Symmetry breaking and low energy conformational fluctuations in amorphous graphene

Abstract

Recently, the prospects for amorphous phases of graphene (α‐g) have been explored computationally. Initial models were flat, and contained odd‐member rings, while maintaining threefold coordination and sp2 bonding. Upon relaxation, puckering occurs, and may be traced to the existence of pentagons, in analogy with the situation for fullerenes. In this work, we systematically explore the inherent structures with energy close to the flat starting structure. As expected, the planar symmetry can be broken in various ways, which we characterize for 800‐atom model of α‐g, always using local basis density functional techniques. The classical normal modes of various structural models are discussed, with an emphasis on imaginary modes indicating the evolution from flat to puckered. We also discuss very low energy conformational fluctuations akin to those seen previously in amorphous silicon, and reflect on the nature of the amorphous “ground state” within a network of fixed topology. For completeness, high energy modes were also computed, and are found to be associated with strained parts of the network.

The Atomic Structure of Two-Dimensional Silica

“…Different concepts of classification and comparisons encompassing a number of non-ordered natural and theoretical systems were described in a milestone publication by Weaire and Rivier [71]. In a recent paper [72], the silica film structures in its crystalline and vitreous state were compared to structural elements and configurations of other network structures, e.g., Si(111) 7×7 reconstruction [73], triangle rafts [66], amorphous graphene [74], copper oxide [75], molecular network structures [76], and bubble rafts [77,78].…”

“…Four-to nine-membered rings occur, six-membered rings exhibit the highest occurrence. d A computational model for a sheet of amorphous graphene [74]. On part of the image, C positions are indicated with small green circles and different ring sizes are shown with colored circles.…”

Topological Investigation of Two-Dimensional Amorphous Materials

“…The top part of Figure 4 shows a theoretical model for amorphous graphene. This model was published by Li and Drabold [20]. Other groups have been working with amorphous carbon models as well [21] and experimentalists are trying to create amorphous graphene by e-beam irradiation, [22][23][24] or reduction of graphene oxide [25].…”

“…These methods typically yield isolated defects and small amorphous patches embedded in mostly crystalline graphene sheets. The model of an amorphous graphene sheet presented by Li et al [20] was large enough to allow statistical evaluation. Carbon positions are marked with small green circles and the different sized rings with larger colored circles.…”

Electronic signatures of topological disorder in amorphous graphene

“…As we previously pointed out, the planar symmetry of amorphous graphene is unstable with respect to tiny external out-of-plane distortions, giving rise to pentagonal puckering and lowering the total energy [14,22]. In the following, localisation properties of eigenstates for both planar and puckered models are explored.…”