Correlation Effects And Topological Electronic Properties In Graphene-like BC₃ Adsorption System

Since the preparation of graphene by Novoselov, the researches on graphenelike nanomaterials rise as one frontier of condensed matter physics. A serial of graphenelike nanomaterials such as BN, Silicene are fabricated and investigated. The electronic properties of these graphenelike nano-materials can be tuned through various methods such as cropping,wrapping, adsorption and creating defects, thus transformed to various functional materials. Through doping graphene with boron atoms, we could obtain another graphenelike nano-materials: BC3. Since boron is an electron-deficient element, the binding strength of graphenelike BC3 with metallic atoms is much stronger than graphene. The covalent electrons of metallic adatoms transfer to the conduction band of BC3, which introduces electron doping. This leads to rich physical properties of doped BC3. In this thesis, we employ first principles calculations, renormalization group and cluster expansion to investigate the adsorption of alkali and Tl adatoms on BC3, as well as the resulting electron correlation e?ects and topological electronic structures.Our first principles calculations show that the covalent s electrons of alkali adatoms transfer to BC3 substrate and fill the first conduction band. When the adatom concentration reaches one adatom per unit cell, the Fermi level crosses the Van Hove singularity of the first conduction band. The density of states near the Fermi level show the logarithm divergence, which leads to ferromagnetic instability. The band structures show Fermi surface nesting which implies spin density wave instability. These two instabilities compete and induce rich magnetic properties in doped BC3. When strain is applied, the Fermi surface changes and the competition between di?erent magnetic instabilities is tuned. The strain derived quantum phase transitions are demonstrated by our calculations. We further investigate the one dimensional doped BC3 system. The first principles results show that the magnetism in one dimensional doped BC3 system is more stable than that in two dimensional system. The half metallicity emerges in particular one dimensional doped BC3 structures.We investigate the possibility of superconductor in doped BC3. We fit the tight binding Hamiltonian of the first conduction band using the first principles results and construct a Hubbard model. We employ renormalization group to calculate the renormalization flow of the interaction between electrons and the resulting order states. The results show that the p + ip′topological superconductor is the ground state in the weak coupling limit. The ferromagnetic state is the ground state when the Hubbard U is large. When the spin orbit coupling is taken into account, the random phase approximation calculations show that the time invariant p + ip′topological superconductor is the ground state.The adsorption of Tl atoms is investigated through first principles method. Our results shows that the 6p covalent electrons of Tl atoms transfer to BC3 and fill the first conduction band. When Tl concentration reaches two adatoms per unit cell, the Fermi level reaches the Dirac point. In the systems with weak intervalley scattering, the Dirac cone is invulnerable to the adsorption. Due to the strong spin-orbit coupling of Tl atoms,a spin-orbit gap of 0.26 eV opens at the Dirac point. In the system with strong intervalley scattering, the topological electronic properties of the adsorbed BC3 depend on the competition between intervalley scattering and spin-orbit coupling, namely depend on the adsorption configuration. The cluster expansion method is employed to calculate the most stable ordered structures of Tl atoms on BC3, as well as the corresponding topological electronic properties.