Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers
Many-body ground states from decomposition of ideal higher Chern bands: Applications to chirally twisted graphene multilayers
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DOI：
10.1103/physrevresearch.5.023166
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发表时间：
2023-06-01
影响因子：
4.2
通讯作者：
Vishwanath, Ashvin
中科院分区：
文献类型：
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作者：
Dong, Junkai;Ledwith, Patrick J.;Vishwanath, Ashvin
受扭曲石墨烯多层膜的高陈恩带的激励，我们考虑具有理想量子几何的任意陈恩数C的平带。虽然C bbb101带与朗道能级不同，但我们发现这些带具有精确的分数阶陈氏绝缘子（FCI）基态，用于短程相互作用。我们展示了如何将理想的高陈氏带分解成单独的陈氏数为1的理想带，这些理想带通过平移和旋转对称交织在一起。分解带具有实空间和动量空间平移相结合的SU(C)作用。值得注意的是，它们还允许解析构建精确的多体基态，例如广义量子霍尔铁磁体和fci，包括在短程相互作用极限下的风味单线态Halperin态和Laughlin铁磁体。在此极限下，SU(C)作用提升为基态子空间上的对称性。风味单重态是平移对称的，风味铁磁体对应于平移破碎态，并允许带电斯基米子激发，对应于空间变化的密度波形。我们通过对扭曲手性多层石墨烯理想带的数值模拟证实了我们的分析预测，并讨论了相对于Bernal双层扭曲的单层石墨烯等实验可获得系统的结果。
Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C > 1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short-range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground-state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.