The commensurate state and lock-in in a holographic model

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)]. In addition, at lower temperature the pinning effect 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.