Tight binding model of ab stacked bilayer graphene

AB stacked Bilayer graphene is a material of huge scientific interest due to the promise of superior electronic properties even when compared to monolayer graphene due to more ?? orbital overlaps in the x-y plane. In this research the Nearest Neighbor Tight-Binding (NNTB) model of AB stacked bilayer graphene will be developed. Using this NNTB approximation, a numerical analysis simulator that uses the Non- Equilibrium Greens Function (NEGF) equations to describe the quantum transport of the electrons in the bilayer graphene crystal is built using MATLAB. From this numerical analysis simulation, various metrics of interest such as the E-K dispersion relation, density of states (DOS) and the transmission coefficients will be obtained for each of the specified lattice width and length. Electronic properties of two variants of the bilayer graphene are investigated in this simulation, which are the zigzag edge and the armchair edge types. The program constructs a fitting device Hamiltonian for the NEFG equation from the specified type, width, and length. The NEGF simulation obtains the solution for the dispersion relation, DOS and transmission coefficient for each of the eigen energies iteratively until the solution converges to a minimum error threshold value. The DOS simulation showed there is a huge concentration of quantum states in the mid-band for the zigzag edge, and for the armchair edge the number of states is the largest at the 1st quartile-band and 3rd quartile-band region. Transmission coefficient of both zigzag and armchair edges show similar distribution throughout the energy spectrum; however, the coefficients magnitude of the zigzag edge is larger. Dispersion relation of zigzag edge showed no bandgap, though the armchair edge showed an alternating trend of semiconducting (with bandgap) from the 3n-1 and 3n series and metallic (no bandgap) for 3n+1 series in agreement with contemporary research