Spatially Resolved Transient Dynamics of Charge Density Waves in ${\mathrm{NbSe}}_3$

We have developed methods for acquiring temporally and spatially resolved spectrograms of the velocity of sliding charge-density waves (CDWs), allowing unprecedented access to CDW dynamics. Complex transients arising from the interplay between elastic and plastic processes occur when the driving field direction is reversed. A transient spectral component due to shear elasticity can be unambiguously identified, and allows the most direct determination to date of the CDW’s shear elastic modulus. Near current contacts, initially elastic displacements are followed by an elastic-to-plastic transition. A simple model provides a semiquantitative account of many aspects of these transients.

Figure 1

Experimental configuration. Current pulses are applied to a ${\text{NbSe}}_3$ crystal, and voltages across any two voltage contact pairs are simultaneously measured using two cryogenic differential amplifiers. For all crystals, the crystallographic $b$ and $c$ axes were along the length $L$ and width, respectively.

Figure 2

Spectrogram of voltage across a contact pair near the middle of sample 1, measured in response to the periodic bias current shown in the lower panel. Note the transient spectral broadening at the start of each pulse and the asymmetry with respect to bias current direction. The inset shows the power spectral density (PSD) of the washboard frequency peak $50\mu \mathrm{s}$ after the beginning of the third pulse. The steady-state FWHM was approximately 20 kHz, corresponding to a quality factor of 800.

Figure 3

Spectrogram of power spectral density (PSD) of voltage across contacts at (top, pair 1) $d_1=75\mu \mathrm{m}$ and (middle, pair 2) $d_2=175\mu \mathrm{m}$ from the lower current contact in Fig. 1, in response to the bias current pulses shown in the bottom panel. For the first positive current pulse, the spectral peak for pair 2 is initially sharp, but $250\mu \mathrm{s}$ later it undergoes a sudden broadening and a steep drop in mean frequency. The steady-state spectral FWHM was approximately 250 and 300 kHz for positive and negative current pulses, respectively.

Figure 4

Calculated local washboard frequencies at 30 uniformly spaced positions across the width of a sample, in response to the bias current profile of Fig. 2, calculated using Eq. (6) and parameters deduced from measurements on sample 1, as described in the text.