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Charge density wave sliding driven by an interplay of conventional and Hall voltages in NbSe$_3$ microbridges

Collective charge-density wave (CDW) transport was measured under a high magnetic field in NbSe$_3$ microbridges which have been cut transversely and at an angle to the chains' direction. We give evidences that the CDW sliding is driven by the Hall voltage generated by the inter-chain current of normal carriers. We have discovered a re-entrance effect of the Hall-driven sliding above a crossover temperature at which the Hall constant has been known to change sign. For the narrow channel, cut at 45$^\circ$ relative to the chain axis, we observed an evolution from the Hall-driven sliding at low temperatures, to the conventional sliding at higher temperatures, which corroborates with falling of the Hall constant. In this course, the nonlinear contribution to the conductivity coming from the collective sliding changes sign. The quantization of Shapiro-steps, generated presumably by a coherent sequence of phase slips, indicates that their governing changes from the applied voltage to the current.