Rev. High Pressure Sci. Technol., Vol. 7 (1998) 493•`495

Quantum Hall Effect and Interlayer Resistance for the Organic Conductor (TMTSF)2AsF6

S. Uji, C. Terakura, M. Takashita, T. Terashima, H. Aoki, J. S. Brooks, S. Tanaka, S. Maki, J. Yamada, S. Nakatsuji and H. Anzai *)T sukuba Magnet Laboratory, National Research Institute for Metals, Tsukuba, Ibaraki 305, Japan +)Departmentof Physics, Florida State University, Tallahassee, Florida 32306, USA + +)Himeji Institute of Technology, Akohgun, Hyogo 678-12, Japan

Resistance measurements for the one dimensional organic conductor (TMTSF)2AsF6 have been perfonned to investigate the chiral surface state, which is realized on the side of the single crystal in the field induced spin- density-wave(SDW) phases (quantum Hall phases). The interlayer resistance in the integer quantum Hall phase is found to show a steep increase below the SDW transition, have a maximum and then become constant. The steep increaseof the resistance results from the carrier decreasedue to the nesting of the one dimensional Fermi surfaces. The temperature independentresistance at low temperatures suggests diffusive motion of the electron by the formation of the chiral surface state. The sharp peak of the interlayer resistance is found between the adjacentquantum Hall phases at low temperatures. [organic conductor, spin-density-wave,quantum Hall effect, chiral surface state]

1. Introduction of the most interesting features of the chiral surface state is The quantum Hall effect (QHE) is one of the most the fact that the back scattering is prohibited. The electronic striking phenomena observed in the two dimensional (2D) transport along the Interlayer direction is a good probe for the electron systems. In a quantum Hall phase, all the electronic understanding of the chiral surface state. states at the Fermi level are localized within the bulk of the In order to investigate the chiral surface state, we have sample. However, extended states (edge states) are present at performedthe Hall, and a- and c-axes resistance measurements the edge of the sample and are expected to be insensitive to at high magnetic fields up to 16 T over a wide temperature scattering due to disorder. range for the (TMTSF)2AsF6 salt. For the quasi-one-dimensional organic conductors (TMTSF)2X, where TMTSF denotes tetramethyltetraselenafulvaleneand X=AsF6, PF6, etc., the metallic phase is stabilized by applying high pressures [1]. A schematic picture of the Fermi surface is presented in Fig. 1. When the magnetic field is applied perpendicular to the conductiveplane (ab-plane), a cascade type spin-density-wave is induced (Fig. 1). The field induced spin-density-wave (FISDW) transitions take place at high magnetic fields below -2 K, which is characterizedby plateaus in the Hall resistance [2,3]. The overall behavior of the FISDW transitions is well understood in the framework of standard theory [1]. This theory is based on the assumption that a small closed orbit is formed by an imperfect nesting of the corrugated 1D Fermi surfaces. The nesting vector in the FISDW phase changes with magnetic field so that the Fermi level is kept between Landau levels, which result from the Landau quantization of the small closed orbit. This field dependentnesting minimizes the free energy and enables us to observe the quantized Hall resistance in a wide field region. This is the first QHE in bulk materials. For 3D systems such as the TMTSF crystals, the integer quantum Hall state is expected to be present in each layer when the quantum Hall gap Fg (=hwc) is larger than the transfer integral t between the payers. In the field region Fig. 1. (a) Schematic picture of the Fermi surface for where the electronicsystem is in the quantum Hall state, the (TMTSF)2AsF6. Q denotes the SDW nesting vector. (b) surfaceof the sample is enveloped by a sheath of the extended Geometry of a 3D quantum Hall sample. (c) Phase diagram at edge states (Fig. 1), and a pure 2D electronic system, so called 8 kbar determined by this work. N denotes the quantum chiral surfacestate, is formed on the side of the sample. One number in the quantum Hall phases (FISDW phases). 494

2, Experiment phase to another for N<5. The overall peak structure does A standard Cu(Be) clamp cell was used for the pressure not change up to 0.15 K, but the peaks become broad with experiments. Electrical contact to the sample was made with increasing temperature above 0.15 K. At 2.1 K, the peaks are 10µm gold wires and a silver paint. Experiments were carried completely smeared out and only kinks are evident. The out by a 16 T superconducting magnet with a dilution resistance at the valley between the peaks are almost field refrigerator at Tsukuba Magnet Laboratory, NRIM. independent above 8 T. Figure 4 shows the temperature dependence of Rzz at several magnetic fields. The 3. Results superconducting transition is seen below 1 K at zero field. Figure 2 presents the Hall resistance (Rxy) and a-axis The arrows indicate the transition to the FISDW phase. In the resistance (Rxx) at 0.04 K. The superconductivity induced by quantum Hall phases for N•¬5, as temperature decreases, Ra high pressures is seen at low fields in Rxx. The Hall (closed circles) increases in the FISDW phase, has a resistance is negligibly small in the metallic phase but shows maximum and then becomes constant at low temperatures. an uptum at the threshold field (•`5 T), followed by a series of Rzz has the same value independent of the quantum number at Hall steps. These steps correspond to the FISDW phases, low temperatures. On the other hand, in the transition whose quantum numbers are also shown in Fig. 2. The Hall regions between the quantum Hall phases, the resistance (open step for the N=1 phase is not evident, which may be due to circles) does not have clear maxiiitum behavior. somewhat low pressure or sample inhomogeneous. The resistance Rxx shows peak structures corresponding to the onset of the field induced SDW phases. These peaks are not so evident as compared with the reported results [2,3]. R, does not drop to zero in the quantum Hall phases in contrast to the cases of 2D electron gas in semiconductor heterostructures. Hysteresis is observable for Rxy and Rxx .

Fig. 3. C-axis resistance (Ra) at various temperatures.

4. Discussion Recently, Balents and Fisher [4] theoretically treated layered samples in integer quantum Hall phase with a random

potential, and argued that the chiral surface state has drastic differences from ordinary dirty 2D systems. They showed that the electron motion along the x direction is ballistic, and the back scattering is necessarily precluded as schematically Fig. 2. Hall (Rxy) and a-axis (Rxx) resistances of shown in Fig. 1. The motion along the z direction is (TMTSF)2AsF6 at 8 kbar for T=0.04 K. diffusive. They predicted that the chiral surface state gives the temperature independent conductivity ƒÂzz along the interlayer

Figure 3 presents the c-axis resistance (Rzz) at various (z) direction, temperatures. At 0.04 K, Ra steeply increases above the transition field and shows a characteristic structure due to the FISDW transitions. A remarkable feature is the observation (1) of the sharp peaks, which are evident at 0.04K and 0.6K.

These peaks are seen at transitions from one quantum Hall where c is the interlayer distance, Ą is the scattering time, and 495

v is the Fermi velocity in the edge state. As shown in Figs. state, which is not clear at present, exists between the 3 and 4, Ra in the quantum Hall phases, which is directly quantum Hall phases. The experimental results suggest that given by 1/ƒÐzz for B//z, has the same value independent of the electron scattering is restricted in the quantum Hall the quantum number at low temperatures, so that the phases (low resistance) because of the fonnation of the chiral predicted result Eq. (1) is not consistent with the surface state, but the scattering is restored (high resistance) in experimental results. The reason of the inconsistency is not the transition regions. clear. They also discussed the behavior in the magnetic field Recently, Valfell et al, carefully measured the Hall regions between adjacent quantum Hall phases. In the resistance for (TMTSF)ZPF6, and obtained the temperature framework of the standard theory [1], the FISDW transition dependence of the transition width from one quantum Hall is the first order, which is associated with a discontinuous phase to another [5]. Their data strongly suggests that the change of the SDW nesting vector. Therefore, the standard broadening of the transition is due to some disorder. This theory may suggest steep change of Rzz from one quantum disorder may be understood in the framework of Imry and Ma state to another. This transition is very contrast to the case theory [6], which argues that a domain structure (coexistence of the 2D electron gas, where the extended electronic state of two different phases) rather than an unifonn structure is appears between the adjacent quantum Hall phases. In the energetically favorable near the first order transition in the experimental data, Rzz has peaks between the quantum Hall presence of a disorder potential coupling to the order phases. One possible interpretation is that an intenmediate parameter. Actually, the inverse of the transition width determined from the peak width (inset of Fig. 4) follows a BCS like temperature dependence, which is consistent with their work [5]. Therefore, the increase of the scattering at the transitions (resistance peaks) may be a consequence of the domain structure. As temperature decreases, the electronic system goes into the SDW phase from the metallic phase, and the energy

gap at the Fermi level opens by the nesting of the Fenmi surface. Since the energy gap increases with decreasing temperature, the steep increase of Rzz below the transition temperature (Fig. 4) is probably due to the carrier decrease by the SDW energy gap. As temperature further decreases, the thennal fluctuation between the Landau levels is suppressed because kT<< hƒÖc. Therefore, the resistance in the quantum Hall phases should decrease because the scattering is restricted due to the formation of the chiral surface state as shown by the closed circles (N=1,2,3, and 5) in Fig. 4. The temperature independent Rzz at low temperatures suggest that the electron motion is diffusive rather than hopping process, as predicted theoretically [4].

5. Conclusion The interlayer resistance in the quantum Hall phase for the bulk system is independent of temperature and of the

quantum number at low temperatures (kT <

(kT<

References

[1] For a review, see T. Ishiguro and K. Yamaji, Organic Superconductors (Sprinnger-Verlag, Berlin, 1990)

[2] J. R. Cooper, W. Kang, P. Auban, G. Montambaux, Fig. 4. Temperature dependence of the resistance Ra at D. Jerome, and K. Bechgaard, Phys. Rev. Lett., 63, 1984 various magnetic fields. Closed circles : Ra in quantum (3989). T. Hannahs, J. S. Brooks, W. Kang, L. Y. Chiang, Hall phases for N=1,2,3 and 5, and at 6 T and zero field. and P. M. Chaikin, Phys. Rev. Left., 63, 1988 (1989) Open circles : Ra in the transition regions between the [4] L. Balents and M. P. A. Fisher, Phys. Rev. Lett., 76, quantum Hall phases. Arrows indicate the FISDW transition 2782 (1996), J. T. Chalker and A. Dohmen, Phys. Rev. from the high temperature metallic phase. Inset : Inverse of Left., 75, 4496 (1995) the peak widths of Rzz, 1/•¢B, at the transitions from N=3 to [ 5] S. Valfells, J. S. Brooks, Z. Wang, S. Takasaki, J. 2 phase (B=11.5T) and from N=2 to 1 phase (B=14T). Yamada, and H. Anzai, Phys. Rev. B 54, 16413 (1996)

[6] Y. Imry and S-K Ma, Phys. Rev. Lett., 35, 1399 (1975)