# Commensurate lock-in in holographic non-homogeneous lattices

## TL;DR

This paper investigates how spontaneous stripe formations in a holographic model lock into an underlying ionic lattice, revealing conditions for commensurate and incommensurate phases through perturbative analysis.

## Contribution

It provides the first holographic demonstration of commensurate lock-in between spontaneous stripes and an ionic lattice, analyzing wave-vector behaviors across various lattice parameters.

## Key findings

- First observation of commensurate lock-in in holography
- Identification of incommensurate regimes with finite lattice amplitude
- Analysis of wave-vector dependence on lattice period and amplitude

## Abstract

We consider the spontaneous formation of striped structures in a holographic model which possesses explicit translational symmetry breaking, dual to an ionic lattice with spatially modulated chemical potential. We focus on the perturbative study of the marginal modes which drive the transition to a phase exhibiting spontaneous stripes. We study the wave-vectors of the instabilities with largest critical temperature in a wide range of backgrounds characterized by the period and the amplitude of the chemical potential modulation. We report the first holographic observation of the commensurate lock-in between the spontaneous stripes and the underlying ionic lattice, which takes place when the amplitude of the lattice is large enough. We also observe an incommensurate regime in which the amplitude of the lattice is finite, but the preferred stripe wave-vector is different from that of the lattice.