S. Takahashi , A. Betancur-Rodiguez and S. Hill University of Florida

1. Study of Periodic-Orbit Resonance in Q1D conductor (TMTSF)2ClO4-Are Lebed’s magic angles truly magic? S. Takahashi, A. Betancur-Rodiguez and S. Hill University of Florida S. Takasaki, J. Yamada and H. Anzai University of Hyogo Outline: 1. Lebed’s magic angle effect in (TMTSF)2X. 2. Semiclassical description of the Lebed effect at microwave frequencies. 3. Microwave experiment.

2. (TMTSF)2X and Lebed’s magic angle effect • (TMTSF)2X are Q1D conductors, e.g. ta:tb:tc~300:25:2 meV for (TMTSF)2ClO4. • The nesting can be increased by magnetic field along c*. • Angle-dependent magnetoresistance oscillations (AMRO) (A. G. Lebed, JETP Lett.43, 174 (86), T. Osada et al., PRL66, 1525 (91), M. J. Naughton et al.,PRL67, 3712 (91)) • Anomaly of the Nernst effect (W. Wu et al., PRL94, 097004 (2005), E. S. Choi et al., cond-mat/0501649) • Lebed’s magic angles p and q: integer, b' = b sing, c* = c sinb sina*, a*: the angle between b* and c*. • A number of theories are proposed, but not conclusive. -Semiclassical or not? 8 T 7.5 T 7 T 6 T 5 T 4 T 3 T W. Kang et al., Synth. Metal133-134, 15 (03)

3. Semiclassical description of Lebed effect • Commensurability effect (T. Osada et al., PRB46, 1812 (92), S. J. Blundell et al., PRB53, 5609 (96)) • dc conductivity szz(w = 0) D(EF): a density of states at EF, t: a scattering time, m and n: integers, vF: the Fermi velocity. • Maxima of szz(0) appears at • Resonance condition

4. Periodic-orbit resonance (POR)-ac Lebed effect • ac conductivity szz(w) • Maxima of szz(0) appears at • Resonance condition B: magnetic fields, Rpq = |pb' + qc'|, qpqn: new resonance angles. (T. Osada et al., PRB46, 1812 (92), S. J. Blundell et al., PRB55, R6129 (97)) • B, qpqnand w sweep • “Periodic-Orbit Resonances (POR)”. (S. Hill, PRB55, 4931 (97), A. Ardavan et al., PRL81, 713 (98) A. E. Kovalev et al., PRB66,134513(02), S. Takahashi et al., PRB72,024540(05)) • Similarly, one can use a pulsed electric field. (K. Kobayashi et al., Synth. Metal133-134, 71 (03))

5. Resonance condition and simulation of POR • Simulation of w/B, • and the conductivity szz(w)

6. Angle-dependent microwave spectroscopy a-(BEDT-TTF)2KHg(SCN)4 A. E. Kovalev et al., PRB66 134513(2002) Frequency Range: 8-700GHz Cryogenics System: 0.5-400K Magnet System: Axial Magnets - Oxford Instruments (17 T) - NHMFL (45 T) Split Coil Magnet - QD PPMS (7 T) Angle Control: Trans. field + axial rotation Rotating Cavity Transverse B M. Mola et al., Rev. Sci. Instrum.71 186 (2000) S. Takahashi and S. Hill, Rev. Sci. Instrum.76 023114 (2005)

7. Microwave experiment in(TMTSF)2ClO4 Angle Sweep Field Sweep • Microwave transmission ~ 1/szz • PORs are observed by sweeping angles. • PORs depend on the magnetic field. • Microwave absorption ~ szz • PORs are observed by sweeping fields. • PORs depend on the angle.

8. Angle dependence of POR n=62GHz, T=2.5K, w t =1.2 • FISDW phase was observed. • The angle dependence of the critical field BSDW is given by because of the 2D nature of the FISDW. • We found p/q = 0, -1 and 1 • resonances. • All data fit semiclassical resonance • condition well.

9. Summary • We found periodic-orbit resonances which correspond to the same Lebed resonances observed in dc AMRO experiments. • This is simply understood by the semiclassical arguments. Thus, the Lebed’s magic angles are not ‘magic’ at microwave frequencies. • We are working on (TMTSF)2PF6.