Symmetry breaking and the fermionic fractional Chern insulator in topologically trivial bands

Subjecting a topologically nontrivial class of noninteracting electronic states to interactions can sometimes yield a ``fractional'' topologically ordered version of that class. For example, electrons in topological bands with integer-quantized Hall conductivity can generate fractional quantum Hall (FQH) states upon addition of repulsive interactions. However, of all existing material band structures, the topologically nontrivial ones are rare. Here, the author demonstrates theoretically in a minimal setting how strong interactions and symmetry breaking can induce FQH-type topological order even in topologically trivial bands. This finding shows that even topologically trivial band structures -- the vast majority -- can host topological order.