Related papers: Topological defects in 1D elastic waves
Topological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with…
A two-dimensional electron gas in a high magnetic field displays macroscopically degenerate Landau levels, which can be split into Hofstadter subbands by means of a weak periodic potential. By carefully engineering such a potential, one can…
Recent studies of 2D moir\'e materials have opened opportunities for advancing condensed matter physics. However, the effect of 1D moir\'e potentials on topological and correlated phases remains largely unexplored. Here we reveal a sequence…
We describe the double wall tube with cylindrical dislocation in the framework of the geometric theory of defects. The induced metric is found. The dispersion relation is obtained for the propagation of torsional elastic waves in the double…
Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to…
In this paper we propose a self--consistent approach to the description of temporal dynamics of localized states. This approach is based on exactly solvable quantum mechanical models with multi-well potentials and their propagators. States…
Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused…
Topological lasers are of growing interest as a way to achieve disorder-robust single mode lasing using arrays of coupled resonators. We study lasing in a two-dimensional coupled resonator lattice exhibiting transitions between trivial and…
A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
By means of Monte Carlo simulations we show that there are two qualitatively different modes of localization of classical waves in 1-{\em D} random periodic-on-average systems. States from pass bands and band edges of the underlying band…
We study a class of periodic Schr\"odinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic…
The low-energy band-structure of electrons propagating on a lateral surface of a heterostructure consisting of three dimensional topological insulator (TI) and magnetic insulator layers has been calculated. The energy spectrum is highly…
We investigate the self-organization of strongly interacting particles confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice models with short-range interactions. We show that many-body states with topological…
We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC) with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. Unlike previously studied 2D models…
Topological defects are one of the most conspicuous features of liquid crystals. In two dimensional nematics, they have been shown to behave effectively as particles with both, charge and orientation, which dictate their interactions. Here,…
It is well-known that localized topological defects (solitons) experience recoil when they suffer an impact by incident particles. Higher-dimensional topological defects develop distinctive wave patterns propagating along their worldvolume…
We experimentally demonstrate, for the first time, formation of point-like topological defects in the edge state structure in the quantum Hall effect regime. By using of a selective population technique, we investigate equilibration…
The spectrum of electromagnetic waves in periodic linear structures, such as periodic waveguides or chains of microelements i.e. spheres, cavities, exhibit the sequence of stop bands for propagating waves. Breaking the translational…
A twist between two systems offers the possibility to drastically change the underlying physical properties. To that end, we study the bandstructure of twisted moir\'e potentials in detail. At sets of commensurate twisting angles, the low…