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Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…
We propose a simple approach to realize two-dimensional Floquet topological superfluid by periodically tuning the depth of square optical lattice potentials. We show that the periodic driving can induce topological phase transitions between…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…
The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In…
Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of…
We introduce $\mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the…
Recent experimental advances in Floquet engineering and controlling dissipation in open systems have brought about unprecedented flexibility in tailoring novel phenomena without any static and Hermitian analogues. It can be epitomized by…
We study the effect of driving a two-dimensional honeycomb system out of equilibrium using an elliptically polarized light as a time-dependent perturbation. In particular, we try to understand the topological phase diagram of this driven…
Topological invariants, such as the Chern number, characterise topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states.…
Fractional quantum Hall effect (FQHE) is a prime example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order, and time reversal symmetry breaking. Recently, a lattice…
We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional…
Floquet topological insulators have been widely investigated in lower-dimensional systems. However, Floquet topological insulators induced by time-periodic driving in higher-dimensional systems remain unexplored. In this work, we study the…
Nonequilibrium topological matter has been a fruitful topic of both theoretical and experimental interest. A great variety of exotic topological phases unavailable in static systems may emerge under nonequilibrium situations, often…
We propose a generic scattering matrix model implementable in photonics to engineer a new Floquet metallic phase that combines two distinct topological properties: the winding of the bulk bands and the existence of robust chiral edge…
For decades, the topological phenomena in quantum systems have always been catching our attention. Recently, there are many interests on the systems where topologically protected edge states exist, even in the presence of non-Hermiticity.…
We explore the impact of commensurate multifrequency driving protocols on the stability of topological edge modes in topological 1D systems of spinless fermions. Using Floquet theory, we show that all the topological phase transitions can…
We show that one-dimensional Floquet trimer arrays with periodically oscillating waveguides support two different and co-existing types of topological Floquet edge states in two different topological gaps in Floquet spectrum. In these…
The topology of electrons on a lattice subject to a periodic driving is captured by the three-dimensional winding number of the propagator that describes time-evolution within a cycle. This index captures the homotopy class of such a…
It is by now well established that periodically driven quantum many-body systems can realize topological nonequilibrium phases without any equilibrium counterpart. Here we show that, even in the absence of time translation symmetry,…
Non-Hermitian systems exhibit two distinct topological classifications based on their gap structure: line-gap and point-gap topologies. Although point-gap topology is intrinsic to non-Hermitian systems, its systematic construction remains a…