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.

This CDW strain (  x) profiles were measured in NbSe 3 by transport (Cornell) and x-ray (Grenoble) measurements. [Note: since x j = ja +  cos(qx +  ),  x ≡ Δq] contact strain bulk polarization Time after current reversal bulk polarization current conversion Into sliding CDW

Electro-transmittance of blue bronze (K 0.3 MoO 3 ) 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 ~ 5  m thick sample (T ~ 3%) and transverse polarization.)  The spatial variation was similar to the NbSe 3 strain variation, and we assumed that  T/T α ∂φ/∂x.  T / T (%) Linear variation for V ≤ V T : polarization of CDW (when depinned in interior) Extra strain near (~ 100  m) contact for V > V T (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).

TaS 3 T = 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 + (-i  0 )  ] (  < 1: distribution of relaxation times (  ) broadens.) TaS 3, #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 NbSe 3.

Reverses rapidly at contact but more uniformly in center: strain reversal driven by local strain and CDW current, Time after current reversal NbSe 3 Delay ~ few  s (away from contact). No delay at contact. (We have 50  m resolution.)

TaS 3   R/R = (  R/R) 0 / [1 – (  0 ) 2 + (-i  0 )  ]    V -p, p ≈ 1.5, with no (obvious) divergence near dc thresholds.   increases away from contact, where strain (∂φ/∂x) decreases. (Similar to NbSe 3 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  (kHz)

=V T 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 resolution 253 Hz, x=0 253 Hz, 2V T X=0, 2V T  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 to  T/T = (  T/T) 0 / [1 – (  0 ) 2 + (-i  0 )  ] (  0 strongly position dependent) (doesn’t include decay for frequencies <  x /2  ~ 50 Hz)

Blue Bronze #2, T = 80 K, = 890 cm -1 ? Time constants (  0,  0 -1 ) an order of magnitude larger than for crystal #1 !! ?

#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 + (-i  0 )  ]

Expected response to low-frequency square-wave DECAY OF ELECTRO-OPTIC RESPONSE  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 NbSe 3 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 TaS 3. 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 ?

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