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 $\Lambda$ 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: $C_D=C_1+C_2-C_3$. Altogether, our dark-state scheme realizes a nearly flat Bloch band with predictable and tunable Chern number $C_D$. We illustrate our method based on a $\Lambda$ system, formed of the bands of the Harper-Hofstadter model, which leads to a nearly flat Chern band with $C_D=2$. 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.

arXiv comment25 pages, 7 figures, including Appendices. Substantial revisions, including a mathematical proof of the sum rule

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Cited by in corpus (6)

• Topological features of Haldane model on a dice lattice: role of flat band on transport properties
• Isolated flat bands in 2D lattices based on a novel path-exchange symmetry
• Novel topological phases of a semi-Dirac Chern insulator in presence of extended range hopping
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• Simulating a Chern Insulator with C = $\pm$2 on Synthetic Floquet Lattice