Aubry transition with small distortions

We show that when the Aubry transition occurs in incommensurately distorted structures, the amplitude of the distortions is not necessarily large as suggested by the standard Frenkel-Kontorova mechanical model. By modifying the shape of the potential in such a way that the mechanical force is locally stronger (i.e. increasing the nonlinearities), the transition may occur at a small amplitude of the potential with small distortions. A "phason" gap then opens, while the phonon spectrum resembles a standard undistorted spectrum at higher energies. This may explain the existence of pinned phases with small distortions as experimentally observed in charge-density waves.