Related papers: Topologically Protected States in One-Dimensional …
It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon…
We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive two coupled equations for the energy and the effective width of edge states at a given momentum in a semi-infinite…
The twig edge states in graphene-like structures are viewed as the fourth states complementary to their zigzag, bearded, and armchair counterparts. In this work, we study a rod-in-plasma system in honeycomb lattice with twig edge truncation…
We consider the Dirac operator with a periodic potential on the half-line with the Dirichlet boundary condition at zero. Its spectrum consists of an absolutely continuous part plus at most one eigenvalue in each open gap. The Dirac…
We study wave propagation in 2D honeycomb structures with a non-commensurate or ``irrational'' line defect or edge. Our model is a Schr\"odinger operator which interpolates, across the edge, between two distinct bulk (asymptotic)…
Just like insulators can host topological Dirac states at their edges, superconductors can also exhibit topological phases characterized by Majorana edge states. Remarkable zero-energy states have been recently observed at the two ends of…
This paper is a mathematical analysis of conduction effects at interfaces between insulators. Motivated by work of Haldane-Raghu , we continue the study of a linear PDE initiated in papers of Fefferman-Lee-Thorp-Weinstein. This PDE is…
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…
Quantum materials that host a flat band, such as pseudospin-1 lattices and magic-angle twisted bilayer graphene, can exhibit drastically new physical phenomena including unconventional superconductivity, orbital ferromagnetism, and Chern…
Topological insulators are characterized by specially protected conduction on their outer boundaries. We show that the protected edge conduction exhibited by 2-D topological insulators (and also Chern insulators) is independent of…
Topological insulators in the Bi$_2$Se$_3$ family manifest helical Dirac surface states that span the topologically ordered bulk band gap. Recent scanning tunneling microscopy measurements have discovered additional states in the bulk band…
The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are…
Topological insulators possess protected boundary states which are robust against disorders and have immense implications in both fermionic and bosonic systems. Harnessing these topological effects in non-equilibrium scenarios is highly…
We present an all-dielectric photonic crystal structure that supports two-dimensionally confined helical topological edge states. The topological properties of the system are controlled by the crystal parameters. An interface between two…
In this report we give a brief introduction on the occurrence of topologically protected one-dimensional electronic states in group IV two-dimensional graphene-like materials. We discuss the effect of spin-orbit coupling on the electronic…
Photonic topological insulators supporting unidirectional topologically protected edge states represent attractive platform for realization of disorder- and backscattering-immune transport of edge excitations in both linear and nonlinear…
We report ab initio calculations showing that a single one-dimensional extended defect can originate topologically-protected metallic states in the bulk of two-dimensional topological insulators. We find that a narrow extended defect…
Gapless Dirac surface states are protected at the interface of topological and normal band insulators. In a binary superlattice bearing such interfaces, we establish that valley-dependent dimerization of symmetry-unrelated Dirac surface…
We propose helical topological superconductivity away from the Fermi surface in three-dimensional time-reversal-symmetric odd-parity multiband superconductors. In these systems, pairing between electrons originating from different bands is…
Two-dimensional (2D) metallic altermagnets present exciting opportunities for both fundamental research and practical innovations. Their ability to enhance tunneling magnetoresistance in magnetic tunnel junctions, combined with the direct…