Using scanning tunneling microscopy with Fe-coated W tips and first-principles calculations, we show that the interface of epitaxial graphene/SiC(0001) is a warped graphene layer with hexagon-pentagon-heptagon (H(5,6,7)) defects that break the honeycomb symmetry, thereby inducing a gap and states below E(F near the K point. Although the next graphene layer assumes the perfect honeycomb lattice,...

............................................................................................................................. ii Dedication .......................................................................................................................... iv Acknowledgement ............................................................................................................... v T...

Because of its unique physical properties, graphene, a 2D honeycomb arrangement of carbon atoms, has attracted tremendous attention. Silicene, the graphene equivalent for silicon, could follow this trend, opening new perspectives for applications, especially due to its compatibility with Si-based electronics. Silicene has been theoretically predicted as a buckled honeycomb arrangement of Si ato...

We have previously used inverse statistical-mechanical methods to optimize isotropic pair interactions with multiple extrema to yield low-coordinated crystal classical ground states (e.g., honeycomb and diamond structures) in d-dimensional Euclidean space R. Here we demonstrate the counterintuitive result that no extrema are required to produce such low-coordinated classical ground states. Spec...

Finite-size corrections to scaling of critical correlation lengths and free energies of Ising and three-state Potts ferromagnets are analysed by numerical methods, on strips of width N sites of square, triangular and honeycomb lattices. Strong evidence is given that the amplitudes of the ‘analytical’ correction terms, N−2, are identically zero for triangular and honeycomb Ising systems. For Pot...

Hexagonal mesh and torus, as well as honeycomb and certain other pruned torus networks, are known to belong to the class of Cayley graphs which are node-symmetric and possess other interesting mathematical properties. In this paper, we use Cayley-graph formulations for the aforementioned networks, along with some of our previous results on subgraphs and coset graphs, to draw conclusions relatin...

We report calculations of the electronic structure of silicene and the stability of its weakly buckled honeycomb lattice in an external electric field oriented perpendicular to the monolayer of Si atoms. The electric field produces a tunable band gap in the Dirac-type electronic spectrum, the gap being suppressed by a factor of about eight by the high polarizability of the system. At low electr...

We present a Markov-chain Monte Carlo algorithm of worm type that correctly simulates the fully-packed loop model on the honeycomb lattice, and we prove that it is ergodic and has uniform stationary distribution. The fully-packed loop model on the honeycomb lattice is equivalent to the zero-temperature triangular-lattice antiferromagnetic Ising model, which is fully frustrated and notoriously d...

We consider a weak version of the cosmological principle. The large scale mass distribution associated to this principle must have the geometrical structures known as regular honeycombs. We give the most important parameters that characterize the honeycombs associated to the closed, open, and flat Robertson-Walker models. These parameters can be used to determinate by observations which is the ...

We show by a combination of computer simulation and experimental characterization guided self-assembly of coherent nano-precipitates into a mesocrystal having a honeycomb structure in bulk materials. The structure consists of different orientation variants of a product phase precipitated out of the parent phase by heterogeneous nucleation on a hexagonal dislocation network. The predicted honeyc...