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Surfing the organic Fermi sea

Microwave spectroscopy of organic superconductors and conductors Stephen Hill , NHMFL and Florida State University. Introduction to organic conductors/superconductors Fermi surfaces: emphasis on quasi-1D systems Magnetic field effects: DC transport/Hall effect

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Surfing the organic Fermi sea

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  1. Microwave spectroscopy of organic superconductors and conductors Stephen Hill, NHMFL and Florida State University • Introduction to organic conductors/superconductors • Fermi surfaces: emphasis on quasi-1D systems • Magnetic field effects: DC transport/Hall effect • Optical and microwave magneto- conductivity • Open orbit cyclotron resonance, or periodic-orbit resonance • Experimental details and some example results • Lebed magic angle effects • Mystery of missing spectral weight • Summary • Review in Springer Book (Ed: A. Lebed, 2008); arXiv:cond-mat/0608490 Surfing the organic Fermi sea

  2. Organic Building Blocks for Conductors S Se C H bis-ethylenedithio-tetrathiafulvalene a.k.a. BEDT-TTF, or ET for short Various donor molecules TTF tetrathiafulvalene, or "TTF" for short tetramethyl-tetrathiafulvalene, or "TMTTF" for short tetramethyl-tetraselenafulvalene, or "TMTSF" for short tetraselenafulvalene, or "TSF" for short TSF p-orbitals TMTTF TMTSF

  3. Quasi-1D organic conductors (TMTSF)2X a c Use stable organic molecules as building blocks to tailor completely new materials TMTSF, or Bechgaard salts (TMTSF)2 + X  (TMTSF)2+X A2X X = ClO4, PF6, ReO4, NO3, AsF6 • Grown electrochemically • Very high purity • Partially filled Se p-orbitals, 1 hole per two-TMTSF molecules • 1/2 filled (1 hole per unit cell) (TMTSF)2ClO4 Organic Superconductors Ishiguro, Yamaji, Saito (Springer, 2001)

  4. Quasi-1D organic conductors (TMTSF)2X • (TMTSF)2X are Q1D conductors • Partially filled Se p-orbitals overlap • ta:tb:tc~200:20:1 meV for ClO4 • Conductivity highest along chains • sa:sb:sc ~ 106:104:25 (W.cm)-1 @ 4 K (TMTSF)2ClO4 a c (TMTSF)2PF6 c Triclinic • (TMTSF)2X are Q1D conductors

  5. Quasi-2D (BEDT-TTF)2X conductors t2 t1 U k-(ET)2Cu(NCS)2 a c b b: c: a = 106:106:~102 (W.cm)-1 @ 10 K

  6. Spin-liquid phase also d-wave? Mott- Hubbard insulator Phase diagram of the Quasi-2D Conductors k-(BEDT-TTF)2X X=I3 Cu[N(CN)2]Br Cu(NCS)2 Cu[N(CN)2]Cl Similar to Cuprates F. Kagawa et al., PRL 93, 127001 (2004).

  7. kz kx ky Fermi surface of low-dimensional conductors Tight-binding approximation (near-neighbor hopping): 3D Quasi-2D (Q2D) BEDT-TTF salts

  8. kz kx ky Fermi surface of low-dimensional conductors Tight-binding approximation (near-neighbor hopping): Quasi-1D (Q1D) Bechgaard salts Q2D

  9. kb ka 2p b ka ka kc kc 2p/c 2p/c kc Fermi surface of low-dimensional conductors Tight-binding approximation (near-neighbor hopping): Extended zone scheme

  10. Phonon dispersion relation p/a Kohn anomaly/Peierls instability Charge density wave • A single wavevector (Q = 2kF) can map one surface onto the other •  Instability: any interaction singular at Q = 2kF Metal Insulator

  11. Phase diagram of the Quasi-1D Conductors (TMTTF)2PF6 (TMTTF)2Br (TMTSF)2PF6 Resistivity (W.cm) Spin density wave (TMTSF)2ClO4 Temperature (K) Exotic (p-wave) superconductivity mediated by spin fluctuations? R. Louatiet al., PRB 62, 5957 (2000); Y. Tanumaet al., PRB 66, 094507 (2002); Zhang et al., PRL 97, 047001 (2006). D. Jerome, Chem. Rev. 104, 5565 (2004)

  12. Magnetic field-induced dimensional crossover //c* Field-induced spin density wave: FISDW Lorentz force: Fermi velocity: Field-induced spin density wave B=c* high- field (TMTSF)2ClO4 low-field Confinement, enhanced nesting S. K. McKernan et al., PRL75 1630 (1995)

  13. Standard theory of the FISDW Imperfect nesting a a Q2D pockets Q b b Q Landau quantization • Energy gain due to Landau quantization • Nesting vector adjusts • Cascade of first-order phase transitions EF Magnetic field Perfect nesting Lebed, Chaikin, Montambeaux, et al. (early ’90s)

  14. Quantized Hall Effect in (TMTSF)2X Balicas et al., PRL 75, 2000 (1995) Cho et al., Phys. Rev. B 59, 9814 (1999) Magnetic field (tesla) 0 5 10 15 Hall resistance (mW) (TMTSF)2PF6 First observed in (TMTSF)2ClO4 Hannahs et al., Phys. Rev. Lett. 63, 1988-1991 (1989)

  15. Collective mode Gap Non-Drude optical conductivity – (TMTSF)2ClO4 Low energy mode: few % of spectral weight (KK) 10K 100K 200K 300K Schwartz et al., Phys. Rev. B 58, 1261 (1998) Ng et al., J. Phys. Colloq. France 44, 867 (1983) D. Jerome, Chem. Rev. 104, 5591 (2004) Hill et al., arXiv:cond-mat/0608490

  16. Non-Drude response (B = 0) in other Q1D salts 0.1 cm-1 Dressel et al., Phys. Rev. Lett 90, 167002 (1998) Schwartz et al., Phys. Rev. B 58, 1261 (1998) D. Jerome, Chem. Rev. 104, 5591 (2004) Hill et al., arXiv:cond-mat/0608490

  17. t-1 Optical conductivity – Reminder of Drude model (B = 0) Boltzmann equation:

  18. so(w=0) t-1 Spectral weight # free carriers Optical conductivity – Reminder of Drude model (B = 0) Boltzmann equation:

  19. 2p/c Oscillatory velocity components: Cyclotron Resonance or Periodic Orbit Resonance (POR) • Lorentz force: S. Hill, PRB55, 4391 (97); Blundell et al., PRB55, R6129 (97).

  20. Oscillatory velocity 2/t Sweep the field: wQ1D vF×B ~ 30 GHz/T (m* = mo) Cyclotron Resonance or Periodic Orbit Resonance (POR) Boltzmann equation: w = wQ1D S. Hill and S. Takahashi, arXiv:cond-mat/0608490

  21. Limitations: • Still require DC [s(w = 0)] reference to get spectral weight • Sensitive to c-axis conductivity (no resonance in sa) • Assumes isotropic scattering • Requires wt > 1 (problem or most conductors) Cyclotron Resonance or Periodic Orbit Resonance (POR) Advantages over broadband optics: • Narrow-band resonant technique (cavities → sensitivity) • No instrumental response to subtract • Can scan from wc = 0 to >1 THz (~30 cm-1) • Measure loss, not reflectivity (R≈ 1 for large s) • One can obtain both s1 and s2 directly • Therefore, no need for Kramers-Kronig & extrapolation • One also obtains m* (or vF) in very straightforward manner See Pompeo Scheffler posters *

  22. Rotating cavity + high fields Frequency Range: 8 – 900 GHz (ABmm VNA) - Waveguide probe (f < 350 GHz) - Corrugated probe/light pipe (f > 200 GHz) Temperature range: 0.5 - 400 K Magnet System: Axial Magnets - Ox. Inst. (17 T), NHMFL (33 & 45 T) Split-pair & vector magnet (7T & 9/5/1 T) S. Hill, Phys. Rev. B 62, 8699 (2000). S. Takahashi, Rev. Sci. Instrum.76 023114 (2005). Also: M. Mola et al. Rev. Sci. Instrum.71, 186 (2000).

  23. http://www.magnet.fsu.edu/

  24. Angle-dependence and harmonics of POR Resonance in AC conductivity Periodic Orbit Resonance (POR) AC Resonance Corrugation Resonance in DC conductivity Angle-dependent Magneto- Resistance Oscillation (AMRO) Blundell et al., PRB55, R6129 (97); Kovalevet al., Phys. Rev. B 66, 134513 (2002). Resonance in DC conductivity

  25. Harmonic POR reveal the Fourier components of FS warping • Implications for nesting Angle-dependence and harmonics of POR AC Resonance Corrugation Resonance in DC conductivity

  26. (TMTSF)2X p = -1 p/q = -1 p/q = 0 p/q = 1 POR for a general Q1D FS: oblique lattice model c* b′ Kovalev et al., Phys. Rev. B 66, 134513 (2002).

  27. p = -1 p/q = -1 p/q = 0 p/q = 1 Lebed magic angle effects: Kang et al., Synth. Met.133-134, 15 (2003) AMRO for a general Q1D FS: w = 0 (DC) • For ALL values of B FISDW c* b′

  28. B c c c B I I B I b b b Lebed ‘Magic Angle’ Effects in (TMTSF)2X Dimensional & FL/NFL crossovers • Lebed effect • Danner-Kang-Chaikin • 3rd angular effect Lebed: “commensurabilities” Lebed, JETP Lett.43, 174 (86); Danner et al., PRL72, 3714 (94); Osada et al., PRL77, 5261 (96)

  29. W. Kang et al., Synth. Met.133-134, 15 (‘03) Lattice vectors Is the metallic state of (TMTSF)2X unconventional? The Quantum-Classical Metal (non-Fermi liquid implied) Clarke, Strong, Chaikin, Chashechkina, Science 279, 2071 (1998). Strong, Clarke, Anderson, Phys. Rev. Lett.73, 1007 (1994). Are the Lebed magic angles truly magic, i.e. a fixed angle effect? 8 T 7.5 T FISDW 7 T 6 T Also evidence from optics: Missing spectral weight Dressel et al., PRL 77, 398 (96) 5 T 4 T 3 T

  30. p = -1 p/q = -1 p/q = 0 p/q = 1 POR for a general Q1D FS: wt > 1 (GHz) c* b′ POR angle not ‘magic’

  31. p = -1 p/q = -1 p/q = 0 p/q = 1 POR for a general Q1D FS: wt > 1 (GHz) c* b′ POR angle not ‘magic’

  32. Microwave experiment in(TMTSF)2ClO4 Angle Sweep Kang et al., Synth. Met.133-134, 15 (2003) 8 T 7.5 T 7 T 6 T 5 T 4 T 3 T Microwave data DC AMRO data • Microwave transmission: DT -Dszz • POR angles depend on the magnetic field strength S. Takahashi et al., PRB72 024540(2005)

  33. Microwave experiment in(TMTSF)2ClO4 Field Sweep 52.1 GHz T = 2 K S. Takahashi et al., PRB72 024540(2005) • Microwave absorption ~ szz • Resonances are observed by sweeping fields  ‘magic angles’ must be field dependent, i.e. they are NOT magic!

  34. Angle dependence of POR ‘Magic angles’ are NOT magic! High-field measurements n = 62 GHz, T=2.5 K, w t ≈ 2 • FISDW transition is observed • Angle dependence given by • BFISDW→ orientation of sample • Assignment of resonances (p,q) vF = 0.7 × 105 m/s S. Takahashi et al., PRB72 024540(2005) + ISCOM 05

  35. Fermi surface reconstruction Q1D POR in a-(ET)2KHg(SCN)4 • a-(BEDT-TTF)2KHg(SCN)4 undergoes CDW transition at 8 K • Many POR observed for T < TCDW • Due to highly anharmonic warping of the reconstructed Fermi surface A. E. Kovalev et al., PRB66 134513(2002)

  36. } Coherent Spectral weight in POR • (TMTSF)2ClO4 • a-(BEDT-TTF)2KHg(SCN)4 • k-(BEDT-TTF)2I3 This work *Cooling rate dependent ** Bechgaard et al., Phys. Rev. Lett 46, 852 (1981) • POR angle dep. Suggests we really are seeing the full FS! Hill et al., arXiv:cond-mat/0608490

  37. Recent measurements of sa(w=0): 103 - 104 (W.cm)-1 @10K • Schwartz et al., Phys. Rev. B 58, 1261 (1998). • Dressel et al., Phys. Rev. B 71, 075104 (2005). Calibrating against DC conductivity – a problem!! s = 106 (W.cm)-1 Bechgaard et al., Phys. Rev. Lett 46, 852 (1981) D. Jerome, Chem. Rev. 104, 5591 (2004) Hill et al., arXiv:cond-mat/0608490

  38. POR and superconductivity From conductivity From POR linewidth (TMTSF)2ClO4 (TMTSF)2(ClO4)(1-x)(ReO4)x • Vary t by cooling at different rates • POR linewidth directly measures t • Conductivity also sensitive to the spectrum • Supports (triplet) p-wave N. Joo et al., Eur. Phys. J. B40, 43 (04) Abrikosov-Gor’kov S. Takahashi et al., Proc. AIP, Volume 850, 619 (2006); LT24.

  39. Summary • Organic charge-transfer salts provide a wonderland full of rich physical phenomena of relevance to many contemporary problems in condensed matter physics • Observation of cyclotron/periodic orbit resonance • POR evolve from the Lebed ‘magic angles’. However, these angles are NOT ‘magic’ at microwave frequencies. Indeed, the metallic state of (TMTSF)2ClO4 seems quite conventional • One may also argue on basis of spectral weight that metallic states of most organics are quite normal • Scattering time deduced from POR supports the idea that superconducting state in (TMTSF)2X is p-wave • Open-orbit resonances in Q2D conductors provide angle-resolved information concerning the spectrum

  40. Acknowledgements • Former postdoc and students: AlexeyKovalev (postdoc) • Susumu Takahashi • Monty Mola Samples: - Univ. of Hyogo (Japan): S. Takasaki, J. Yamada, H. Anzai - Sonoma State University: J. S. Qualls - Toho University (Japan): K. Kawamo and M. Tamura - Institute for Molecular Science, Okazaki (Japan): H. Kobayashi • Funding: US National Science Foundation • University of Florida • National High Magnetic Field Laboratory • Research Corporation

  41. New AC conductivity resonance for Q2D FS:Angle-resolved mapping of vF and t • Resonance dominated by extremal perpendicular velocity, vext. • Resonance appears when magnetic field is applied in the in-plane direction. • AC conductivity s(w) is dominated by open trajectories • DC conductivity dominated by self-crossing trajectories. Resonance condition:

  42. Determination of vF (f) – akin to ARPES Experiments in k-(BEDT-TTF)2I3. vF,y = 0.62 × 105 m/s; vF,x = 1.3 × 105 m/s A. E. Kovalev et al., PRL91, 216402 (03) S. Takahashi et al., J. Appl. Phys.97, 10B106 (05)

  43. Anion- ordering SDW Anion ordering in (TMTSF)2ClO4 Order-disorder transition of non-magnetic ClO4 anion Anion-ordering TAO ~ 24 K Superlattice (1, 2, 1) Cooling rate dependence: <0.1 K/min (relaxed) Metalic/superconducting >50K/min (quenched) Insulating (SDW) Schwenk et al., PRB 29 500 (1984)

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