  We investigate theoretically the possibility to observe dynamical mode
locking, in the form of Shapiro steps, when a time-periodic potential or force
modulation is applied to a two-dimensional (2D) lattice of colloidal particles
that are dragged by an external force over an optically generated periodic
potential. Here we present realistic molecular dynamics simulations of a 2D
experimental setup, where the colloid sliding is realized through the motion of
soliton lines between locally commensurate patches or domains, and where the
Shapiro steps are predicted and analyzed. Interestingly, the jump between one
step and the next is seen to correspond to a fixed number of colloids jumping
from one patch to the next, across the soliton line boundary, during each AC
cycle. In addition to ordinary "integer" steps, coinciding here with the
synchronous rigid advancement of the whole colloid monolayer, our main
prediction is the existence of additional smaller "subharmonic" steps due to
localized solitonic regions of incommensurate layers executing synchronized
slips, while the majority of the colloids remains pinned to a potential
minimum. The current availability and wide parameter tunability of colloid
monolayers makes these predictions potentially easy to access in an
experimentally rich 2D geometrical configuration.
