Topological Quantum Phase Transitions And Topological Flat Bands On The Two-Dimensional Star Lattice

In the field of condensed matter physics according to the different physical properties, material can be divided into different states of matter, such as Solid, Liquid, Gas and Plasma and so on. Over past decade years, topological quantum states of matter have shed new light on the forefront of condensed matter physics. Haldane was pioneering to introduce a two-band tight-binding model on the two-dimensional (2D) honeycomb lattice with hopping integrals modulated by staggered magnetic fluxes, and this simple two-band model is considered as the prototype example of topological band insulators. There are two types of insulating states in the Haldane model when the lower band is fully filled and the upper band is empty, and the distinction between them is the topological property of the. occupied lower band which is encoded into the Chern number:A trivial Chern number C=0corresponds to a normal band insulator, while a nontrivial Chern number C=±1corresponds to a topological band insulator. Topological bands with nonzero Chern numbers have also been found in some other two-dimensional lattice models which are the natural extensions of the original Haldane model, e.g., the checkerboard lattice, the kagome lattice, the Lieb lattice, and the square-octagon lattice. Recently, a series of lattice models with the nontrivial topological flat bands (TFBs)have been proposed in some two-dimensional lattice systems. Proposals of TFBs have provided a possible route to realize the intriguing fractional quantum Hall effect (FQHE) without Landau levels (LLs) as demonstrated in the recent systematic numerical works. Such TQPTs and TFBs in this star-lattice model might be possible to be realized in optical lattices by manipulating cold atoms, considering the very recent experimental advances of creating artificial staggered gauge fields.Here, we study a tight-binding model on the star lattice (also called the decorated honeycomb lattice or the triangle-honeycomb lattice) with staggered fluxes and short range hoppings. We discuss topological quantum phase transitions (TQPTs) when tuning the next-nearest-neighbor parameter t2,while the others being fixed and observe some topological bands with high Chern numbers.and we explain that parabola and so-called Fermi pocket are account for high Chern numbers.when tuning the parameter t2from0.0to1.0, we have observed a series of TQPTs and the Chern numbers of the six bands are found to change from C={+1,0,0,0,0,-1} to C={-1,+2,0,0,-2+1} and then to C={-1,-1,+3,-3,+1,+1}. Besides, we find that in some parameter regions, the system exhibits interesting topological flat bands with Chern number. C=-1and a large gap above them, and the flatness ratio of the band gap over the bandwidth can be as high as85. Such a TFB has also been demonstrated to be another ideal platform for realizing a robust1/2FQHE of interacting hard-core bosons without LLs by the exact diagonalization (ED) Method. The major achievements of the article have been published(Phys.Rev.B, the first author).