Abstract
The focus of this thesis is the study of the electronic and vibrational properties of single layer graphene, silicene and germanene, and bilayer graphene and silicene. Specifically the electronic band structure and Fermi velocity of the carriers as well as the phonon dispersion are calculated; Raman active modes are identified as well. Material stability and electron-phonon effects are also investigated. It is found that in both silicene and germanene linear band dispersion behaviour is found in a planar and a low buckling configuration where the Fermi velocity is 5 105 m/s; about 35% lower than in graphene. From the phonon dispersion curves, the electron-phonon coupling matrix elements are shown to be about a factor of 25 lower when compared with graphene. The applicability of the Born-Oppenheimer approximation to carrier relaxation in silicene and germanene is found to be invalid, as it is in graphene. The phonon dispersion curves show that free-standing bilayer graphene with AB stacking is stable whereas AA stacking is marginally unstable and an optical identification method to distinguish between the two different stacking configurations is proposed. Results for bilayer silicene show there are eight geometries with an energy minimum; it is found that a low buckling AA and a high buckling AA’ stacking configuration have the lowest energies for their groups. Metallic properties are found for all configurations although unusual band structure is found in low buckling forms including linear dispersion behaviour in AA’ form (vf ≈ 5.3 105 m/s). The phonon dispersion curves show that only AB stacked low buckling bilayer silicene was completely stable although it had a higher energy state than AA stacking. The high buckling configuration also shows significant changes to the properties of in-plane vibrational modes suggesting that they can be controlled or engineered by the introduction of additional layers.