Effect of Jumping Energy Coefficient on Armchair-Type Graphene Energy Gap

This work examines the electronic band structure of bilayer armchair-type graphene nanoribbons arranged in the AB stacking pattern. The investigation is conducted using the long-wave generalised effective Hamiltonian and the tight approximation method. This investigation involved calculating the energy gap values for various electron hopping energy levels between two layers. Additionally, the widths were varied from N = 1 to N = 10, with increments of 5 until reaching N = 50. An evident correlation was detected between the electron hopping energies and the energy gap and width of the nanoribbon. Specifically, as the electron hopping energy dropped, both the energy gap and the breadth of the nanoribbon increased. The nanoscale had a non-uniform impact on the energy gap values, unlike the abrupt change in energy caused by certain boundary conditions when solving the Schrödinger equation around the Dirac points K in the Fermi plane. At certain values, the material exhibits metallic behaviour, while at others it acts as a semiconductor. Hence, this study provides valuable insights into the properties of graphene. Theoretical confirmation suggests that the energy gap can be manipulated by adjusting the hopping energies of electrons between two layers of armchair-type graphene nanoribbons with a specific stacking pattern (AB-AB). Additionally, the width of the nanoribbon also influences this effect.