to NMR(Nuclear Magnetic Resonance) • Nuclear spin carries angular momentum, and magnetic moment, . • Zeeman splitting in strong magnetic field: • Resonance condition:  Magnetic moment; Angular momentum; Resonance Condition; Zeeman splitting for I=1/2

  9. NMR can detect CO/CD • Nuclei in material see local fields given by the environments in addition to the external field. • What we detect with NMR are the information of the local field; Local field distribution Central shift  Local field at each nuclear site

  10. Interaction with electrons • Orbital motion and Chemical shift • Spin interaction and Knight shift  Orbital motion   Spin Local fields are produced by surrounding electrons!

  11.   Interaction with electrons • Orbital motion and Chemical shift • Spin interaction and Knight shift Shielding current  Magnetic shielding current gives local field. Chemists concerns the isotropic part of the chemical shift tensor. It is usually small compared with the spin contribution.

  12.   Interaction with electrons • Orbital motion and Chemical shift • Spin interaction and Knight shift  Spin magnetization

  13.   Interaction with electrons • Orbital motion and Chemical shift • Spin interaction and Knight shift  Spin magnetization Lone-pair spin contribution is also anisotropic and much larger than orbital contribution in the present systems.

  14. Hyperfine interaction • Hyperfine interaction • Hyperfine interaction tensor • Knight shift ~ proportional to electron spin susceptibility ~ anisotropic due to the hyperfine tensor for a pure p-electron with uniaxial symmetry

  15. Hyperfine interaction • Inhomogeneity of Knight shift causes inhomogeneous broadening. • Inhomogeneous width should be proportional to the Knight shift. ~ proportional to electron spin susceptibility ~ anisotropic due to the hyperfine tensor    

  16. Typical Materials, exhibiting CO • 1/4-filled Organic molecular conductors, of the chemical form of A2D • Q-1D system DI-DCNQI2Ag (K. Hiraki, 1998) TMTTF2X (PF6, AsF6, …) (D.S. Chow, 2000) • 2D ET salts -ET2I3, (Y. Takano, 2001) -ET2RbZn(SCN)4 (K. Miyagawa, 2000, R. Chiba, 2001) X-ray, Raman & IR spectroscopy also confirmed CO in various materials

  17. Outline • Introduction to NMR technique to probe charge degree of freedom • Charge fluctuation and charge ordering in θ-phase BEDT-TTF salts • Charge disproportionation in the zero-gap state of α-BEDT-TTF2I3 • Coupling with the permanent electric dipolar moment of anion in TMTSF2FSO3 • Charge disproportionation in λ type BETS salts • Summary

  18. -(ET)2MZn(SCN)4 (M=Rb,Cs) H. Mori et al., Phys. Rev. B57, 12 023(1998)

  19. Electric and Magnetic property electric resistivity spin susceptibility RbZn salt CsZn salt

  20. Unusual broadening above TMI Charge ordered transition in q-(ET)2RbZn(SCN)4 Charge Order T<190K Spin-singlet T<30K K. Miyagawa et al., 2000

  21. Mechanism of the broadening above TMI ? at 204K Observed excess width is anisotropic! ~proportional to the central shift TMI Angular dependence of the 2nd moment is proportional to K2 Inhomogeneous broadening due to the distribution ofK

  22. Inhomogeneous and homogeneous 13C-NMR lineshape in -RbZn Metal state LR-CO Below 30 K TMI T2-1 enhancement due to slow dynamics of CD T2 measurement Double peak about 90 K & 70 K (Chiba, 2004) Inhomogeneous broadening due to CD

  23. Inhomogeneous and homogeneous linewidth Dynamics of Inhomogeneous local field T2-1 life time of Zeeman Level tc-1 correlation frequency 2nd moment for the inhomogeneous field

  24. Inhomogeneous and homogeneous13C-NMR lineshape in -CsZn Crossover into different broadening Inhomogeneous broadening due to large CD Slow dynamics ~kHz Motional narrowing

  25. T dependence of 1/T2 in q-RbZn& -CsZn Explained by expanded exponential correlation; (t) = <2>exp(-(t/c)) with c~exp(-/kBT) Salt Rb Cs    /kB 7600 K 5100 K <2>1/2 3.3 kHz 1.4 kHz

  26. Angular dependence of NMR lineshape of -CsZn 295 K 101 K 5 K spin vanishes! Nonmagnetic ground state

  27. Comparison of -CsZn and -RbZn salts at 5K charge rich charge poor charge : ~ +0.5 charge ordered state

  28. -phase Salts Spin-singlet without CD ! Domains with finite  coexist! Chiba, PRB 2007

  29. What is the origin of slow dynamics of CD in -phase salts? Competition between different types of CO may be responsible. • -RbZn salt withLR-CO of (0, 0, 1/2) below 190K • Diffuse X-ray scattering withq=(1/4, k, 1/3) is observed above TMI. • Spin-singlet ground state with LR-CO. • -CsZn salt withoutLR-CO • Diffuse X-ray scatterings with q1=(2/3, k, 1/3)and q2=(0, k, 1/2) are observed below 120K. • Coexistence of spin-singlet domain and paramagnetic domain without any sign of CO.

  30. Outline • Introduction to NMR technique to probe charge degree of freedom • Charge fluctuations and charge ordering in θ-phase BEDT-TTF salts • Charge disproportionation in the zero-gap state of α-BEDT-TTF2I3 • Coupling with the permanent electric dipolar moment of anion in TMTSF2FSO3 • Charge disproportionation in λ type BETS salts • Summary

  31. Ambient Pressure Metal-Insulator Transition with CO Under hydrostatic pressure Anomalous NGS state with high mobility Under Uniaxial strain SC within CO-state CO NGS along a-axis Metal SC along b-axis Various ground states in α-(BEDT-TTF)2I3 Tajima et al. (2003)

  32. Zero Gap State under pressure Fermi Surface Contact Point & Zero Gap State (ZGS) Y M AmbientPressure electron G X hole pa=2kbar CP Dirac cone pa > 3kbar M (pa=4kbar) CP (contact point) Γ Kobayashi et al., JPSJ (2005)

  33. The first ZGS in a bulk system was confirmed! All peculiar ground states are explained on the basis of unified band parameters! CO / ZGS (NGS) / SC Further questions: How does CO behave under pressure? What is the relation between CO and the ZGS? How about in other isostructural salts?

  34. C C Development of CD above TMI • CO of CD aboveTMI Because of site-dependence? Precursor effect of CO? • Pattern of CO：C > Bcf.Ｘ-ray • Relation to the ZGS under pressure H S. Moroto 2003 Y. Takano 1999

  35. H0 a-ET2I3 Measurements under pressure • P = 0.1 ~ 1.1 GPa • H0 = 7 T (75 MHz) in the ab-plane Pressure cell by Prof. W. Kang, Ewha Womans Univ., Seoul

  36. T-dependence of Local Susceptibilities under pressure Local susceptibility is the smallest on ‘B’ molecule. B molecule is a charge-poor site!

  37. Charge Ordering determined by Synchrotron X-ray Diffraction CD in the metallic state at ambient pressure: ‘B’ molecule is charge-rich! ~ inconsistent to the NMR results? Title: Charge Ordering in $\alpha$-(BEDT-TTF)$_2$I$_3$ by Synchrotron X-ray DiffractionAuthors: by Toru Kakiuchi, Yusuke Wakabayashi, Hiroshi Sawa, Toshihiro Takahashi, Toshikazu NakamuraPublished: October 25, 2007J. Phys. Soc. Jpn., Vol.76, No.11, p.113702 Kakiuchi et al., JPSJ (2007)

  38. Theory explains this difficulty Transfer energies evaluated from first principle calculation by Kino Contact Point & Zero Gap State (ZGS) A,A'= +0.54 B= +0.64 C= +0.29 B molecule is charge-rich! Contact Point Dirac cone Katayama et al., JPSJ (2008)

  39. Theory explains this difficulty Local susceptibility is proportional to the density of state around the contact point, and not to the local charge! Katayama et al., Eur.Phys. (2009)

  40. Theory explains this difficulty U=0.4, Vp=0.05, Vc=0.17 Local susceptibility is determined by the density of states around the contact point.

  41. Conclusions 1. Non-stripe CO develops at low temperatures and under pressure. It does not break the lattice symmetry. 2. Charge-rich ‘B’ molecule has the smallest local susceptibility. It is consistent with X-ray and theoretical analysis. 3. Non-stripe CO may be relevant to the stabilization of the ZGS. T ZGS ZG

  42. What is the origin of CO in the metallic state of a-I3 salt? T Non-stripe CO should come from a band nature together with Coulomb interaction. Characteristic time of charge dynamics, if any, should be much shorter than the NMR time scale. The mechanism of CD is quite different from the case of the q-salt. ZGS ZG

  43. Outline • Introduction to NMR technique to probe charge degree of freedom • Charge fluctuation and charge ordering in θ-phase BEDT-TTF salts • Charge disproportionation in the zero-gap state of α-BEDT-TTF2I3 • Coupling with the permanent electric dipolar moment of anion in TMTSF2FSO3 • Charge disproportionation in λ type BETS salts • Summary

  44. Crystal Structure of (TMTSF)2FSO3 Bechgaard Salt with asymmetric anion, FSO3 FSO3- TMTSF molecule a- axis

  45. (TMTSF)2FSO3 under Pressure Phase diagram Resistivity Thermoelectric power Y. J. Jo etal., 2003

  46. 77Se-NMR Lineshape • 4 sharp peaks • ~4 Se-sites in a unit cell Line broadening Sharp component appears Coexistence of sharp & broad components with short delay ~ 3 s with long delay ~ 600 s

  47. 77Se-NMR T1-1 No anomaly at 90 K. Double comp. of T1-1 below 40 K. Broader line has shorter T1 Sharper line has longer T1

  48. Angular dependence of 77Se-NMR Lineshape

  49. Angular dependence of 77Se-NMR Lineshape Inhomogeneous width assuming CD of 0.6~0.4

  50. Enhancement of 77Se-NMR T2-1 0.65 GPa Double Peaks of T2-1 around 90 K & 70 K. 90 K: the phase boundary (I). 70 K: inside the intermediate phase. Possibility of slow Charge fluctuations as in the q-ET salt. Anomalous T2-1 enhancement was not observed at ambient pressure.

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