It has been widely accepted that silicene is a topological insulator, and its gap closes first and then opens again with increasing electric field, which indicates a topological phase transition from the quantum spin Hall state to the band insulator state. However, due to the relatively large atomic spacing of silicene, which reduces the bandwidth, the electron–electron interaction in this system is considerably strong and cannot be ignored. The Hubbard interaction, intrinsic spin orbital coupling(SOC), and electric field are taken into consideration in our tight-binding model, with which the phase diagram of silicene is carefully investigated on the mean field level. We have found that when the magnitudes of the two mass terms produced by the Hubbard interaction and electric potential are close to each other, the intrinsic SOC flips the sign of the mass term at either K or K for one spin and leads to the emergence of the spin-polarized quantum anomalous Hall state.
In recent years,three-dimensional topological insulators(3DTI) as a novel state of quantum matter have become a hot topic in the fields of condensed matter physics and materials sciences.To fulfill many spectacularly novel quantum phenomena predicted in 3DTI,real host materials are of crucial importance.In this review paper,we first introduce general methods of searching for new 3DTI based on the density-functional theory.Then,we review the recent progress on materials realization of 3DTI including simple elements,binary compounds,ternary compounds,and quaternary compounds.In these potential host materials,some of them have already been confirmed by experiments while the others are not yet.The 3DTI discussed here does not contain the materials with strong electron-electron correlation.Lastly,we give a brief summary and some outlooks in further studies.
By solving the total energy equation, we obtain the formula of exchange-correlation functional for the first time. This functional is usually determined by fitting experimental data or the numerical results of models. In the uniform electron gas limit, our exchangecorrelation functional can exactly reproduce the results of Perdew-Zunger parameterization from the jellium model. By making use of a particular solution, our exchange-correlation functional could take into accotmt the case of non-uniform electron density, and its validity can be confirmed through comparisons of the band structure, equilibrium lattice constant, and bulk modulus of aluminum and silicon. The absence of mechanical prescriptions for the systematic improvement of exchange-correlation functional hinders further development of density-functional theory （DFT）, and the formula of exchange-correlation functional given in this study might provide a new perspective to help DFT out of this awkward situation.
