CHARGE-DENSITY-WAVE PINNING AND FINITE-SIZE EFFECTS IN NBSE3

We present a detailed experimental study of the effects of finite crystal size, impurities, and temperature on the properties of charge-density waves (CDW's) in NbSe3. Finite-size effects in NbSe3 are controlled by the crystal thickness t. They are large in crystals of ordinary thickness, and remain significant in high-purity crystals having thicknesses approaching 0.1 mm. In sufficiently thick Ta- and Ti-doped crystals, the threshold electric field E(T) for CDW depinning is independent of thickness and varies with the residual resistance ratio r(R) as E(T) is-proportional-to- r(R)-1.9 and r(R)-1.4, respectively. In thin crystals, E(T) increases with decreasing thickness as E(T) = K/t, where K is roughly proportional to the impurity concentration. E(T) is strongly temperature dependent. The fractional increase in E(T) as T-->0 is independent of thickness but decreases rapidly with increasing impurity concentration. The divergence of E(T) near T(P)2 = 59 K is described by E(T) is-proportional-to (1-R(H)/R(L))-0.95, where R(H) and R(L) are the high-field resistance , respectively. In extremely thin crystals (t < 0.1-mu-m) near T(P)2, the sharp threshold vanishes and nonlinear conduction occurs at arbitrarily small fields. Finite-size effects are observed in several other CDW properties. In thin crystals, the crossover frequency omega(co) in the ac conductivity varies as t-1, the low-frequency dielectric constant epsilon(omega = 1 MHz) varies as t, and the width of the 1/1 Shapiro step varies as t-1. Most NbSe3 crystals have irregular cross sections, in which the crystal thickness varies in a series of steps across the crystal width. Such crystals exhibit large f-alpha noise, complicated coherent oscillation spectra, and complicated mode-locking behavior, when compared with crystals with nearly rectangular cross sections. Analysis of these results indicates that (1) pinning of CDW's in Ta- and Ti-doped NbSe3 is weak; (2) the size dependence of CDW properties is due to a crossover in the dimensionality of the pinning from three to two dimensions which occurs when the crystal thickness becomes smaller than the CDW's bulk transverse phase-phase correlation length; (3) the vanishing of ET in thin crystals near T(P)2 is due to thermally assisted depinning of the CDW; and (4) f-alpha-noise and complicated mode-locking behavior are a consequence of CDW velocity shear occurring along steps in crystal thickness. These results have significant implications for the study of nearly every aspect of CDW's in NbSe3.