Ground-state phase diagrams for an oriented atomic chain on a triangular lattice.

Abstract

The ground-state phase diagram is determined for a chain of atoms (a system with coordination number 2) in a two-dimensional potential with the symmetry of a triangular lattice. The atoms on the chain interact with nearest-neighbor oriented harmonic bonds. The underlying vector nature of the interaction introduces a steric component to the length-scale competition that leads to true two-dimensional periodically modulated ground-state configurations. This system is a generalization to higher dimensions of the Frenkel-Kontorova (or discrete sine-Gordon) model. The model is solved on a discrete spatial grid (a discretized Frenkel-Kontorova model), and it is shown that this system has generic features like nonminimally periodic structures and bands of superdegenerate points that are not present in the continuum limit. Further, it is shown that the limiting process from the discrete to the continuum phase diagrams is not uniform in the sense that the fractional area of the phase diagrams occupied by the bands goes to a constant in the limit that the grid spacing goes to zero. The phase diagrams are obtained by solving the Griffiths and Chou minimax eigenvalue equation.