Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
Theoretical Division, T-4 and CNLS, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev Lett. 2023 May 26;130(21):216401. doi: 10.1103/PhysRevLett.130.216401.
We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.
我们研究了在周期性应变下具有二次带交叉点的二维材料中的扁平能带及其拓扑结构。与石墨烯中的狄拉克点不同，应变在那里充当矢量势，对于二次带交叉点，应变充当具有角动量ℓ=2 的director 势。我们证明了当应变场的强度达到某些“魔法”值时，在手性极限下，在电荷中性点处会出现精确的具有 C=±1 的扁平能带，这与魔术角扭曲双层石墨烯非常相似。这些扁平带具有实现分数陈绝缘体的理想量子几何形状，并且总是脆弱的拓扑结构。对于某些点群，可以将扁平带的数量加倍，并且在整数填充时，相互作用的哈密顿量可以精确求解。我们进一步证明了这些扁平带在手性极限偏离时的稳定性，并讨论了在二维材料中的可能实现。
