Wang Jie, Liu Zhao
Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA.
Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China.
Phys Rev Lett. 2022 Apr 29;128(17):176403. doi: 10.1103/PhysRevLett.128.176403.
We propose models of twisted multilayer graphene that exhibit exactly flat Bloch bands with arbitrary Chern numbers and ideal band geometries. The models are constructed by twisting two sheets of Bernal-stacked multiple graphene layers with only intersublattice couplings. Analytically we show that flatband wave functions in these models exhibit a momentum space holomorphic character, leading to ideal band geometries. We also explicitly demonstrate a generic "wave function exchange" mechanism that generates the high Chern numbers of these ideal flatbands. The ideal band geometries and high Chern numbers of the flatbands imply the possibility of hosting exotic fractional Chern insulators which do not have analogues in continuum Landau levels. We numerically verify that these exotic fractional Chern insulators are model states for short-range interactions, characterized by exact ground-state degeneracies at zero energy and infinite particle-cut entanglement gaps.
我们提出了扭曲多层石墨烯模型，这些模型展现出具有任意陈数和理想能带几何结构的精确平坦布洛赫能带。这些模型是通过仅利用亚晶格间耦合来扭曲两层伯纳尔堆叠的多层石墨烯构建而成的。通过分析我们表明，这些模型中的平带波函数表现出动量空间全纯特性，从而导致理想的能带几何结构。我们还明确展示了一种通用的“波函数交换”机制，该机制产生了这些理想平带的高陈数。平带的理想能带几何结构和高陈数意味着存在奇异分数陈绝缘体的可能性，而这些绝缘体在连续朗道能级中没有类似物。我们通过数值验证，这些奇异分数陈绝缘体是短程相互作用的模型态，其特征是在零能量处具有精确的基态简并性和无限的粒子-截断纠缠能隙。
