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)