Post on 04-Jan-2016
Dynamics of the electro-optic response of charge-density-wave conductors
L. Ladino, M. Freamat, M. Uddin, R.C. Rai, J.W. BrillUniversity of Kentucky
Samples from R.E. Thorne, Cornell U.
This CDW strain (x) profiles were measured in NbSe3 by transport (Cornell) and x-ray (Grenoble) measurements. [Note: since xj = ja + cos(qx + ), x ≡ Δq]
contact strain
bulk polarization
Time after current reversal
bulk polarization
current conversionInto sliding CDW
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.
T/T ~ 0.5% for ~ 5m thick sample (T ~ 3%) and transverse polarization.)
The spatial variation was similar to the NbSe3 strain variation, and we assumed that T/T α ∂φ/∂x.
T /
T
(%)
Linear variation for V ≤ VT: polarization of CDW (when depinned in interior)
Extra strain near (~ 100m) contact for V > VT (dc current threshold).
Broadband changes in transmission due to intraband absorption of thermally excited electrons screening the CDW deformation.
Also: phonons affected ( ~ ~ 0.01 cm-1) by the CDW strain; these changes dominate the electro-reflectance.
E conducting chains
Electro-Reflectance:
R = R(V+) – R(V-)
Electro-Transmittance:
T = T(V+) – T(V-)
IR Microscope
Use the electro-optic response to measure the frequency, voltage, and spatial dependence of CDW “repolarization” (without multiple contacts).
TaS3T = 80 K, = 860 cm-1, parallel polarization, = 253 Hz
150 mV
60 mV
95 mV
Spectra and spatial dependence may be affected by diffraction effects and irregular (micro-faceted) surface.
left contact
Frequency of peak in quadrature and shoulder in in-phase component increase with increasing voltage: → CDW repolarization time decreases with increasing voltage.
R/R = (R/R)0 / [1 – (0)2 + (-i0)]
( < 1: distribution of relaxation times () broadens.)
TaS3, #1,
•Relaxation time 0 strongly V dependent.•Delay time (~ 100 s) not strongly V-dependent.•Delay time greater for positive repolarization than negative.• Delay and relaxation times much longer than for NbSe3.
Reverses rapidly at contact but more uniformly in center: strain
reversal driven by local strain and CDW current,
Time after current reversal
NbSe3
Delay ~ few s (away from contact).
No delay at contact. (We have 50 m resolution.)
TaS3 R/R = (R/R)0 / [1 – (0)2 + (-i0)]
• V-p, p ≈ 1.5, with no (obvious) divergence near dc thresholds.
• increases away from contact, where strain (∂φ/∂x) decreases. (Similar to NbSe3 results: repolarization is driven (partly) by local strain.)
• decreases (distribution of ’s broadens) as approach onset.
• Inertia has no strong voltage dependence and increases (slightly) away from contact.
0
/ 2
(kH
z)
=VT
Contact strain only ~ 50 m
Bulk strain
Blue Bronze, Crystal #1, 80 K, = 850 cm-1, 25 Hz
“Zero strain” position depends on voltage
Blue Bronze #1, T = 80 K, R: 850 cm-1; T: 820 cm-1; 50 m resolution253 Hz, x=0
253 Hz, 2VT
X=0, 2VT
R/R and T/T have same frequency,
position, voltage dependence → CDW strain (and current) uniform through cross-section.
in-phase
- quadrature
Blue Bronze #1 Electro-Transmittance, T = 80 K, = 820 cm-1
Fits toT/T = (T/T)0 / [1 – (0)2 + (-i0)] (0 strongly position dependent)
(doesn’t include decay for frequencies < x/2 ~ 50 Hz)
0.000
0.001
0.002
0.003
0.004
0.005
0.006
100 1000
0.000
0.001
0.002
0.003
0.004 T /
T
(Hz)
x=0
IN-PHASE
QUADRATURE
4.1 Von
2.3 Von
1.5 Von
DECAY
INERTIA
-0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
x = 200 m
T /
T
100 1000
0.0000
0.0005
0.0010
0.0015
(Hz)
IN-PHASE
QUADRATURE
INERTIA
DECAY
1.5 VON
2.3 VON
4.1 VON
Blue Bronze #2, T = 80 K, = 890 cm-1
? Time constants (0, 0-1) an order of magnitude larger than for crystal #1 !! ?
t (ms)
-1.0 -0.5 0.0 0.5 1.0
(
a.u.
)
-0.096
-0.095
-0.094
-0.093
-0.092delay ~ 0.1 ms
Blue Bronze #1, V = 4.1 Von, 906 Hz
x=0
x=200 m
#2, #1▲, ▲ … x = 0
♦, ♦ … x = 100 m ■, ■ … x = 200 m
• 0 ~ V-1 (#1),1/V-2 (#2)
• ? time scales much longer for #2 than #1 ?
• ~ 1 for #1, but decreases (distribution of relaxation times broaden) at small voltages for #2.
•Relaxation time increases slightly away from contact
• Delay time (0-1)
increases rapidly as move away from contact. (Inertia is NOT a contact effect.)
Blue Bronze, T = 80 K T/T = (T/T)0 / [1 – (0)2 + (-i0)]
Expected response to low-frequency square-wave
t /2
resp
onse
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
delay
relaxation
decay
0 0.25 0.5 0.75 1.0
DECAY OF ELECTRO-OPTIC RESPONSE
-0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
Blue Bronze #1, x = 200 mT/T = (T/T)0 / [1 - (0)
2 -i(- x20/
T /
T
100 1000
0.0000
0.0005
0.0010
0.0015
(Hz)
IN-PHASE
QUADRATURE
INERTIA
DECAY
1.5 VON
2.3 VON
4.1 VON
x/2 is cross-over frequency (no clear V or x dependence).
Adelman, et al
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 (decay ~ 20 s).
Could the electro-optic response have a contribution from the CDW force (mechanism ???)
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 s → 20 ms
[0 ~ V-p (p=1-2): why dependence so weak?]
Delay time 0-1: < 40 s → 3 ms ? Why so long ?
Decay time x-1: 2 ms → > 80 ms: ? What is this ?
x=150 m
V (mV)5 10 15 20 25 30
T /
T
0.0000
0.0005
0.0010
0.0015
253 Hz, in-phase
253 Hz, quadrature
25 Hz, in-phaseVT
Blue Bronze #1
Blue Bronze #2
Critical Measurements ?: Must overcome unstable peak (#1) or increase in (#2)