Topological flat bands on porous models

Abstract Topological flat bands (TFBs) play a crucial role in the study of fractional Chern insulators (FCIs). However, the flatness of the TFBs is commonly sensitive to the hopping parameters and to obtain TFBs usually requires long-range hopping terms which lead to a tedious process to find TFBs in a large parameter space. In this paper, we report that TFB models are obtained in the porous models by tuning the finite neighbor hopping potentials and the staggered magnetic fluxes. As concrete examples, two porous network models are considered, the graphenylene-like and the porous-honeycomb models, which contain 12 and 18 atoms in supercells, respectively. TFBs with Chern number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> appear with the nearest-neighbor hopping term and staggered magnetic fluxes because of the existence of nanoholes. By considering the next-nearest-neighbor hopping process with staggered magnetic fluxes, the TFBs with a high Chern number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">C</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> are achieved. Subsequently, several FCIs are systematically investigated when hard-core bosons are filled into these TFB models. Our study provides a compelling pathway for the realization of TFBs in two-dimensional materials with nanoholes.