On 2D Periodic Hexagonal Cells

TL;DR

This paper explores the unique directional properties and symmetry of 2D hexagonal cells, exemplified by graphene, analyzing their structural and electronic features through various band structure visualizations.

Contribution

It provides a detailed analysis of the characteristic symmetry and directional features of 2D hexagonal cells, with visualizations of their electronic and vibrational properties.

Findings

Hexagonal cells exhibit sixfold symmetry.

Characteristic directional features are identified.

Band structures are visualized for these systems.

Abstract

Graphene, the new wondrous material, is a perfect example of a two-dimensional hexagonal crystal unlike any other. Here we exhibit some of the characteristic directional features associated with hexagonal cells, emphasising the sixfold symmetry. We depict the X-ray, vibrational and electronic band structures to be expected in such systems via 2 dimensional contour plots.