Electronic Structures Of Dirac Fermion Systems

Dirac fermion systems,such as graphene and topological insulators,have been the focus of extensive research in condensed matter physics and material science in the past few years,due to their peculiar topological properties and attractive application potential in electronic devices.In this thesis,employing first-principles calculations based on maximally localized Wannier functions,we investigate the electronic structures of different Dirac fermion systems and develop a new theoretical computational method.Firstly,we investigate the physical origin of the existence or absence of Dirac cones in two-dimensional carbon-based materials.We find that acetylenic linkages in graphyne can be reduced into an effective hopping term between vertex atoms,and thus various graphynes may be described by a unified tight-binding model on a honeycomb lattice.Critically,whether Dirac cones exist or not in graphynes is determined by the combination of hopping terms.Based on the unified model proposed,several additional two-dimensional carbon-based materials are revealed to possess Dirac cones.Secondly,we present a general group theoretical method to unfold energy bands of supercell calculations to primitive Brillouin zone using group theoretical techniques,where an isomorphic factor group is introduced to connect the primitive translation group with the supercell translation group via a direct product.Originating from the translation group symmetry,our method gives an uniform description of unfolding approaches based on various basis sets,and therefore,should be easy to implement in both tightbinding model and existing ab initio code packages using different basis sets.This makes the method applicable to a variety of problems involving the use of supercells,such as defects,disorder,and interfacial reconstructions.Then,we analyze the emergence of Chern-insulating state from semi-Dirac systems.We demonstrate that a TiO2/VO2 heterostructure that was previously proposed as a prototypical semi-Dirac system becomes a Chern insulator(quantum anomalous Hall insulator)in the presence of spin-orbit coupling.We show that this occurs only when the semi-Dirac structure is of a special type(“type-II”)that can be formed by the merging of three conventional Dirac points.Our results reveal how the nontrivial topology with nonzero Chern number emerges naturally from this kind of semi-Dirac structure,establishing a general scenario that provides a new route to the formation of Chern-insulating states in practical materials systems.Moreover,we predict topological insulators in bismuth-based III-V semiconductors.We propose a general strategy to realize topological insulators in conventional III-V semiconductors by bismuth substitution and external strain.These proposed topological insulators can be easily integrated into various semiconductor electronic devices and modulated by well-developed modern semiconductor technologies.At last,we systemically investigate the electronic properties of the interface between quantum spin Hall(QSH)and quantum anomalous Hall(QAH)insulators.A robust chiral gapless state,which substantially differs from edge states of QSH or QAH insulators,is predicted at the QSH/QAH interface using an effective Hamiltonian model.Due to the physically protected junction structure,the interface state is expected to be more stable and insensitive than topological boundary states against edge defects and chemical decoration.Hence our results of the interface states provide a promising route towards enhancing the performance and stability of low-dissipation topological electronics in real environment.