Band gap opening in graphene: a short theoretical study

Graphene, being a gapless semiconductor, cannot be used in pristine form for nano-electronic applications. Therefore, it is essential to generate a finite gap in the energy dispersion at Dirac point. We present here the tight-binding model Hamiltonian taking into account of various interactions for tuning band gap in graphene. The model Hamiltonian describes the hopping of the π-electrons up to third nearest-neighbours, substrate effects, Coulomb interaction at two sub-lattices, electron–phonon interaction in graphene-on-substrates and high phonon frequency vibrations, besides the bi-layer graphene. We have solved the Hamiltonian using Zubarev’s double time single particle Green’s function technique. The quasi-particle energies, electron band dispersions, the expression for effective band gap and the density of states (DOS) are calculated numerically. The results are discussed by varying different model parameters of the system. It is observed that the electron DOS and band dispersion exhibit linear energy dependence near Dirac point for nearest-neighbour hopping integral. However, the second and third nearest-neighbour hoppings provide asymmetry in DOS. The band dispersions exhibit wider band gaps with stronger substrate effect. The modified gap in graphene-on-substrate attains its maximum value for Coulomb interaction energy UC = 1.7 t₁ . The critical Coulomb interaction is enhanced to UC = 2.5 t₁ to produce maximum band gap in the presence of electron–phonon interaction and phonon vibration. The bi-layer graphene exhibits Mexican hat type band gap near Dirac point for transverse gating potential. The other conclusions for the present work are described in the text.