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Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility…

The edge states of two-dimensional time-reversal topological insulators support a perfect helical conductance on wide ribbons due to the absence of backscattering. Here, we study the changes in the transport properties of topological…

An important characteristic of topological band insulators is the necessary presence of in-gap edge states on the sample boundary. We utilize this fact to show that when the boundary is reconnected with a twist, there are always zero-energy…

Topology is quickly becoming a cornerstone in our understanding of electronic systems. Like their electronic counterparts, bosonic systems can exhibit a topological band structure, but in real materials it is difficult to ascertain their…

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…

Topological defects with symmetry-breaking phase transitions have captured much attention. Vortex generated by topological defects exhibits exotic properties and its flow direction can be switched by altering the spin configurations.…

We report on the possibility to detect hinge spin polarization in magnetic topological insulators by resistance measurements. By implementing a three-dimensional model of magnetic topological insulators into a multi-terminal device with…

The proposition that band geometry alone can protect optical states against disorder has proven not merely theoretically elegant but experimentally incontrovertible. A key attribute of photonic topological systems is their capacity to…

Electron tunneling through a single magnetic barrier in a HgTe topological insulator has been theoretically investigated. We find that the perpendicular magnetic field would not lead to spin-flip of the edge states due to the conservation…

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.…

Topological states of quantum matter exhibit unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk. Such immunity from backscattering makes topological surface or edge states ideal…

Topological phases feature robust edge states that are protected against the effects of defects and disorder. The robustness of these states presents opportunities to design technologies that are tolerant to fabrication errors and resilient…

We show that the decorated honeycomb lattice supports a number of topological insulating phases with a non-trivial Z_2 invariant and time-reversal symmetry protected gapless edge modes. We investigate the stability of these phases with…

Topological photonics revolutionizes some of the traditional approaches to light propagation and manipulation, and it provides unprecedented means for developing novel photonic devices. Recently discovered higher-order topological phases go…

Solid-state topological insulating phases, characterized by spin-momentum locked edge modes, provide a powerful route for spin and charge manipulation in electronic devices. We propose to control charge and spin transport in the helical…

Topological insulators are studied via tight-binding approximations of longitudinally driven photonic lattices with three lattice sites per unit cell. Two cases are considered in detail: Lieb and Kagome lattices. The lattice is decomposed…

Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without…

Existence of robust edge modes at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, topological insulators. Such electronic states were originally predicted…

The unique electronic properties of the surface electrons in a topological insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum…

We show that one-dimensional Floquet trimer arrays with periodically oscillating waveguides support two different and co-existing types of topological Floquet edge states in two different topological gaps in Floquet spectrum. In these…