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

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.

Strange transverse effects

Torsional Strain of TaS3 Whiskers on the Charge-DensityWave DepinningV.Ya. Pokrovskii, S. G. Zybtsev, and I. G. Gorlova, PRL 98, 206404 (2007)

What happens in the transverse direction at threshold electric field?

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 regimeH. S. J. van der Zant, et al., PRL 87, 126401(2001)Anomalous Asymmetry of Magnetoresistance in NbSe3 Single CrystalsA. A. Sinchenko, et al, JETP Lett., 84, 271 (2006).

0 50 100 150 200 250 3000

500

1000

1500

2000

2500

R (

Oh

m)

T (K)

NbSe3

Experimental

Two Peierls transitions atTP2=59 K and TP1=144 K

w=20 μh= 0.1-0.4 μpotential probes (4,5,6,7)= 3 μcurrent probes (2,3,8,9)= 10 μd1,2=d2,4=d6,8=d8,10=100 μd4,6=50 μ

Rtr=Vtr/I

RL=VL/I

Transverse electric field: to be important it should exist

4 6

73

2 8

9

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) at variation of the electric field direction

0 50 100 150 200 250

-0.10

-0.05

0.00

0.05

0.100 50 100 150 200 250

0

5

10

Rxy

(O

hm)

T (K)

a)

b)

Rxx

(O

hm)

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.misalignment of potential probes is negligible

50 100 150 200 250

-0.2

0.0

0.2

0.4

Rtr=

Vtr/I

(O

hm)

T (K)

50 100 150 200

-0.10

-0.05

0.00

0.05

R

xy (

Ohm

)

T (K)

j0

j0

j1

j2

R(T+ T)

R(T)

R(T)

R(T)

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, 094531 (2011).

In real samples the transverse electric field exists always

Φ1 Φ2

Transverse conductivity at sliding state of CDW

4 6

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2 8

9

0

4

8

12

16

20

RL (

Ohm

) 0.02 mA 0.10 mA 0.25 mA 0.50 mA 0.75 mA 1.00 mA 1.25 mA 1.50 mA

0 100 200 3000.0

0.5

1.0

1.5

5

10

15

20

25

Rtr (

Ohm

)T (K)

I=0.02 mA

RL(O

hm)

0 50 100 150 200 2500.0

0.5

1.0

1.5

Rtr (

Oh

m)

T (K)

a)

b)

Temperature dependencies of longitudinal resistance RL(T) and transverse Rtr(T) at different currents

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.

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?

Transverse and longitudinal IVcharacteristics4 6

73

2 8

9

-0.4 -0.2 0.0 0.2 0.4

-0.2

-0.1

0.0

0.1

0.2 Vtr (mV)

I (mA)

-0.4 0.0 0.4

-0.004

0.000

0.004 Vtr (mV)

I (mA)

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.

55 K 120 K

4 6

73

2 8

9

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.

55 K 120 K

4 6

73

2 8

9

-0.4 -0.2 0.0 0.2 0.4

-0.2

-0.1

0.0

0.1

0.2 Vtr (mV)

I (mA)

-0.4 0.0 0.4

-0.004

0.000

0.004 Vtr (mV)

I (mA)

-0.4 0.0 0.4

-0.004

0.000

0.004 Vtr (mV)

I (mA)

4 6

73

2 8

9

Transverse and longitudinal IVcharacteristics

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.31.0

1.2

1.4

1.6

1.8

2.0

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

12

14

16

dVtr/d

I (O

hm)

I (mA)

120 K

dV

L/d

I (O

hm)

-0.4 -0.2 0.0 0.2 0.4

1.2

1.4

1.6

1.8

2.0

-0.4 -0.2 0.0 0.2 0.4

12

13

14

15

dVtr/d

I (O

hm)

I (mA)

130 K

dV

L/d

I (O

hm)

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.

4 6

73

2 8

9

Tentative explanationUnder 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) 106404.

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 ?

Joint application of dc and rf driving fields

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.50.2

0.3

0.4

0.5

0.6

0.7

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

14

16

dVtr/d

I (O

hm)

I (mA)

135 K49.64 MH

dV

L/d

I (O

hm)

-1.0 -0.5 0.0 0.5 1.00.2

0.3

0.4

0.5

0.6

0.7

-1.0 -0.5 0.0 0.5 1.0

12

13

14

15

16

17

18

19

dVtr/d

I (O

hm)

I (mA)

120 K19.02 MH50 mV

dV

L/d

I (O

hm)

0.4 0.5 0.6 0.70.4

0.5

0.6

0.7

12.5

13.0

13.5

I (mA)

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.

c-axis bridg in magnetic field

(Latyshev, Sinchenko, Monceau 2008-2011)

I

I

B

EH

chain direction

-200 0 2000.0000

0.0004

0.0008

0.0012

dI/

dV

(O

hm

-1)

V (mV)

20T 17.5T 15T 12.5T 10T 7.5T 5T

-300 0 300

2.0x10-4

4.0x10-4

6.0x10-4

dI/d

V (

Ohm

-1)

V (mV)

20.0 T 17.5 T 15.0 T 12.5 T 10.0 T

197 MG 1 V1.5 K

Shapiro steps without CDW sliding

0.05 0.10

0.00

0.04

0.08

Ic (

mA

)

1/B (T-1)

1.5 K4.2 K8.0 K15.0 K25.0 K30.0 K

-300 -200 -100 0 100 200 3001.0x10-4

2.0x10-4

3.0x10-4

4.0x10-4

dI/d

V (

Ohm

-1)

V (mV)

F=197 MHz F=0T=1.5 K

B=20 T

Conclusion

1. At an electric field less than the longitudinal thresholdone for CDW sliding a sharp decrease in transverse conductivitytakes place; that may result from induced phase shifts between CDWchains.

2. Under the joint application of dc and rf driving fieldspronounced current Shapiro steps in transverse transport have beenobserved. The results were tentatively explained in the frame ofArtemenko-Volkov theory .

Thank you very much for attention