GROUND-STATE, SPECTRUM, AND PHASE-DIAGRAM OF 2-DIMENSIONAL INCOMMENSURATE CRYSTALS

A model of a monolayer of atoms adsorbed on a crystalline surface is discussed. When the initial incommensurability, δ, between a reciprocal lattice vector of the monolayer and one of the substrate is small, the monolayer has a one-dimensional superstructure with period depending on δ. For δ>δc(T) the state is incommensurate; δc(T) decreases and vanishes at a Tc given by the elastic moduli of the monolayer. The spectrum of small oscillations has two acoustic branches, one vanishing at the phase transition. © 1978 The American Physical Society.