ABSTRACT
To fully comprehend the essential electronic properties of 2D condensed matter with the significant geometric symmetries, the intrinsic atomic interactions, and any external fields, this chapter proposes the generalized tight-binding model to diagonalize the various Hamiltonians efficiently. The field-induced independent Hamiltonian matrix elements will be derived in the analytic form, especially for those under a uniform perpendicular magnetic field. Finally, a giant magnetic Hermitian matrix can be accurately solved by the exact diagonalization method. The bilayer AB-bt silicene system is very suitable for a full understanding of the magneto-electronic theoretical model, mainly owing to the observable buckling structure, the comparable intralayer and interlayer hopping integrals, and the significant layer-dependent spin-orbital interactions. In general, there are two kinds of theoretical models in studying the magnetic quantization phenomena, namely, the low-energy elective-mass approximation and the tight-binding model.
