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Topological insulators are materials where current does not flow through the bulk, but along the boundaries, only. They are of particular practical importance, since it is considerably more difficult, by ``conventional'' means, to affect…

Topological insulators are a new class of materials that have attracted significant attention in contemporary condensed matter physics. They are different from the regular insulators and they display novel quantum properties that also…

Ternary semiconducting or metallic half-Heusler compounds with an atomic composition 1:1:1 are widely studied for their flexible electronic properties and functionalities. Recently, a new material property of half-Heusler compounds was…

Topological electromagnetism owing to nontrivial momentum-space topology of electrons in insulators gives rise to diverse anomalous magnetoelectric responses. While conventional inductors and capacitors are based on classical…

The method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires…

Topologically protected gapless edge 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…

Excitonic insulators are insulating states formed by the coherent condensation of electron and hole pairs into BCS-like states. Isotropic spatial wave functions are commonly considered for excitonic condensates since the attractive…

Dirac-like surface states on surfaces of topological insulators have a chiral spin structure that suppresses back-scattering and protects the coherence of these states in the presence of non-magnetic scatterers. In contrast, magnetic…

An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing requirements on the existence of pseudo…

In the ferromagnetic insulator with Dzyaloshinskii-Moriya interaction, we theoretically predict and numerically verify a topological magnon insulator, where the charge-free magnon is topologically protected to transport along the edge while…

Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy…

Topological insulators (TIs) represent a novel quantum state of matter, characterized by edge or surface-states, showing up on the topological character of the bulk wave functions. Allowing electrons to move along their surface, but not…

Classical wave fields are real-valued, ensuring the wave states at opposite frequencies and momenta to be inherently identical. Such a particle-hole symmetry can open up new possibilities for topological phenomena in classical systems. Here…

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five…

The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $\theta$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous…

The Hopf insulator is a weak topological insulator characterized by an insulating bulk with conducting edge states protected by an integer-valued linking number invariant. The state exists in three-dimensional two-band models. We…

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in…

We study theoretically the distributions of charge and spin polarization of a topological insulator ribbon, with a realistic rectangular cross section. Due to constriction in two lateral directions, the surface states discretize into a…

Control and manipulation of electromagnetic waves has reached a new level with the recent understanding of topological states of matter. These metamaterials have the potential to revolutionize many areas in traditional electromagnetic…

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…