Dynamics of the electrooptic response of chargedensitywave conductors

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Dynamics of the electro-optic response of
charge-density-wave conductors L. Ladino, M.
Freamat, M. Uddin, R.C. Rai, J.W.
Brill University of Kentucky
Samples from R.E. Thorne, Cornell U.
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This CDW strain (df/dx) profiles were measured in
NbSe3 by transport (Cornell) and x-ray (Grenoble)
measurements. Note since xj ja d cos(qx
f), df/dx ?q
Time after current reversal
current conversion Into sliding CDW
contact strain
bulk polarization
bulk polarization
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Electro-transmittance of blue bronze (K0.3MoO3)

• For photon energies less than the CDW gap
  and voltages near threshold, the infrared
  transmission (T) increases at the positive
  current contact and decreases at negative.
• (DT/T 0.5 for 5mm thick sample (T 3) and
  transverse polarization.)
• The spatial variation was similar to the NbSe3
  strain variation, and we assumed that DT/T a
  ?f/?x.

Extra strain near ( 100mm) contact for V gt VT
(dc current threshold).
DT / T ()
Linear variation for V VT polarization of CDW
(when depinned in interior)
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Broadband changes in transmission due to
intraband absorption of thermally excited
electrons screening the CDW deformation. Also
phonons affected (DG Dn 0.01 cm-1) by the CDW
strain these changes dominate the
electro-reflectance.
E ? conducting chains
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Use the electro-optic response to measure the
frequency, voltage, and spatial dependence of CDW
repolarization (without multiple contacts).
IR Microscope
Electro-Reflectance DR R(V) R(V-)
Electro-Transmittance DT T(V) T(V-)
w
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TaS3T 80 K, n 860 cm-1, parallel
polarization, w/2p 253 Hz
left contact
150 mV
95 mV
60 mV
Spectra and spatial dependence may be affected by
diffraction effects and irregular (micro-faceted)
surface.
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TaS3, 1,
Frequency of peak in quadrature and shoulder in
in-phase component increase with increasing
voltage ? CDW repolarization time decreases with
increasing voltage. DR/R (DR/R)0 / 1
(w/w0)2 (-iwt0)g (g lt 1 distribution of
relaxation times (t) broadens.)
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• Relaxation time t0 strongly V dependent.
• Delay time ( 100 ms) not strongly V-dependent.
• Delay time greater for positive repolarization
  than negative.
• Delay and relaxation times much longer than for
  NbSe3.

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NbSe3
Time after current reversal
Reverses rapidly at contact but more uniformly in
center strain reversal driven by local strain
and CDW current,
Delay few ms (away from contact). No delay at
contact. (We have 50 mm resolution.)
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TaS3
DR/R (DR/R)0 / 1 (w/w0)2 (-iwt0)g

• t0 ? V-p, p 1.5, with no (obvious) divergence
  near dc thresholds.
• t0 increases away from contact, where strain
  (?f/?x) decreases. (Similar to NbSe3 results
  repolarization is driven (partly) by local
  strain.)
• g decreases (distribution of ts broadens) as
  approach onset.
• Inertia has no strong voltage dependence and
  increases (slightly) away from contact.

w0 / 2p (kHz)
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Blue Bronze, Crystal 1, 80 K, n 850 cm-1, 25 Hz
Contact strain only 50 mm
Bulk strain
Zero strain position depends on voltage
VT
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Blue Bronze 1, T 80 K, R 850 cm-1 T 820
cm-1 50 mm resolution
253 Hz, x0
X0, 2VT
253 Hz, 2VT
in-phase
DR/R and DT/T have same frequency, position,
voltage dependence ? CDW strain (and current)
uniform through cross-section.
- quadrature
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Blue Bronze 1 Electro-Transmittance, T 80 K,
n 820 cm-1

Fits to DT/T (DT/T)0 / 1 (w/w0)2
(-iwt0)g (w0 strongly position dependent)
(doesnt include decay for frequencies lt Wx/2p
50 Hz)
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Blue Bronze 2, T 80 K, n 890 cm-1
? Time constants (t0, w0-1) an order of
magnitude larger than for crystal 1 !! ?
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(No Transcript)
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Blue Bronze, T 80 K DT/T (DT/T)0 / 1
(w/w0)2 (-iwt0)g

• t0 V-1 (1),1/V-2 (2)
• ? time scales much longer for 2 than 1 ?
• g 1 for 1, but decreases (distribution of
  relaxation times broaden) at small voltages for
  2.
• Relaxation time increases slightly away from
  contact
• Delay time (w0-1) increases rapidly as move away
  from contact. (Inertia is NOT a contact effect.)

2, 1 ?, ? x 0 ?, ? x 100 mm ,
x 200 mm
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DECAY OF ELECTRO-OPTIC RESPONSE
Expected response to low-frequency square-wave
Wx/2p is cross-over frequency (no clear V or x
dependence).
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The CDW strain is not expected to decay (and no
decay was observed in NbSe3 transport). However,
the CDW force (gradient of decay) was found to
decay (tdecay 20 ms). Could the electro-optic
response have a contribution from the CDW force
(mechanism ???)
Adelman, et al
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Summary

• We used electro-optic response as a
  non-perturbative probe of CDW repolarization
  dynamics in blue bronze and TaS3. The response
  is governed by three (voltage, position, and
  sample dependent) time constants
• Relaxation time 100 ms ? 20 ms
• t0 V-p (p1-2) why
  dependence so weak?
• Delay time w0-1 lt 40 ms ? 3 ms ?
  Why so long ?
• Decay time Wx-1 2 ms ? gt 80 ms ?
  What is this ?

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Critical Measurements ? Must overcome unstable
peak (1) or increase in g (2)
Blue Bronze 2
Blue Bronze 1