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arXiv:2506.11520 · Physical Review A

Topologically nontrivial and trivial flat bands via weak and strong interlayer coupling in twisted bilayer honeycomb optical lattices for ultracold atoms

Wenjie Sui, Wei Han, Zheng Han, Zengming Meng, Jing Zhang

Published Jun 6, 2025• 4 citations
arXivHTMLPDF

Abstract

In recent years, flat electronic bands in twisted bilayer graphene (TBG) have attracted significant attention due to their intriguing topological properties, extremely slow electron velocities, and enhanced density of states. Extending twisted bilayer systems to new configurations is highly desirable, as it offers promising opportunities to explore flat bands beyond TBG. Here, we study both topological and trivial flat bands in a twisted bilayer honeycomb lattice for ultracold atoms and present the evolution of the flat bands with different interlayer coupling strength (ICS). Our results demonstrate that an isolated topological flat band can emerge at the Dirac-point energy for a specific value of weak ICS, referred to as the ``critical coupling.'' This occurs over a wide range of twist angles, surpassing the limits of the magic angle in TBG systems. When the ICS is slightly increased beyond the critical coupling value, the topological flat band exhibits degenerate band crossings with both the upper and lower adjacent bands at the high-symmetry ${\mathrm{\ensuremath{\Gamma}}}_{s}$ point. As the ICS is further increased into the strong coupling regime, trivial flat bands arise around Dirac-point energy. Meanwhile, more trivial flat bands appear, extending from the lowest to higher energy bands, and remain flat as the ICS increases. The topological properties of the flat bands are studied through the winding pattern of the Wilson loop spectrum. Our research provides deeper insights into the formation of flat bands in ultracold atoms with highly controllable twisted bilayer optical lattices, and may contribute to the discovery of new strongly correlated states of matter.

DOI
10.1103/physreva.111.063306

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Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.