Graphene: Carbon in Two Dimensions, by Mikhail I. Katsnelson

Graphene : carbon in two dimensions

Carbon is one of the most intriguing elements in the Periodic Table. It forms many allotropes, some known from ancient times (diamond and graphite) and some discovered 10-20 years ago (fullerenes and nanotubes). Interestingly, the two-dimensional form (graphene) was only obtained very recently, immediately attracting a great deal of attention. Electrons in graphene, obeying a linear dispersion ...

Hilbert’s Fourth Problem in Two Dimensions I

Hilbert’s fourth problems asks to construct and study the geometries in which the straight line segment is the shortest connection between two points. In this paper the reader shall find an elementary introduction to the problem and its solutions in dimension two by Busemann, Pogorelov, and Ambartzumian. The relationship between integral geometry and inverse problems in variational calculus is ...

Piezoelectricity in two dimensions: Graphene vs. molybdenum disulfide

Two dimensional Dirac carbon allotropes from graphene.

Using a structural search method in combination with first-principles calculations, we found lots of low energy 2D carbon allotropes and examined all possible Dirac points around their Fermi levels. Three amazing 2D Dirac carbon allotropes have been discovered, named as S-graphene, D-graphene and E-graphene. By analyzing the topology correlations among S-, T, net W graphene and graphene, we fou...

From point defects in graphene to two-dimensional amorphous carbon.

While crystalline two-dimensional materials have become an experimental reality during the past few years, an amorphous 2D material has not been reported before. Here, using electron irradiation we create an sp2-hybridized one-atom-thick flat carbon membrane with a random arrangement of polygons, including four-membered carbon rings. We show how the transformation occurs step by step by nucleat...