Sliding of a charge density wave probed by coherent X-Ray Diffraction

E. PinsolleLaboratoire de physique des solides, Orsay

Synchrotron Sources

Experiment caried out by:

E. PinsolleV. JacquesD. Le bolloc’hA. SinchenkoP. Monceau

Experiment done at the ESRF on the beamline ID10A

NbSe3 sample

Sample dimensions:2mm x 10μm x 10μm

3 types of chains:-first one with Peierls transition at 145K-second one with Peierls transition at 59K-last one with no transition.

Threshold current 0.9 mA

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Signature of CDW in X-ray diffraction

Gap opening at the fermi level.Electron density modulation

-2kF +2kF

Spawning of satellites around initial Bragg peak.

Satellite reflection (0 1.25 0)

Experimental setup

Incident X ray beam

Chain axis

Diffracted Beam CCD camera

Gold contacts

Two interest of this experiment:-Coherent beam sensitive to phase defects.-Micrometer scale beam.

Above the threshold

Bellow the threshold 2D diffraction

patternsIncreasing current values

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I=0.8 mA

I=1.4 mA

I=1.8 mA

I=0.2 mA

I=0.4 mA

I=0.6 mA

I=1.6 mA

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First Result:Satellite in transverse direction.

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I=0 mA

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Satellite in the transverse direction for different current value, bellow (colon 1) and above (colon 2) the threshold. (IS=0.9 mA)

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Satellite with I=1.8 mA

Satellite with I=0.2 mA

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I=0 mA

I=1.8 mA

I=1.6 mA

I=0.8 mA

I=0.6 mA

I=1.4 mAI=0.4 mA

I=0.2 mA I=0 mA

The shift of the satellite change sign when we exceed the threshold.

-No speckle and no shape change.

The shift δq= +/- 0.26 10-4 Å-1 which correspond in the real space to a change of the wave length δλ=+/-8.10-4 Å

Second Result:Satellite in

longitudinal direction.

Satellite in direction of chain axis for different current value, under (colon 1) and above (colon 2) the threshold. (IS=0.9 mA)

Speckle signature of creepBellow thresholdPhase equation:

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2 zyxv

tEe F

-We suppose to be in a stationary case. - Correlations in longitudinal direction are much higher than in transverse direction.

This lead to the following phase equation:

2

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2 yvEe F

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I=0 mA

I=1.4 mA

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I=0.6 mA

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Influence of stepsabove threshold

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I=0 mA

I=1.4 mA

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I=0.6 mA

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I=0 mA

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I=0.6 mA

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Chain axis

The CDW must vanish at the interface of the step.

Nb Se3 is known to have step at the surface

If some strong pinning defects are present on chain dn, this fixe the phase on these chain (φ(dn)=0) and leads to the solution:

))((21 nn

Fn dydy

veE

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simulation from the previous theory compared to

experiment.

dn dn-2dn-1

φn Φn-1

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Speckle signature of creepBellow threshold

2kF contractionBellow the threshold.Theoretical explanation:

cntotal nnn ein nnn where

The total number of carriers is conserved. But when some current is applied we create a disequilibrium of the normal carrier densities.

xnn cn

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I=0 mA

I=1.8 mA

I=1.6 mA

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I=0.6 mA

I=1.4 mAI=0.4 mA

I=0.2 mA I=0 mA

Approximate view of the band structure

δq

Current conversionabove the threshold.

Stress experienced by the CDW

iF

iiF N

nxN

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I=0 mA

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I=1.6 mA

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I=0.2 mA I=0 mA

Un

Chain axisGold contacts Gold contacts

δλ δq

δλ=0

P. Monceau et al. Plastic sliding of charge density waves. Physical review B

Conclusion

Thank you for your attention!

Different behaviors of the CDW under current probed by coherent X ray diffraction:

Bellow the threshold:

Along the transverse direction. We observe phase defects which is the signature of creep phenomenon.

Along longitudinal direction. Condensation of normal electrons in the CDW.

Above the threshold: Along transverse direction. Influence of

steps on the CDW.

Along longitudinal direction. Current conversion far from contacts.