# Generating a second-order topological insulator with multiple corner states by periodic driving

## TL;DR

This paper explores how periodic driving can induce second-order topological insulator phases with multiple corner states in a modified BHZ model, revealing new topological phenomena and invariant characterizations.

## Contribution

It demonstrates the emergence of multiple corner states through periodic driving in a modified BHZ model, expanding understanding of Floquet topological phases.

## Key findings

- Periodic driving induces multiple corner states.
- Corner states can be labeled by eigenvalues of a specific operator.
- Topological invariants like Chern and winding numbers explain phase transitions.

## Abstract

We study the effects of periodic driving on a variant of the Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence of driving, the model has both topological and nontopological phases depending on the different parameter values. We also study the anisotropic BHZ model and show that, unlike the isotropic model, it has a nontopological phase which has states localized on only two of the four edges of a finite-sized square. When an appropriate term is added, the edge states get gapped and gapless states appear at the four corners of a square; we have shown that these corner states can be labeled by the eigenvalues of a certain operator. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear depending on the driving frequency and other parameters. We discuss to what extent the system can be characterized by topological invariants such as the Chern number and a diagonal winding number. We have shown that the locations of the jumps in these invariants can be understood in terms of the Floquet operator at both the time-reversal invariant momenta and other momenta which have no special symmetries.