Ikı boyutlu ve ıkı boyutumsu malzemelerın sıkı bağ metoduyla modellenmesı

Since the advent of graphene, two-dimensional (2D) materials have consistently been studied owing to their exceptional electronic and optical properties. While graphene is completely two-dimensional in nature, its other analogues from the group IV A elements in the periodic table have been proven to have a low-buckled structure which adds up the exotic properties exhibited by them. The semiconductor industry is striving for such materials exhibiting exotic electronic, optical and mechanical properties. In this thesis work we are primarily working towards a generalized tight-binding (TB) model for the 2D family of group IV A elements. Graphene has been studied extensively and we have successfully reproduced its energy band-structure accounting up to the third nearest neighbor contributions. The results have been checked extensively by performing simulations over a large set of avail- able parameters and are found to be accurate. The other graphene analogues (viz; silicene, germanene and stanene) exhibiting a hexagonal 2D structure have been reported to have a buckling associated to them. We have analytically built up a TB model by considering the orbital projections along the bond length which accounts for the buckling in these 2D structures. Electronic band-structures have been reproduced and compared by taking into account the nearest neighbor and next-nearest neighbor contributions. Since these Structures exhibit a Dirac like cone at the Dirac point and showing linear dispersion, study of electronic band-structures in detail becomes indispensable. After the famous Kane and Mele paper on Quantum Spin Hall Effect in Graphene, condensed matter physicists have been looking for similar phenomena in other 2D materials. We have successfully included the spin-orbit coupling (SOC) contribution to our unperturbed Hamiltonian and were able to produce splitting around the Dirac points. Since, Silicene and its other analogues exhibit same structure with different amount of buckling, we were able to track down the whole energy band-structure. Alongside this thesis also focuses on calculating optical properties of these materials. In essence, this thesis work is an insight to the electronic and optical properties of the hexagonal 2D structures from the carbon family group. Derived structures from these 2D materials (viz; quantum dot, nano ribbon) could easily be studied utilizing the tight-binding formulation presented here. The proposed future work is the inclusion of nitrides and transition metal dichalcogenides (TMDCs) in the TB model.