  We theoretically investigate the effects of surface acoustic waves (SAWs) on
an electric-field-driven sliding motion of a one-dimensional charge density
wave (CDW), which is initially pinned by impurities. By numerically analyzing
an extended Fukuyama-Lee-Rice model, we show that a mechanical vibration of the
SAW, which, in the model, is assumed to affect the CDW via the pinning site in
the form of temporally oscillating pinning parameters, induces Shapiro steps
with self-similarity, i.e., the devil's staircase, in the current-voltage
characteristics. It is also found that when the SAW acts as the vibration in
the pinning strength, the mechanism of the mode locking (harmonic and
subharmonic responses) leading to the occurrence of the Shapiro steps is
modified, and as a result, the fractal dimension and parameter dependence of
the SAW-induced staircase can be considerably different from those for the
conventional ac-electric-field-induced one. This suggests that an
unconventional type of fractal phenomena can emerge in the SAW-induced CDW
dynamics.
