Topological insulators (TIs) have attracted a lot of attention in condensed matter physics in recent years. Materials such a conventional insulator have an energy gap in the bulk, but they cannot be linked to the ordinary insulators by adiabatic change without closing the gap. The two-dimensional (2D) TIs (3D TIs) have gapless edge states (surface states), which are topologically protected by time reversal symmetry resulting the robustness against nonmagnetic scattering. Such properties make TIs perfect candidates for low dissipation spintronic devices, magnetic devices, lasers and transistors, and the discovery of topological phase with large energy gap in the bulk as well as their theoretical and empirical understanding have attracted a lot of attention. In addition, the TI phase in some 2D materials can be improved or induced by applying electric feld, strain or functionalization. Our = goal is to use tools such as the Tight-Binding (TB) Approximation to explain and possibly predict interesting behaviors in such materials. Honeycomb structures of group IV elements have been considered as suitable suggestions as 2D TIs. Here we consider hydrogenated germanium-tin monolayer (ML GeSnH2), which have shown by Density Functional Theory (DFT) calculations that this ML can be transformed into a large band gap TI by applying biaxial tensile strain. We propose an e?ective TB Hamiltonian with spin-orbit coupling for ML GeSnH2 near the Fermi level. The parameters of the TB model will be calculated by ftting procedure. Our model predicts a phase transition from normal insulator (NI) to TI phase at 7:5% biaxial tensile strain in agreement with DFT calculations. Also, we will show the existence of topologically protected gapless edge states in zigzag nanoribbons of GeSnH2 in the presence of biaxial strain. We will study the other interesting electronic properties of this system by computing the quantum traort properties of disordered GeSnH2 nanoribbons using landauer-buttiker formalism, which allows us to determine the universality class of the conductance ?uctuations in di?usive regime. By numerically calculating the electronic traort in the presence of disorder and considering the symmetry of the system, we will investigate the universality of the conductance ?uctuations in the absence and presence of a magnetic feld. We also will investigate the formation of Landau levels by applying an external magnetic feld to ML GeSnH2 in TI phase. It will be shown that an external applied magnetic feld produces a special phase which is a combination of the quantum Hall (QH) and quantum spin Hall (QSH) phases and at a critical magnetic feld strength the QSH phase completely disappears
