Executive Summary : | The theoretical proposal aims to address two aspects of Hopf insulators. The first one involves finding flatbands with non-standard topological invariant, namely Hopf invariant in contrast to the commonly known Chern or Z₂ invariant. These non-trivial flatbands are expected to be used as venues for fractional Hall phenomena with arbitrary fillings, where fractional states are in general limited. Further, the project aims to find if a genuine 3D Hopf insulator can be constructed from a two dimensional lattice model with a finite Chern number . The second project involves studying magnon-induced Hopf insulators. Specifically, the aim is to investigate if magnons favor Hopf insulators. The outcome may hint us on if properties of magnons encode Hopf transition, which can be easily verified in experiments. |