Solving the secular equation of the system for eigenenergy – 2D hexagonal materials

Abstract With the advent of the metal–insulator transition (MIT) as a tool for adjusting the properties of lower dimensions materials, with nanoscale dimensions in one or more of the coordinate directions, it is worthwhile to derive analytical formulas for the electronic energy in k-space, for a generic two-dimensional hexagonal lattice as a prelude for their use in nanoscopic transport devices (using the MIT) or other solid state devices. This is done in the tight binding (TB) approximation, since it allows a tractable analytical development, with some refinements possible. This lattice structure is applicable to many 2D materials like graphene, BN, MoS2, and many others. This chapter treats the exact solution based upon the Hamiltonian matrix elements (Section 5.1 ), an approximate solution viewing various parameters as possessing orders (Section 5.2 ), unnormalizing the parameters in eigenenergy (Section 5.3 ), and unnormalizing the eigenenergy (Section 5.4 ).