Related papers: Engineering topology in waveguide arrays
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…
We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced…
The sublattice symmetry on a bipartite lattice is commonly regarded as the chiral symmetry in the AIII class of the tenfold Altland-Zirnbauer classification. Here, we reveal the spatial nature of sublattice symmetry, and show that this…
We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
Periodically driven (Floquet) crystals are described by their quasi-energy spectrum. Their topological properties are characterized by invariants attached to the gaps of this spectrum. In this article, we define such invariants in all space…
Topology concepts have significantly deepened of our understanding in recent years of the electronic properties of one-dimensional (1D) nano structures such as the graphene nanoribbons. Controlling topological electronic properties of GNRs…
Symmetry is one of the cornerstones of modern physics and has profound implications in different areas. In symmetry-protected topological systems, symmetries are responsible for protecting surface states, which are at the heart of the…
Periodically driven systems with internal and spatial symmetries can exhibit a variety of anomalous boundary behaviors at both the zero and $\pi$ quasienergies despite the trivial bulk Floquet bands. These phenomena are called anomalous…
We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations.…
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and…
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…
Symmetries play a major role in identifying topological phases of matter and in establishing a direct connection between protected edge states and topological bulk invariants via the bulk-boundary correspondence. One-dimensional lattices…
We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classification for insulators and superconductors. In particular, charge…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
Discrete-time quantum walks have been shown to simulate all known topological phases in one and two dimensions. Being periodically driven quantum systems, their topological description, however, is more complex than that of closed…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
Time-periodic perturbations can be used to engineer topological properties of matter by altering the Floquet band structure. This is demonstrated for a spin Hall insulator in the presence of monochromatic circularly polarized light. The…
In this study, a tight-binding model on square octagon lattice with nearest-neighbour and next-nearest-neighbour hoppings is considered. The system is topologically trivial although it exhibits quadratic band-touching points in its…
The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band…