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Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects or local disorder, and can even survive some…
Recent experiments showed that the surface of a three dimensional topological insulator develops gaps in the Floquet-Bloch band spectrum when illuminated with a circularly polarized laser. These Floquet-Bloch bands are characterized by…
Periodically driven systems play a prominent role in optical lattices. In these ultracold atomic systems, driving is used to create a variety of interesting behaviours, of which an important example is provided by topological states of…
Moir\'e network formation in graphene bilayers breaks stacking symmetry, giving rise to domain walls that host topologically protected one-dimensional states. Here we show that these systems undergo an additional symmetry breaking at the…
Novel topological properties that arose in the periodically driven system are unique, in which there are two kinds of quasienergy gaps, the zero quasienergy gap and the $\pi$ quasienergy gap. The corresponding edge modes would traverse…
Topological phases of matter have attracted much attention over the years. Motivated by analogy with photonic lattices, here we examine the edge states of a one-dimensional trimer lattice in the phases with and without inversion symmetry…
M\"obius topological insulators have dispersive edge bands with M\"obius twists in momentum space, which are protected by the combination of chiral and $Z_2$-projective translational symmetries. In this work, we reveal a unique type of…
Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the…
Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here…
We develop a theoretical framework that lays out the fundamental rules under which a periodic (Floquet) driving scheme can induce non-reciprocal transport. Our approach utilizes an extended Hilbert space where a Floquet network with an…
Engineering dissipative dynamics in open quantum systems is under active focus, especially in topological settings where resilient edge modes are expected to exhibit decay rates distinct from the bulk. In this letter, we propose an…
Non-Abelian topological phases, which go beyond traditional Abelian topological band theory, are garnering increasing attention. This is further spurred by periodic driving, leading to predictions of many novel multi-gap Floquet topological…
We consider the differential conductance of a periodically driven system connected to infinite electrodes. We focus on the situation where the dissipation occurs predominantly in these electrodes. Using analytical arguments and a detailed…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
We present a joint experimental and theoretical study of the driven Su-Schrieffer-Heeger model implemented by arrays of evanescently coupled plasmonic waveguides. Floquet theory predicts that this system hosts for suitable driving…
A time periodic driving on a topologically trivial system induces edge modes and topological properties. In this work we consider triplet and singlet superconductors subject to periodic variations of the chemical potential, spin-orbit…
We investigate the topological properties of a resonantly shaken one-dimensional optical lattice system, where the lattice position is periodically driven with two harmonic frequencies to generate one- and two-photon couplings between the…
In this work, we discuss properties with no static counterpart arising in Floquet topological insulators with a dynamical chiral symmetry (DCS), i.e., a chiral symmetry which is present while driving. We explore the topological properties…
The engineering of synthetic materials characterised by more than one class of topological invariants is one of the current challenges of solid-state based and synthetic materials. Using a synthetic photonic lattice implemented in a…
We propose Floquet chiral topological superconducting systems hosting Floquet Majorana fermions, which consist of hexagonal lattices in proximity to superconductors with shining circularly polarized light. Specially for bilayer graphene…