  Using first-principles plane wave calculations, we investigate two
dimensional honeycomb structure of Group IV elements and their binary
compounds, as well as the compounds of Group III-V elements. Based on structure
optimization and phonon mode calculations, we determine that 22 different
honeycomb materials are stable and correspond to local minima on the
Born-Oppenheimer surface. We also find that all the binary compounds containing
one of the first row elements, B, C or N have planar stable structures. On the
other hand, in the honeycomb structures of Si, Ge and other binary compounds
the alternating atoms of hexagons are buckled, since the stability is
maintained by puckering. For those honeycomb materials which were found stable,
we calculated optimized structures, cohesive energies, phonon modes, electronic
band structures, effective cation and anion charges, and some elastic
constants. The band gaps calculated within Density Functional Theory using
Local Density Approximation are corrected by GW0 method. Si and Ge in honeycomb
structure are semimetal and have linear band crossing at the Fermi level which
attributes massless Fermion character to charge carriers as in graphene.
However, all binary compounds are found to be semiconductor with band gaps
depending on the constituent atoms. We present a method to reveal elastic
constants of 2D honeycomb structures from the strain energy and calculate the
Poisson's ratio as well as in-plane stiffness values. Preliminary results show
that the nearly lattice matched heterostructures of ...
