An Existence Criterion for Low-Dimensional Materials

TL;DR

This paper introduces an energy stability criterion for low-dimensional materials, explaining which structures like graphene and silicene can exist stably based on interatomic potentials.

Contribution

It establishes a new atomistic-based criterion for predicting the stability of low-D materials, addressing fundamental questions about their existence.

Findings

Identifies four permissible low-D structures: 1-D chains, 2-D honeycomb, square, and triangular lattices.

Explains the stable existence of graphene, silicene, and germanene.

Shows stability depends on derivatives of interatomic potentials.

Abstract

The discovery of graphene and other two-dimensional (2-D) materials has stimulated a general interest in low-dimensional (low-D) materials. Whereas long time ago, Peierls and Landau's theoretical work demonstrated that any one- and two-dimensional materials could not exist in any finite temperature environment. Then, two basic issues became a central concern for many researchers: How can stable low-D materials exist? What kind of low-D materials are stable? Here, we establish an energy stability criterion for low-D materials, which seeks to provide a clear answer to these questions. For a certain kind of element, the stability of its specific low-D structure is determined by several derivatives of its interatomic potential. This atomistic-based approach is then applied to study any straight/planar, low-D, equal-bond-length elemental materials. We found that 1-D monatomic chains, 2-D honeycomb lattices, square lattices, and triangular lattices are the only four permissible structures, and the stability of these structures can only be understood by assuming multi-body interatomic potentials. Using this approach, the stable existence of graphene, silicene and germanene can be explained.