Strain Induced Flat bands and fragile topology

Materials with flat electronic bands offer an important pathway towards the realization of strongly correlated phenomena such as the fractional quantum Hall effect and unconventional superconductivity. Recently, magic-angle twisted bilayer graphene has gained considerable attention because of the experimental observation of the unconventional superconductivity and orbital Chern insulators. In this talk, we study the flat bands and their topological properties in two dimensional materials under periodic strain. In monolayer graphene, strain acts as a gauge field but preserves time reversal symmetry. In a recent study, it was shown that monolayer graphene under periodic strain fields can support counter-propagating edge states on the same edge. We show that in other systems strain fields may not act as a gauge field but can still produce rich and unexpected phenomena, such as flat bands and fragile topology.