School of Science Department of Physics 62 Theoretical Study of Properties of Real Materials Supervisor: LIU Junwei / PHYS Student: KWOK Yuk Lam / PHYS-IRE Course: UROP2100, Fall In order to obtain information about crystal lattices, such as band structure and density of wave function, a Python package is built. The final target is that it works for arbitrary crystal lattices the user wish to understand. This report describe the outline of the codes and provides further explanations for important parts and concepts. We have also built a self-checking function that could verify our calculated Hamiltonian in the k-space from symmetries. To demonstrate our results, we present two examples in 2-dimension and 3- dimension respectively. Finally, as this is an ongoing project, our future directions would be discussed. Theoretical Study of Properties of Real Materials Supervisor: LIU Junwei / PHYS Student: LIU Yidai / PHYS-IRE Course: UROP1100, Spring Graphene is a strictly 2D crystal exhibiting many outstanding physical properties. Though having a short history, it has already shown great potential in both theoretical study and application. In this report, the energy bands of graphene are calculated using the tight-binding model, the existence of Dirac cones is derived using different methods, the energy bands are classified into pi and sigma bands, and the characteristic features such as the merging of bands at symmetry points are studied form the symmetry point of view. Theoretical Study of Properties of Real Materials Supervisor: LIU Junwei / PHYS Student: NGUYEN Xuan Tan / PHYS-IRE Course: UROP1100, Spring UROP2100, Summer The crystalline structure of CrSb in the NiAs phase exhibits interesting magnetic properties as the spins of Cr atoms lies along the c axis, with ferromagnetic (FM) couplings between Cr atoms within the hexagonal basal plane and antiferromagnetic (AFM) couplings between adjacent planes. The layered antiferromagnetic order of this material, in addition to its large spin-orbit coupling and high Néel temperature, can empower possible future applications in AFM spintronics. To understand the electronic and spintronic properties of CrSb, an eight-band tight-binding model is formulated and the electronic band structure is analysed using the spatial symmetry group of the crystal.