Description of the electronic structure of periodic crystalline solids is usually based on extended Bloch functions (BF’s). Bolch functions are obtained by diagonalization of the effective one-electron Hamiltonian. These states are assigned with quantum number k for the crystal momentum, together with a band index n. Therefore this representation is suitable for description of reciprocal space properties, e.g. band structure, Fermi surface, … . But these functions are not useful for describing real space properties of electron such as conductance. An alternative description can be derived in terms of localized Wannier functions (WF’s), which are defined in real space via Fourier transformation performed on the Bloch functions. In contrast to BF’s, WF’s are useful, for example, in visualizing chemical bonds or in describing the dielectric properties of insulator materials. Wannier functions can be used as an accurate and minimal basis set in the construction of model Hamiltonian for large-scale systems and for efficient computation of material properties such as the Hall coefficient and anomalous Hall coefficient. K-space derivatives can be taken analytically via determining matrix elements of operator between WF’s. Therefore quantities such as group velocity and effective mass can be calculated with Wannier interpolation. However one major problem in practical calculations with this representation is the non uniqueness of WF’s, related to the phase arbitrariness of the BF’s. Marzari and Vanderbilt have solved this non uniqueness with introducing spread functional and minimizing it with respect to the variety of BF’s. They have called it Maximally Localized Wannier Functions(MLWF’s) . The locality of MLWF’s can be exploited to compute band structure, density of states at the modest computational cost. On the other hand, production and injection of spin polarized current into a semiconductor devices are very important. Half-metallic ferromagnetisms because of have 100% spin polarization at the Fermi level, are promising materials for efficient spin injection into semiconductor. The recent discovery of ferromagnetism in CrAs thin films grown on GaAs has attracted increasing interest in the CrAs/GaAS interface. In this thesis, by using
