三维Lieb lattice模型的能谱结构

Energy spectrum of 3D Lieb lattice model

Lieb lattice模型的特殊拓扑结构导致其具有异常的能谱结构,比如零能平带、低能下的狄拉克能谱等。选取2种三维Lieb lattice模型,分别写出其在动量空间中电子跃迁的哈密顿矩阵,将该哈密顿矩阵对角化可计算出其能谱。结果显示若不考虑自旋轨道耦合作用,其能谱图像由3条能带组成,且3条能带交于动量空间一点没有能带间隙。若在其次近邻跃迁上施加自旋轨道耦合作用则可以在能带间打开间隙,且随着自旋轨道耦合强度的增加其能带间隙也将逐渐增大。因此,可以得到结论三维Lieb lattice模型与二维Lieb lattice模型相似,若想在其能带间打开一个完整的能带间隙则可以在模型的次近邻跃迁上施加自旋轨道耦合作用。随着其能带间隙的打开,该模型所呈现出的物态也将由拓扑半金属态转变为拓扑绝缘体态。

The special topological structure of the Lieb lattice model causes it to have abnormal energy spectrum structures,such as zero-energy flat band,Dirac energy spectrum at low energy,etc.We choose two kinds of 3D Lieb lattice models and the Hamiltonian matrix of electron hopping are denoted in momentum space respectively.The energy spectrum is calculated by diagonalizing the Hamiltonian matrix.The results show that the energy spectrum consists of three energy bands without considering the effect of spin-orbit coupling,and the three bands intersect at a point without an energy band gap.If the spin-orbit coupling is applied to the next-neighbor transition,the gap can be opened between the energy bands,and the band gap will gradually increase with the increase of the spin-orbit coupling strength.Therefore,it can be concluded that the 3D Lieb lattice model is similar to the 2D Lieb lattice model.In order to open a complete gap between the energy bands,spin orbital coupling can be applied to the second-nearest neighbor hopping of the model.With the opening of its energy band gap,the physical state presented by the model will also change from the topological semimetal state to the topological insulator state.