Topological Quantum Phase Transitions And Topological Flat Bands Of Electrons On The Two-dimensional Kagome Lattice

Recently, in the Condensed Matter Physics field, the study of the topological quantum phase transitions and topological states has progressed significantly in the past several years. Topological states of matter are quantum states which are distinguished from ordinary states by nontrivial topological property, and are intrinsically related to the topologically invariant Chern number. In1988, in the well-known Haldane model, it obtains some corresponding results. At the same time, the topological bands (TB) with nonzero Chern numbers have also obtained a major breakthrough. It has been also found in some other two-dimensional lattice models which are more or less as similar as the original Haldane model, such as checkerboard lattice、kagome lattice、Lieb lattice and star lattice et.al. In recent years, it is noteworthy that topological flat bands (TFBs) with nonzero Chern numbers have been proposed in some2D lattice systems. The proposals of TFBs point out a possible new avenue to realize the FQHE.In this article, we will study the tight-binding electronic peculiar properties on the2D kagome lattice, mainly on the property of the energy spectrum, the density of states, the Hall conductance as well as the edge-state spectrum et al. Firstly, we revisit the basic properties of the tight-binding electrons on the kagome lattice, next the electronic properties is discussed under the two staggered magnetic fluxes and non-Abelian flux. With the variation of fluxes, it leads to quantum Hall transitions and the Chern numbers of Landau subbands are redistributed between neighboring pairs. Here, we mainly focus on the next-nearest-neighbor hopping integral t2with the staggered magnetic flux φ2on the kagome lattice, and when consider the mutative t2and φ2, it can lead the TQPTs. With the two kinds of staggered magnetic fluxes φ1and φ2fixed,when tuning the parameter t2from O to1,we have observed a series of TQPTs and the Chern numbers of the three bands are found to change from C={-1,0,+1} to C={-1,+2,-1} and then to C={+3,-2,-1}.With the parameter t2and the filux φ1fixed,when tuning the flux φ2from0to2π,we also have observed a series of TQPTs and the Chern numbers of the three bands are found to change from C={-1,+2,-1} to C={+1,-2,+1} and then to C={-1,0,+1}.When we consider the parameters t2、φ1and φ2,the system exhibits topological flat bands with nonzero Chern number.In some specific parameter regions,the flatness ratio(the ratio of the band gap over the band width)can be up to170and the TFB with the Chern number C=±1.Finally,we show this system to the non-Abelian gauge fields with fluxes α and β,the subbands have changed in the numbers,as well as the massless Dirac fermions have changed in the numbers and locations. Based on the non-Abelian magnetic fluxes, we also consider the Zeeman splitting g and the next-nearest-neighbor hopping integral t2in order to get a band gap,and the bands have Chern number C:±1.The major achievements of the essay have been submitted(J.Phys.: Condens.Matter,the first author).