Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice

TL;DR

This paper demonstrates the engineering of a nonequilibrium higher order topological insulator on a $$-flux square lattice, protected by emergent chiral symmetry, with robust corner modes classified by a topological invariant.

Contribution

It introduces a novel nonequilibrium higher order topological phase driven by Floquet engineering, absent in static models, and identifies its topological classification and invariants.

Findings

Robust corner modes in the Floquet-engineered phase.

Topological invariant derived from winding number of a 1D sublattice model.

Verification of the phase using numerical and high-frequency Hamiltonian methods.

Abstract

One of the hallmarks of bulk topology is the existence of robust boundary localized states. For instance, a conventional $d$ dimensional topological system hosts $d{-}1$ dimensional surface modes, which are protected by non-spatial symmetries. Recently, this idea has been extended to higher order topological phases with boundary modes that are localized in lower dimensions such as in the corners or in one dimensional hinges of the system. In this work, we demonstrate that a higher order topological phase can be engineered in a nonequilibrium state when the time-independent model does not possess any symmetry protected topological states. The higher order topology is protected by an emerging chiral symmetry, which is generated through the Floquet driving. Using both the exact numerical method and an effective high-frequency Hamiltonian obtained from the Brillouin-Wigner perturbation theory, we verify the emerging topological phase on a $\pi$-flux square lattice. We show that the localized corner modes in our model are robust against a chiral symmetry preserving perturbation and can be classified as `extrinsic' higher order topological phase. Finally, we identify a two dimensional topological invariant from the winding number of the corresponding sublattice symmetric one dimensional model. The latter model belongs to class AIII of ten-fold symmetry classification of topological matter.