Topological exact flat bands in two dimensional materials under periodic strain

Abstract

We study flat bands and their topology in 2D materials with quadratic band crossing points (QBCPs) under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for QBCPs serves as a director potential with angular momentum $\ell =2$. We prove that when the strengths of the strain fields hit certain ``magic" values, exact flat bands with $C=\pm 1$ 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.

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• Nearly flat Chern band in periodically strained monolayer and bilayer graphene
• Engineering the in-plane anomalous Hall effect in Cd${}_3$As${}_2$ thin films
• Contrasting twisted bilayer graphene and transition metal dichalcogenides for fractional Chern insulators: an emergent gauge picture
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• Edge-driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombohedral graphene multilayers
• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• Fractional Chern insulator candidate in twisted bilayer checkboard lattice
• Symmetry-based classification of exact flat bands in single and bilayer moiré systems
• Ideal topological flat bands in chiral symmetric moiré systems from non-holomorphic functions
• Quantum-geometric dipole: a topological boost to flavor ferromagnetism in flat bands
• A generalized framework for straintronics in 2D quantum materials using group theory
• Unconventional Fractional Phases in Multi-Band Vortexable Systems
• Robustness of real-space topology in moiré systems
• Dislocation Patterning as a Mechanism for Flat Band Formation