  We study a holographic model in which the striped structure of charge density
is spontaneously formed over an ionic lattice which breaks the translational
symmetry explicitly. The effect of commensurate lock-in between the spontaneous
stripes and the ionic lattice is observed when the lattice amplitude is large
enough. We investigate the optical conductivity as a function of frequency in
commensurate state and compare its characteristics during the phase transition
from metallic phase to insulating phase. Notably, we find that the DC
resistivity in lock-in state increases algebraically with lowering temperature,
which is in line with the phenomenon observed in the holographic model for
simulating the experimental behavior of Mott insulator in [Nature Phys. 14,
no.10, 1049-1055 (2018)]. Moreover, in unlock-in state we find that the system
may undergo a transient unstable process in which the real part of the
conductivity exhibits a behavior with small negative values, while in lock-in
state we find this phenomenon disappears. In addition, at lower temperature the
pseudogap is observed for both unlock-in and lock-in states. This holographic
model successfully demonstrates the commensurate lock-in signatures, and
provides more information for understanding the interplay between ionic
lattices and electronic lattices by holography.
