Confined states and topological phases in two-dimensional quasicrystalline -flux model

2次元準結晶フラックスモデルにおける閉じ込め状態とトポロジカル相

Ghadimi, R.*; Hori, Masahiro*; 杉本 貴則*; 遠山 貴己

Ghadimi, R.*; Hori, Masahiro*; Sugimoto, Takanori*; Toyama, Takami

Motivated by topological equivalence between an extended Haldane model and a chiral--flux model on a square lattice, we apply -flux models to two-dimensional bipartite quasicrystals with rhombus tiles in order to investigate topological properties in aperiodic systems. Topologically trivial -flux models in the Ammann-Beenker tiling lead to massively degenerate confined states whose energies and fractions differ from the zero-flux model. This is different from the -flux models in the Penrose tiling, where confined states only appear at the center of the bands as is the case of a zero-flux model. Additionally, Dirac cones appear in a certain -flux model of the Ammann-Beenker approximant, which remains even if the size of the approximant increases. Nontrivial topological states with nonzero Bott index are found when staggered tile-dependent hoppings are introduced in the -flux models. This finding suggests a direction in realizing nontrivial topological states without a uniform magnetic field in aperiodic systems.