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The topological band theory predicts that bulk materials with nontrivial topological phases support topological edge states. This phenomenon is universal for various wave systems and has been widely observed for electromagnetic and acoustic…
An exact solution for electromagnetic wave diffraction at the junction of two-dimensional electron systems (2DES) is obtained and analyzed for electric field polarized along the edge. A special emphasis is paid to the metal-contacted and…
The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two dimensional Hamiltonians that yield an unusual class $D$…
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field…
We use topological methods to study various semicontinuity properties of spectra of singular points of plane algebraic curves and of polynomials in two variables at infinity. Using Seifert forms and the Tristram--Levine signatures of links,…
We define a class of insulators with gapless surface states protected from localization due to the statistical properties of a disordered ensemble, namely due to the ensemble's invariance under a certain symmetry. We show that these…
The research in topological materials and meta-materials reached maturity and is now gradually entering the phase of practical applications and devices. However, scaling down the experimental demonstrations definitely presents a challenge.…
The interaction model of two electrons in the edge states of a two-dimensional topological insulator is investigated. Both solutions of the Schr\"odinger equation and solutions of the Bethe-Salpeter equation at different values of the Fermi…
We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry…
We show that edge states similar to those known for topological insulators exist in two-dimensional electron system with one-band spectrum in the presence of heterogeneous spin-orbit interaction (SOI). These states appear at boundaries…
Topological insulators are newly discovered materials with the defining property that any boundary cut into such crystal supports spectrum which is immune to the Anderson localization. The present paper summarizes our efforts on the…
We study the eigenspectrum properties of a one-dimensional molecular chain composed of hexagonal unit cells. The system features two alternating hopping parameters, resulting in a rich energy spectrum with both dispersive and flat bands. By…
We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not…
Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states…
This paper demonstrates the existence of topological models with gapped edge states but protected extended bulk states against disorder. Such systems will be labeled as trivial by the current classification of topological insulators. Our…
We present a separation property for the gaps in the length spectrum of a compact Riemannian manifold with negative curvature. In arbitrary small neighborhoods of the metric for some suitable topology, we show that there are negatively…
We present examples in three symmetry classes of topological insulators in one or two dimensions where the proof of the bulk-edge correspondence is particularly simple. This serves to illustrate the mechanism behind the bulk-edge principle…
We produce many new complete, constant Q-curvature metrics on finitely punctured spheres by gluing together known examples. In our construction we truncate one end of each summand and glue the two summands together "end-to-end," where we've…
The interplay of topological electronic band structures and strong interparticle interactions provides a promising path towards the constructive design of robust, long-range entangled many-body systems. As a prototype for such systems, we…
The unique properties of spin-polarized surface or edge states in topological insulators (TIs) make these quantum coherent systems interesting from the point of view of both fundamental physics and their implementation in low power…