Nearly Flatbands with Nontrivial Topology

TLDR

The authors contrast their short‑range hopping models with prior work that required nonlocal hoppings, noting that their Hamiltonians could be realized in cold‑atom systems. The study aims to elucidate the physics of topological flatbands by analyzing a minimal two‑band checkerboard‑lattice model. They employ a minimal two‑band model on a checkerboard lattice to probe the flatband physics. They theoretically discover 2D tight‑binding models with nearly flatbands carrying nonzero Chern numbers, short‑range hopping, and the potential to realize fractional anomalous quantum Hall states, and the most promising is a square‑lattice three‑band model with only nearest‑neighbor hopping.

Abstract

We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flatband aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.