1. TRANSVERSE CONDUCTIVITY BEHAVIOR NbSe3 AT THRESHOLD ELECTRIC FIELD FOR CDW SLIDING
A. Sinchenko,
National Research Nuclear University MEPhI, Moscow
P. Monceau and T. Crozes
Institut Néel, CNRS, Grenoble
Acknowledgements:
S.A. Brazovskii, S.N. Artemenko, J. Marcus

2. Outline
Motivation. Strange transverse effects in the sliding state of CDW.
Experimental configuration.
Transverse electric field: why it is important. The temperature dependence of transverse voltage in NbSe3 in the static state of CDW.
Transverse voltage in NbSe3 in the sliding state of CDW: temperature evolution of transverse voltage; longitudinal and transverse IV-characteristics. Transverse and longitudinal Shapiro steps.
Possible explanations.
Conclusion.

3. Strange transverse effects
Torsional Strain of TaS3 Whiskers on the Charge-DensityWave Depinning
V.Ya. Pokrovskii, S. G. Zybtsev, and I. G. Gorlova, PRL 98, (2007)
Field-Effect Modulation of Charge-Density-Wave Transport in NbSe3 and TaS3
T.L.Adelman, S.V.Zaitsev-Zotov and R.E.Thorne, PRL 74, 5264 (1995)
Regions of negative absolute resistance are observed in the CDW sliding regime
H. S. J. van der Zant, et al., PRL 87, (2001)
Anomalous Asymmetry of Magnetoresistance in NbSe3 Single Crystals
A. A. Sinchenko, et al, JETP Lett., 84, 271 (2006).
What happens in the transverse direction at threshold electric field?

4. Experimental NbSe3 Two Peierls transitions at TP2=59 K and TP1=144 K
h= μ
potential probes (4,5,6,7)= 3 μ
current probes (2,3,8,9)= 10 μ
d1,2=d2,4=d6,8=d8,10=100 μ
d4,6=50 μ
Rtr=Vtr/I
RL=VL/I

5. Transverse electric field: to be important it should exist
Measurements of Rtr(T) (where Rtr=Vtr/I)
in NbSe3 in static state. Pairs of contacts 4-5 and 6-7 were used for Vtr, contacts 4-6 and 5-7 for longitudinal voltage VL measurements.
Rtr(T) in the case of complete compensation of the electric field at T=300 K (Vtr<10-9 V) (black curve); and RL(T) – blue curve.
Rtr(T) at variation of the electric field direction
misalignment of potential probes is negligible

6. Φ1 Φ2 о – Rtr(T); blue curve – α[RL(T+ΔT)-RL(T)]
at ΔT=0.1 K and α=0.31.
Rtr(T)~dRL(T)/dT
Transverse voltage appears as a result of any inhomogeneouty, impurity or over defects, or because of fluctuation effects.
A. A. Sinchenko, P. Monceau, and T. Crozes, JETP Lett., 93, 56 (2011).
Qualitatively the same effect was observed in superconductors. Qualitatively the same explanation was proposed. A. Segal, M. Karpovski, and A. Gerber, Phys. Rev. B 83, (2011).
In real samples the transverse electric field exists always Φ1 Φ2

7. Transverse conductivity at sliding state of CDW
For studying properties of the transverse conductivity in the longitudinal CDW sliding state it is convenient to have well defined transverse components of the electronic transport. We used the pair of contacts 2-9 or 3-8 as current electrodes. The electric field direction is not strictly parallel to the conducting chains, and a small but finite transverse component Etr exists simultaneously with the longitudinal one, EL.
Temperature dependencies of longitudinal resistance RL(T) and transverse Rtr(T) at different currents
The maxima of RL observed below Tp1 and Tp2 decrease as usual . The opposite picture is observed in Rtr behavior: a strong increase of the transverse voltage takes place below Tp1 and Tp2 leading to the appearance of transverse resistance maxima.
Does the change in transverse voltage result from the current redistribution induced by the CDW sliding?

8. Transverse and longitudinal IVcharacteristics
55 K
120 K
In contrast to longitudinal IVC, a jump (step) of transverse voltage takes place at threshold electric field for CDW sliding. Such type of jump was observed even in the case when the electric field is oriented strongly along the chains.

9. Transverse and longitudinal IVcharacteristics
55 K
120 K
In contrast to longitudinal IVC, a jump (step) of transverse voltage takes place at threshold electric field for CDW sliding. Such type of jump was observed even in the case when the electric field is oriented strongly along the chains.

10. Transverse and longitudinal differential IVcharacteristics
The observed change in transverse conductivity is qualitatively different from longitudinal one and takes place at a current lower than that needed for the CDW to slide. So, the jump in transverse voltage does not result from the current redistribution induced by the CDW sliding. On the contrary, we can propose the inverse statement: the change in transverse conductivity triggers the longitudinal CDW depinning.

11. Tentative explanation
Under an applied longitudinal electric field, the CDW is deformed up to a certain critical value, Et1<Et corresponding to the critical CDW deformation. We assume that at this field the phasing between the neighbouring chains sharply changes leading to the destruction of the transverse CDW coherence.
According to (S.N. Artemenko, JETP 84, (1997), 823) the strong phase difference and the different deformations of the CDW on neighbouring chains result in different shifts of local chemical potential at these chains leads to a strong decrease of the transverse conductivity. The transverse conductivity is a function of the phase difference between neighboring chains, and this effect is similar to the tunneling current between two conductors with charge density waves (S.N. Artemenko and A.F. Volkov, Sov. Phys. JETP 60, (1984),395).
Is in accordance with
R. Danneau, et al, Phys. Rev. Lett.89, (2002)
This current has a term proportional to the cosine of the difference between the phases. When an external alternating signal acts on the sample, a resonance should be observed for a fixed Vtr if the frequencies of the external and characteristic oscillations coincide.
Joint application of dc and rf electrical field ?

12. Joint application of dc and rf driving fields
Shapiro steps for longitudinal transport appear in the dVL/dI(I) characteristic as spikes, that corresponds to voltage steps. On the contrary, for transverse transport minima in the differential resistance are observed that corresponds to Shapiro current steps. Without complete mode locking, Shapiro steps in transverse transport have a larger amplitude and much more pronounced features.
The transverse Shapiro steps precedes the
longitudinal one.
When the CDW slides along one chain but is pinned along neigbouring chains, or if the CDW moves with different velocities in different chains, or if the CDW is pinned but phase slippage takes place, then the phase varies with time and alternating tunneling current is generated transversely to the chain direction with a frequency depending on the longitudinal electric field.

13. c-axis bridg in magnetic field
(Latyshev, Sinchenko, Monceau )

14. Shapiro steps without CDW sliding

15. Thank you very much for attention
Conclusion
1. At an electric field less than the longitudinal threshold
one for CDW sliding a sharp decrease in transverse conductivity
takes place; that may result from induced phase shifts between CDW
chains.
2. Under the joint application of dc and rf driving fields
pronounced current Shapiro steps in transverse transport have been
observed. The results were tentatively explained in the frame of
Artemenko-Volkov theory .
Thank you very much for attention