Floquet second-order topological insulator

Higher-order topological insulators (HOTIs) are a recent entrant to the field of topology in condensed matter physics. Usually, two-dimensional topological insulators host robust one-dimensional edge modes. These are related to the bulk properties via topological invariants such as the Chern number. However, in HOTIs, there are zero-dimensional corner modes, which, in case of a square-shaped sample, say, are confined to the four vertices of the square. In this work, a variant of the well-known Bernevig-Hughes-Zhang (BHZ) model is used to construct a two-dimensional HOTI. When this system is driven periodically by varying one of the model parameters in time, i.e., using a Floquet drive, multiple corner states may appear depending on the driving frequency and other parameters. The system can be characterized by topological invariants such as the Chern number and a diagonal winding number. The behavior of these invariants can be understood in terms of the value of the Floquet operator at some special points in momentum space.