Subharmonic Shapiro Steps and Devil's-Staircase Behavior in Driven Charge-Density-Wave Systems

Abstract

Subharmonic steps in the dc $I\ensuremath{-}V$ characteristics are reported in the model compound Nb${\mathrm{Se}}_{3}$, when subjected to combined dc and ac drives. The steps occur at currents which correspond to frequencies ${\ensuremath{\omega}}_{\mathrm{int}}=(\frac{p}{q}){\ensuremath{\omega}}_{\mathrm{ext}}$, with $p$ and $q$ integers. These steps cannot be explained in terms of the familiar classical equation of motion in a single degree of freedom, because the inertial term is too small. The observed behavior is compared with the devil's staircase, and a fractal dimension of 0.91 \ifmmode\pm\else\textpm\fi{} 0.03 is extracted.