Topology in the Sierpiński-Hofstadter problem
Topology in the Sierpiński-Hofstadter problem
Using the Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski carpet and gasket, we investigate whether fractal lattices embedded in two-dimensional space can support topological phases when subjected to a homogeneous external magnetic field. To this end, we study the localization property of eigenstates, the Chern number, and the evolution of energy level statistics when …