Topological materials with topological phases are a new branches of matterials that have ed many physicists to study in this area . These phases are different from other phases of matter thanks to their topological aspects.They are conductors in their surfaces and are insulators in bulk that can be distinguished by topological invariant from other phases . There are many ways to make these phases, for instance, exposing a honycomb lattice to a high magnetic field at very low temperature . It was proposed by Haldane in 1988 when he was working on a graphene lattice . He was able to introduce the first topological invariant named chern number that is only zero in absence of high magnetic field . Another way was identified by Kane and Mele in 2005 . In their model they could reach to topopogical phase by assuming a great interaction between spin of fermions and their angular momentom and introduced a topological invariant named . In this thesis we have studied the energy bands of honycomb lattice in presence of spin-orbit coupling and draw their phase diagrams . Finally we have studied the effect of uniaxial strain on the topological phase and have compared our results with other studies .
