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We consider the energy spectrum and the spin-parity structure of the eigenstates for a quantum dot made of a strong topological insulator. Using the effective low-energy theory in a finite-length cylinder geometry, numerical calculations…

We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to…

Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…

Topological insulators and superconductors support extended surface states protected against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes A, AI, and AII,…

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…

We study the nature of edge states in extrinsically and spontaneously dimerized states of two-dimensional spin-1/2 antiferromagnets, by performing quantum Monte Carlo simulation. We show that a gapless edge mode emerges in the wide region…

Edge states play a major role in the electron dynamics of topological insulators as they are the only conducting part in such materials. In this work, we consider the Haldane model for a 2D topological insulator, subjected to an intense…

Higher-order topological insulators in two dimensions have states that localize at their corners, called corner states. In this paper, we reveal characteristics of the penetration depth of their corner states by using the…

Topologically protected gapless edge/surface states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with…

The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing…

Two-dimensional topological insulators, and in particular quantum Hall states, are characterized by an insulating bulk and a conducting edge. Fractional states may host both downstream (dictated by the magnetic field) and upstream…

Quadrupole phase, as a novel high-order topological phase, exhibits nontrivial gapless states at the boundaries whose dimension is lower than bulk by two. However, this phase has not been observed experimentally in two-dimensional (2D)…

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a…

Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that $\mathbb{Z}_N$ Berry phase (Berry phase quantized into $2\pi/N$) is a useful tool…

Conventional wisdom dictates that the conducting edge states of two-dimensional topological insulators of the Bi$_2$Se$_3$ family are protected by time-reversal symmetry. However, theoretical bulk calculations and a recent experiment show…

Interface states at a boundary between regions with different spin-orbit interactions (SOIs) in two-dimensional (2D) electron systems are investigated within the one-band effective mass method with generalized boundary conditions for…

We have investigated the energetic stability and the electronic properties of metal-organic topological insulators bilayers (BLs), $(MC_4S_4)_3$-BL, with M=Ni and Pt, using first-principles calculations and tight-binding model. Our findings…

Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…

The study of topological states in electronic structures, which allows robust transport properties against impurities and defects, has been recently extended to the realm of elasticity. This work shows that nontrivial topological flexural…

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…