| Details: |
Simple tight-binding lattice models often give rise to nondispersive, completely flat band states
in their band spectrum. Due to quenching of the kinetic energy, particles living in such flat bands
become completely immobile, forming clusters of compact localized states. Flat bands are
interesting as they offer highly degenerate manifold of single-particle states, which can act as an
ideal platform to study various intriguing strongly correlated phenomena. In this talk, I will
present the appearance of multiple flat band states in a variety of interesting two-dimensional
lattice geometries. I will demonstrate how one can tune the parameters of the underlying tight-
binding Hamiltonian of the system to engineer these flat band states with interesting properties.
With the application of an external magnetic field or an intrinsic spin-orbit interaction, such flat
bands often show interesting topological properties and provide an ideal setup to study the
quantum Hall physics in a lattice model. A possible application of these flat band models can be
anticipated in the field of photonics using single-mode photonic waveguide networks. |