A dark state of Chern bands: Designing flat bands with higher Chern number

Abstract

We introduce a scheme by which flat bands with higher Chern number |C| > 1 can be designed in ultracold gases through a coherent manipulation of Bloch bands. Inspired by quantum-optics methods, our approach consists in creating a “dark Bloch band" by coupling a set of source bands through resonant processes. Considering a Λ system of three bands, the Chern number of the dark band is found to follow a simple sum rule in terms of the Chern numbers of the source bands: CD = C1 + C2 − C3. Altogether, our dark-state scheme realizes a nearly flat Bloch band with predictable and tunable Chern number CD. We illustrate our method based on a Λ system, formed of the bands of the Harper-Hofstadter model, which leads to a nearly flat Chern band with CD = 2. We explore a realistic sequence to load atoms into the dark Chern band, as well as a probing scheme based on Hall drift measurements. Dark Chern bands offer a practical platform where exotic fractional quantum Hall states could be realized in ultracold gases.