Quantum Oscillations in Two Dimensional Dirac and Weyl Semimetals

Since the discovery of the exotic properties of graphene, two dimensional materials such as metal chalcogenides, transition metal oxides and other 2D compounds have gained renewed interest. Graphene, silicene, germanene, graphyne and boron allotropes form a rare class of 2D Dirac materials. The presence of such Dirac points near the Fermi level provides us the option to switch between two carrier types by slightly doping the material and could lead to potential optoelectronic devices. Recently discovered sister compounds WTe₂[2] and MoTe₂[62] have gained significant impetus for extremely pronounced nonsaturating magnetroresistance and topological semimetal hosting type II Weyl points. Further, a new class of two dimensional materials with multiple Dirac cones were discovered following the compound Zr₂Te₂P , and include the compounds Hf₂Te₂P , Zr₂Te₂As and Ti₂Te₂P. Quantum oscillation studies were performed to investigate the detailed Fermi surfaces and the topological properties such as Berry phase were obtained for the newly discovered two dimensional materials at the National High Magnetic Field Laboratory. In this thesis we will address the electronic structure, density of states and Fermi surface in all of these materials using Density Functional Theory and related methodology. The low energy (near Fermi energy) physics of all the materials studied are characterized by Dirac-like or Weyl- like electronic structure. Namely, the electrons obey Dirac-like or Weyl-like equations where the speed of light is replaced by the Fermi velocity. Furthermore, these materials share fundamental topological properties at the electronic low energy spectrum. Therefore, we wish to undertake the task of studying such fundamental properties from first principles.