Peierls and Spin-Density Instability: From Polyacetylene to Graphene

Abstract

The $sp^2$ hydrocarbon conjugated molecules have remarkable properties mainly due to their delocalized $\pi$-electron system. They are at the basis of novel materials that have been produced and studied in the last few decades and which have found an extensive number of applications and are expected to be more and more involved in the development of nanostructures . The properties of these molecules are determined not only by external factors, like doping, but also by their intrinsic structure that can be affected by the presence of the Peierls and spin-density instabilities. The paper presents a short overview on the effects of these types of structural rearrangements on the molecular properties and how they develop from strictly one-dimensional to two-dimensional cases. Specifically, we will consider the one-dimensional polyacetylene polymer, the two-dimensional graphene molecule and, as a case intermediate between one and two dimensions, the quasi-one dimensional polyacenes molecules.