Phonon dispersion curves of stable and metastable B C3 honeycomb epitaxial sheets and their chemical bonding: Experiment and theory

We have investigated experimentally and theoretically the phonon-dispersion curves along the Γ̄ - M̄ axis in two-dimensional surface Brillouin zones of the stable and metastable B C3 honeycomb sheets with different lattice constants. Most of the observed curves agreed with the theoretical ones calculated on the basis of the ab initio theory. There exists a common relationship between the nearest-neighbor stretching force constants and bond lengths of two-dimensional honeycomb structures in various compounds of boron, carbon, and nitrogen; the two-dimensional bonds are discriminated clearly from the one- and three-dimensional bonds. We detected a librational mode of carbon hexagons in B C3; a peculiar mode for a large unit cell of honeycomb sheets such as the 2×2 structure of monolayer graphite and B C3. The restoring force related with the bond bending is insensitive to the change in the B-C bond length.