Related papers: Topological edge states in two-gap unitary systems…
An edge state is a time-harmonic solution of a conservative wave system, e.g. Schroedinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or "edge". Topologically protected edge…
We predict the existence of interaction-driven edge states of bound two-photon quasiparticles in a dimer periodic array of nonlinear optical cavities. Energy spectrum of photon pairs is dramatically richer than in the noninteracting case or…
Recent works have proved the existence of symmetry-protected edge states in certain one-dimensional topological band insulators and superconductors at the gap-closing points which define quantum phase transitions between two topologically…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges.…
Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge states of such an intrinsically interacting…
We study the topological edge states of the Haldane's graphene model with zigzag/armchair lattice edges. The Harper equation for solving the energies of the edge states is derived. The results show that there are two edge states in the bulk…
We study band modulations and topological transitions in a one-dimensional periodic bead-on-string chain. Using an exact transfer-matrix formulation of the wave equation with periodically modulated mass density, combined with numerical…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
The transition to turbulence in many shear flows proceeds along two competing routes, one linked with finite-amplitude disturbances and the other one originating from a linear instability, as in e.g. boundary layer flows. The dynamical…
Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…
We study the structure of topological phases and their boundaries in the Projected Entangled Pair States (PEPS) formalism. We show how topological order in a system can be identified from the structure of the PEPS transfer operator, and…
Topological band theory provides a conceptual framework to predict or even engineer robust metallic states at the boundaries of topologically distinct phases. The bulk-boundary correspondence requires that a topological electronic phase…
The 2D TI edge states are considered within the Volkov-Pankratov (VP) Hamiltonian. A smooth transition between TI and OI is assumed. The edge states are formed in the total gap of homogeneous 2D material. A pair of these states are of…
Topological edge states are robust against symmetry-preserving perturbations and noise, making them promising for quantum information and computation, particularly in topological quantum computation through braiding operations of Majorana…
Topological edge states in electromagnetic systems feature a set of attracting fundamental properties and unveil prospective applications based on disorder robustness and tailored localization. Despite active efforts in implementing…
We use the N-terminal scheme for studying the edge state transportin in two-dimensional topological insulators. We find the universal nonlocal response in the ballistic transport approach. This macroscopic exhibition of the topological…
We introduce modulational instability in non-Hermitian systems to study state conversion of topological edge states. We show that state conversion in non-Hermitian systems leads to topological pumping, which is a way of transferring…
We propose a systematic analysis of the eigenfunctions of two-band systems in two dimensions with a circular edge. Our approach is based on an analytic continuation of the wavenumber, which yields a mapping from the bulk modes to the edge…