Related papers: Nonlinear edge modes from topological 1D lattices
Possible forms of obstructed atomic limits in quasi-one-dimensional systems are studied using line group symmetry. This is accomplished by revisiting the standard theory with an emphasis on its group-theoretical background, synthesizing the…
Conventional topological insulators exhibit exotic gapless edge or surface states, as a result of non-trivial bulk topological properties. In periodically-driven systems the bulk-boundary correspondence is fundamentally modified and…
Topological defects (TDs) in crystal lattices are elementary lattice imperfections that cannot be removed by local perturbations, due to their real space topology. We show that adding TDs into a valley photonic crystal generates a lattice…
We consider a one-dimensional discrete nonlinear Schr\"odinger (DNLS) model with Kerr-type on-site nonlinearity, where the nearest-neighbor coupling constants take two different values ordered in a three-periodic sequence. The existence of…
Topological edge states exist at the interfaces between two topologically-distinct materials. The presence and number of such modes are deterministically predicted from the bulk-band topologies, known as the bulk-edge correspondence. This…
Frames, or lattices consisting of mass points connected by rigid bonds or central force springs, are important model constructs that have applications in such diverse fields as structural engineering, architecture, and materials science.…
The engineering of specialty lasers with unconventional mode structures is one of the modern challenges in the development of integrated coherent sources. Examples include the use of bound states in the continuum, microlasers with orbital…
Topological phases exhibit properties that are conserved for continuous deformations, as demonstrated in topological protections in condensed-matter physics and electromagnetic waves. Despite its ubiquitous nature and recent extensions to…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
The dynamical encirclement around a second order exceptional point (EP) and corresponding chirality driven nonadiabatic modal dynamics have attracted enormous attention in the topological study of various non-Hermitian systems. However,…
Tridiagonal $k$-Toeplitz operators provide a natural framework for modelling one-dimensional $k$-periodic lattice systems. A fundamental connection is obtained between Coburn's lemma for tridiagonal $k$-Toeplitz operators and the existence…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
We construct exactly soluble lattice models for fractionalized, time reversal invariant electronic insulators in 2 and 3 dimensions. The low energy physics of these models is exactly equivalent to a non-interacting topological insulator…
Precise manipulation of the direction and re-direction of vibrational wave energy is a key demand in wave physics and engineering. We consider the paradigm of a finite frame-like structure and the requirement to channel energy away from…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
Active matter is naturally out of equilibrium which results in the emergence of diverse dynamic steady states, including the omnipresent chaotic state known as the active turbulence. However, much less is known how active systems…
Topological states of matter, as quantum Hall systems or topological insulators, cannot be distinguished from ordinary matter by local measurements in the bulk of the material. Instead, global measurements are required, revealing…
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…
We propose a scheme to realize a topological insulator with optical-passive elements, and analyze the effects of Kerr-nonlinearities in its topological behavior. In the linear regime, our design gives rise to an optical spectrum with…
We identify the existence of various symmetry-protected topological states in one-dimensional superlattices with periodically modulated hopping amplitudes or on-site potentials, which can be characterized by the quantized Berry phase $\pi$…