Tunable flat bands from a parent chiral Hamiltonian

Systems with flat bands are interesting as they potentially host many exotic quantum phenomena that would be hard to observe in usual systems with dispersive bands. Multiple approaches were developed to construct flat band systems, with most of them requiring fine-tuning and/or solving a challenging inverse-eigenvalue problem. In this article we work with an idea that uses a parent bipartite system to generate a family of flat bands by means of Hilbert space projections. This method is largely free from fine-tuning constraints and allows us to identify conditions for a Hamiltonian to guarantee flat bands at desired energies, with desired degree of degeneracy. We also show that one can control the touching points of the flat band with dispersive bands at any desirable point in the Brillouin zone. In the process, we identify perturbations that preserve the flat bands or split them controllably. This approach provides easy tunability in designing flat band systems with desired properties.