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Electric field dependent transport in the quantized Hall states of (TMTSF)2ClO4
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Synthetic Metals 70 (1995) 757-758
Electric field dependent transport in the quantized Hall states of (TMTSF)2CI04 W. Kang and S.A. Park Department of Physics, Ewha Womans University, Seoul 120-750, Korea Abstract We studied the depinning of the magnetic field-induced spin-density-wave of the organic superconductor (TMTSF)2 C104, stabilized above 4T and at 300mK. For the sample cross-sectional area of 9.9× 10-4cm ~, the quantized Hall resistance begins to decrease when the sample current increases more than 160#A. One the other hand, the longitudinal resistance at least fifteen times as small as that of the transverse resistance in the quantized Hall region, increases when the non-Ohmic behavior appears. The depinning is observed only in the negative Hall plateau region between 6.2 and 6.8T. No departure from the quantized Hall behavior is observed neither above 7.1T nor below 6.2T. 1. I N T R O D U C T I O N The ground state of Bechgaard salts at low-temperature is either SDW or SC. The competition between them is easily suppressed on applying external pressure which stabilizes the SC. Once being a superconductor a magnetic field of lkOe along the least conducting c-direction is enough to recover the metallic state. Further magnetic field restores SDW nesting and induces the FISDW states exhibiting the quantum Hall effect. The standard theory suggests the competition between the SDW wave vector and the reciprocal of the magnetic length G = 2r/)~ = eHb/h leads a cascade of FISDW transitions. The standard theory explains qualitatively well the experiments performed on almost all the Bechgaard salts like X=C104, ReO4, and PFs. However, the FISDW is assumed to be pinned and to act like a static potential in this model.[1] It is well known for the ordinary density waves that the pinned density waves can overcome the pinning potential under sufficiently high electric field and move along the chain.[2] Since the density wave motion is purely onedimensional, the Hall effect is not affected to the first approximation. However, the interaction between moving density waves and normal carriers creates a backflow current -o~IDw of normal carriers which results in the nonlinear Hall effect. In FISDW, the Hall conductivity is quantized at a~y = 2ue2/h neglecting the motion of FISDW. In the ideal system where the FISDW moves without pinning and damping the contribution due to the FISDW motion precisely cancels the bare q u a n t u m Hall term so that the resultant Hall conductivity is zero. Even in real systems, the Hall conductivity should vanish at the high enough frequency where the dynamics of the FISDW is dominated by inertia, and the pinning and the damping can be neglected.[3] In the intermediate situations where the FISDW is depinned but damped, a finite a~y smaller than the QHE value might be expected.
So far, only a few experimental test of this problem has been performed. Osada et al. found in (TMTSF)2C104 that p ~ (z is in the chain direction) increases rather than decreases as a function of the longitudinal electric filed E~, while the Hall resistivity pxu does not change.[4] In contrast, a decreasing p~x has been reported for (TMTSF)2PF6.[5] More recently, nonlinear resistivity both in p ~ and in p~y is reported in the FISDW states of the same compound.[6] in this paper, we report on the electric field dependent transport observed in the FISDW states of (TMTSF)2C104. Both p ~ and p ~ departs from the Ohmic value above the same well defined threshold value only in the negative Hall state. Very large interaction between the moving FISDW and the normal electron is expected. 2. E X P E R I M E N T S The experiments have been performed in a superconducting solenoid using 3He cryostat. The temperature was maintained at 315mK all along the study. The sample of dimension 3.7 × 0.45 × 0.22ram 3 was aligned with its c* axis normal to the field direction. A pair of Hall contacts were made using silver paint on the gold evaporated pads. The cooling rate in the range 30K to 15K was less than 50mK/min and gave a well relaxed state sample. The differential resistance was measured. To cancel out the admixture of longitudinal and transverse voltage, all the measurements are repeated with positive and negative magnetic filed and the symmetric and antisymmetric parts are taken for the longitudinal(V~) and transverse(VH) resistance, respectively. 3. R E S U L T S Fig. 1 displays the Hall resistance between 5 and 9T. Assigning the highest plateau as n = 0, the lower plateaus could be assigned as n = 3, 5, 7 from the ratio of heights. From the well developed negative plateau we can say that the sample is in the very well relaxed state. We measured dVn/dl and dVt/dl for at least one field value in each FISDW phase.
°This work has been supported by the KOSEF Grant No. 931-0200-009-2 and the Basic Science Research Institute Program, Milfistry of Education, 1994, Project No. BSRI-94-242S. 0379-6779/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02640-K
758
145. Kang, SJI. Park / Synthetic Metals 70 (1995) 757-758
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Fig. 1. Hall resistance between 5 and 9T. Solid and dashed lines are for increasing and decreasing field sweep, respectively. Fig. 2(a) and (b) represents the current dependence of the transverse(R~y) and longitudinal(R==) resistance, respectively, for various fixed magnetic fields. Only the results in the range 6.3T to 7.5T are displayed since there is no detectable deviation from the Ohmic behavior out of this range. We put the result at 7.5T in Fig. 2(a) for comparison. The data were taken in the increasing order of magnetic field so the sample is still in negative plateau state at 6.8T. As the dc current increases, the Hall resistance remains constant in its quantized value before decreasing abruptly above a certain current. In the same region, magnetoresistance which is very small in the quantized Hall region increases. In the curve of 6.3T and 6.8T, it is clear that there are two shoulders both in transverse and in longitudinal resistances which may be understood with the phase mixing due to the presence of tetracritical points.
for the FISDW of (TMTSF)2PF6. Such a large coupling constant was attributed to the Coulomb interaction between the SDW and the normal electrons. If a SDW charge packet propagates along the conducting chains, it carries along the screening normal electrons which appears as a backflow in transport measurements.[6] We applied the same analysis to our results and summarize the backflow constant for (TMTSF)~C104 in Fig. 4. We note that a > 1 for all the field studied. The increasing p~= and strongly nonlinear p=y correspond well with the prediction of a > 1 case. The reason for the very strong coupling between FISDW and quasiparticles and its limited presence only in the negative Hall plateau region is far from being understood. 15
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Fig. 3. Threshold longitudinal electric field for nonlinear electrical electric transport as a function of magnetic field. Fig. 4. Backflow constant c~ as a function of magnetic field.
Fig. 2. Transverse(p=y) and longitudinal(p==) resistance as a function of current in the longitudinal direction for various magnetic fields.
In conclusion, we studied the electric field dependent transport of the magnetic field-induced spin-density-wave of the organic superconductor (TMTSF)2C104 at 300inK. The nonlinear behavior is observed only in the negative Hall plateau region where both p ~ and p~y showed a strong departure from the hnear behavior above a sharp threshold current. Applying the interacting two-fluid model gives ot > 1 for all the field studied and the increasing p=, and strongly nonlinear p~y correspond well with the prediction of a > 1 case. The origin of such a high interaction coefficient remains to be further investigated. Until now, the state in the negative plateau is not considered as one of the subphases of FISDW and remained unexplained. As there is a clear non-linear conductivity and as its electric field dependent transport is well explained with the interacting two-fluid model, it is possible to be a separate FISDW which is superposed with the conventional one.
Although the current density at which the nonlinear transport begins does not change much with the magnetic filed, the evolution of the threshold field is much clearer if we trace the longitudinal electric field(E~) necessary to break into the non-Ohmic behavior. As shown in Fig. 3, the longitudinal electric threshold field is very small between 6.3 and 6.5T, say, well in the negative plateau and increases very fast above 6.5T. It reflects in some part very small longitudinal resistance in the same region. The nonlinear Hall transport in the SDW and CDW systems has been qualitatively understood with an interacting two-fluid model in which a backflow -c~Ic of normal carriers is expected where Ic is the sliding density wave current. The similar analysis might be applied to the FISDW. A magnetic field independent value of c~ = 0.8 4-0.1 is reported recently
REFERENCES 1. L.P. Gor'kov and A.G. Lebed, J. Physique Lett., 45, L433 (1984); G. Montambaux, M. H~ritier and P. Lederer, ibid. 45, L533 (1984); M. H~ritier, G. Montambaux and P. Lederer, ibid. 45, L533 (1984). 2. H. Fukuyama and P.A. Lee, Phys. Rev. B17, 533 (1977); P.A. Lee and T.M. Rice, ibid. 19, 3970 (1978). 3. V.M. Yakovenko, J. Physique IV, C2-307 (1993). 4. T. Osada, N. Miura, I. Oguro and G. Saito, Phys. Rev. Lett., 58 1563 (1987). 5. W. Kang, J.R. Cooper and D. J6rome, Synth. Metals, 43, 2083 (1991). 6. L. Balicas, N. Bi~kup and G. Kriza, J. Physique IV, C2-319 (1993).
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Synthetic Metals 70 (1995) 757-758
Electric field dependent transport in the quantized Hall states of (TMTSF)2CI04 W. Kang and S.A. Park Department of Physics, Ewha Womans University, Seoul 120-750, Korea Abstract We studied the depinning of the magnetic field-induced spin-density-wave of the organic superconductor (TMTSF)2 C104, stabilized above 4T and at 300mK. For the sample cross-sectional area of 9.9× 10-4cm ~, the quantized Hall resistance begins to decrease when the sample current increases more than 160#A. One the other hand, the longitudinal resistance at least fifteen times as small as that of the transverse resistance in the quantized Hall region, increases when the non-Ohmic behavior appears. The depinning is observed only in the negative Hall plateau region between 6.2 and 6.8T. No departure from the quantized Hall behavior is observed neither above 7.1T nor below 6.2T. 1. I N T R O D U C T I O N The ground state of Bechgaard salts at low-temperature is either SDW or SC. The competition between them is easily suppressed on applying external pressure which stabilizes the SC. Once being a superconductor a magnetic field of lkOe along the least conducting c-direction is enough to recover the metallic state. Further magnetic field restores SDW nesting and induces the FISDW states exhibiting the quantum Hall effect. The standard theory suggests the competition between the SDW wave vector and the reciprocal of the magnetic length G = 2r/)~ = eHb/h leads a cascade of FISDW transitions. The standard theory explains qualitatively well the experiments performed on almost all the Bechgaard salts like X=C104, ReO4, and PFs. However, the FISDW is assumed to be pinned and to act like a static potential in this model.[1] It is well known for the ordinary density waves that the pinned density waves can overcome the pinning potential under sufficiently high electric field and move along the chain.[2] Since the density wave motion is purely onedimensional, the Hall effect is not affected to the first approximation. However, the interaction between moving density waves and normal carriers creates a backflow current -o~IDw of normal carriers which results in the nonlinear Hall effect. In FISDW, the Hall conductivity is quantized at a~y = 2ue2/h neglecting the motion of FISDW. In the ideal system where the FISDW moves without pinning and damping the contribution due to the FISDW motion precisely cancels the bare q u a n t u m Hall term so that the resultant Hall conductivity is zero. Even in real systems, the Hall conductivity should vanish at the high enough frequency where the dynamics of the FISDW is dominated by inertia, and the pinning and the damping can be neglected.[3] In the intermediate situations where the FISDW is depinned but damped, a finite a~y smaller than the QHE value might be expected.
So far, only a few experimental test of this problem has been performed. Osada et al. found in (TMTSF)2C104 that p ~ (z is in the chain direction) increases rather than decreases as a function of the longitudinal electric filed E~, while the Hall resistivity pxu does not change.[4] In contrast, a decreasing p~x has been reported for (TMTSF)2PF6.[5] More recently, nonlinear resistivity both in p ~ and in p~y is reported in the FISDW states of the same compound.[6] in this paper, we report on the electric field dependent transport observed in the FISDW states of (TMTSF)2C104. Both p ~ and p ~ departs from the Ohmic value above the same well defined threshold value only in the negative Hall state. Very large interaction between the moving FISDW and the normal electron is expected. 2. E X P E R I M E N T S The experiments have been performed in a superconducting solenoid using 3He cryostat. The temperature was maintained at 315mK all along the study. The sample of dimension 3.7 × 0.45 × 0.22ram 3 was aligned with its c* axis normal to the field direction. A pair of Hall contacts were made using silver paint on the gold evaporated pads. The cooling rate in the range 30K to 15K was less than 50mK/min and gave a well relaxed state sample. The differential resistance was measured. To cancel out the admixture of longitudinal and transverse voltage, all the measurements are repeated with positive and negative magnetic filed and the symmetric and antisymmetric parts are taken for the longitudinal(V~) and transverse(VH) resistance, respectively. 3. R E S U L T S Fig. 1 displays the Hall resistance between 5 and 9T. Assigning the highest plateau as n = 0, the lower plateaus could be assigned as n = 3, 5, 7 from the ratio of heights. From the well developed negative plateau we can say that the sample is in the very well relaxed state. We measured dVn/dl and dVt/dl for at least one field value in each FISDW phase.
°This work has been supported by the KOSEF Grant No. 931-0200-009-2 and the Basic Science Research Institute Program, Milfistry of Education, 1994, Project No. BSRI-94-242S. 0379-6779/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0379-6779(94)02640-K
758
145. Kang, SJI. Park / Synthetic Metals 70 (1995) 757-758
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,
•
,
,
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i
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6O
v
E*o O o
20 I
i i i t
i ! i t
:~ - 2 0 .
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i
6
t
Idognetic
(T~i
Field
i
Fig. 1. Hall resistance between 5 and 9T. Solid and dashed lines are for increasing and decreasing field sweep, respectively. Fig. 2(a) and (b) represents the current dependence of the transverse(R~y) and longitudinal(R==) resistance, respectively, for various fixed magnetic fields. Only the results in the range 6.3T to 7.5T are displayed since there is no detectable deviation from the Ohmic behavior out of this range. We put the result at 7.5T in Fig. 2(a) for comparison. The data were taken in the increasing order of magnetic field so the sample is still in negative plateau state at 6.8T. As the dc current increases, the Hall resistance remains constant in its quantized value before decreasing abruptly above a certain current. In the same region, magnetoresistance which is very small in the quantized Hall region increases. In the curve of 6.3T and 6.8T, it is clear that there are two shoulders both in transverse and in longitudinal resistances which may be understood with the phase mixing due to the presence of tetracritical points.
for the FISDW of (TMTSF)2PF6. Such a large coupling constant was attributed to the Coulomb interaction between the SDW and the normal electrons. If a SDW charge packet propagates along the conducting chains, it carries along the screening normal electrons which appears as a backflow in transport measurements.[6] We applied the same analysis to our results and summarize the backflow constant for (TMTSF)~C104 in Fig. 4. We note that a > 1 for all the field studied. The increasing p~= and strongly nonlinear p=y correspond well with the prediction of a > 1 case. The reason for the very strong coupling between FISDW and quasiparticles and its limited presence only in the negative Hall plateau region is far from being understood. 15
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Fig. 3. Threshold longitudinal electric field for nonlinear electrical electric transport as a function of magnetic field. Fig. 4. Backflow constant c~ as a function of magnetic field.
Fig. 2. Transverse(p=y) and longitudinal(p==) resistance as a function of current in the longitudinal direction for various magnetic fields.
In conclusion, we studied the electric field dependent transport of the magnetic field-induced spin-density-wave of the organic superconductor (TMTSF)2C104 at 300inK. The nonlinear behavior is observed only in the negative Hall plateau region where both p ~ and p~y showed a strong departure from the hnear behavior above a sharp threshold current. Applying the interacting two-fluid model gives ot > 1 for all the field studied and the increasing p=, and strongly nonlinear p~y correspond well with the prediction of a > 1 case. The origin of such a high interaction coefficient remains to be further investigated. Until now, the state in the negative plateau is not considered as one of the subphases of FISDW and remained unexplained. As there is a clear non-linear conductivity and as its electric field dependent transport is well explained with the interacting two-fluid model, it is possible to be a separate FISDW which is superposed with the conventional one.
Although the current density at which the nonlinear transport begins does not change much with the magnetic filed, the evolution of the threshold field is much clearer if we trace the longitudinal electric field(E~) necessary to break into the non-Ohmic behavior. As shown in Fig. 3, the longitudinal electric threshold field is very small between 6.3 and 6.5T, say, well in the negative plateau and increases very fast above 6.5T. It reflects in some part very small longitudinal resistance in the same region. The nonlinear Hall transport in the SDW and CDW systems has been qualitatively understood with an interacting two-fluid model in which a backflow -c~Ic of normal carriers is expected where Ic is the sliding density wave current. The similar analysis might be applied to the FISDW. A magnetic field independent value of c~ = 0.8 4-0.1 is reported recently
REFERENCES 1. L.P. Gor'kov and A.G. Lebed, J. Physique Lett., 45, L433 (1984); G. Montambaux, M. H~ritier and P. Lederer, ibid. 45, L533 (1984); M. H~ritier, G. Montambaux and P. Lederer, ibid. 45, L533 (1984). 2. H. Fukuyama and P.A. Lee, Phys. Rev. B17, 533 (1977); P.A. Lee and T.M. Rice, ibid. 19, 3970 (1978). 3. V.M. Yakovenko, J. Physique IV, C2-307 (1993). 4. T. Osada, N. Miura, I. Oguro and G. Saito, Phys. Rev. Lett., 58 1563 (1987). 5. W. Kang, J.R. Cooper and D. J6rome, Synth. Metals, 43, 2083 (1991). 6. L. Balicas, N. Bi~kup and G. Kriza, J. Physique IV, C2-319 (1993).
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