Charge-density-wave motion in NbSe3. I. Studies of the differential resistancedVdI

Abstract

We have measured the variation of the differential resistance as a function of the electric field for temperatures below those at which the two charge-density waves (CDW) form in Nb${\mathrm{Se}}_{3}$. The shape of the $\frac{\mathrm{dV}}{\mathrm{dI}}$ variation is very sensitive to temperature, particularly below that at which the anomaly due to the lower CDW shows its maximum. We have observed that for some samples a very sharp drop with a deep minimum in $\frac{\mathrm{dV}}{\mathrm{dI}}$ occurs at the critical electric field value where the charge-density wave is depinned. Over a large range of electric field below this dip we have measured low-frequency noise. We develop a model where the phase of the charge-density wave is described as an overdamped oscillator. If we consider the sample as consisting of a unique domain, we find that the differential resistance has an infinite negative value at the critical electric field when the current in the sample is regulated. We also obtain expressions for the variation of the frequency of the modulation of the current carried by the charge-density wave as a function of the electric field and for the amplitudes of the harmonics of this modulated current. To account for a more realistic description of the sample we suppose that it is formed of multiple domains. We explain the low-frequency noise as the depinning of individual domains and the dip in $\frac{\mathrm{dV}}{\mathrm{dI}}$ as resulting from the distribution of the electric critical fields of this assembly of domains. We have also studied the $\frac{\mathrm{dV}}{\mathrm{dI}}$ variation for Nb${\mathrm{Se}}_{3}$ samples doped with tantalum and titanium. The shape of the $\frac{\mathrm{dV}}{\mathrm{dI}}$ variation near the critical field gives a good indication of the distribution of the pinning centers inside the sample.