Nearly-flat bands with nontrivial topology

TL;DR

This paper introduces a class of 2D tight-binding models with nearly-flat bands and nonzero Chern numbers, which can be realized with short-range hopping and may enable fractional quantum Hall states.

Contribution

The authors present new 2D tight-binding models with topologically nontrivial flat bands requiring only short-range hopping, unlike previous models needing nonlocal hoppings.

Findings

Discovery of models with nearly-flat bands and nonzero Chern numbers

Potential realization of fractional quantum Hall states in real materials

A practical square-lattice three-band model with only nearest-neighbor hopping

Abstract

We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands 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. Due to the similarity with 2D continuum Landau levels, these topologically nontrivial nearly-flat bands 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 flat band aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.