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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…
The topic of photonic topological insulators and scattering-protected edge states bridges concepts from condensed matter physics and electromagnetics, and necessitates understanding the Berry potential and related concepts. These notes are…
In recent years, a class of solid state materials, called three-dimensional topological insulators, has emerged. In the bulk, a topological insulator behaves like an ordinary insulator with a band gap. At the surface, conducting gapless…
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…
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…
Topological photonic systems offer light transport that is robust against defects and disorder, promising a new generation of chip-scale photonic devices and facilitating energy-efficient on-chip information routing and processing. However,…
Topological insulators are a new class of insulators in which a bulk gap for electronic excitations is generated by strong spin orbit coupling. These novel materials are distinguished from ordinary insulators by the presence of gapless…
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…
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…
Topological edge solitons propagating along the edge of a photonic topological insulator are localized self-sustained hybrid states that are immune to de-fects/disorders due to protection of the edge states stemming from nontrivial topology…
One dimensional laser-written modulated photonic lattices are known to be particularly suitable for diffraction management purposes. Here, we address the connection between discrete non-diffracting states and topological properties in such…
Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal invariant topological insulators. Because of limitations imposed by nature, topologically non-trivial electronic order…
Topologically protected surface states of three-dimensional topological insulators provide a model framework for studying massless Dirac electrons in two dimensions. Usually a step on the surface of a topological insulator is treated as a…
Photonic topological insulators (PTIs) exhibit robust photonic edge states protected by band topology, similar to electronic edge states in topological band insulators. Standard band theory does not apply to amorphous phases of matter,…
Topological insulators (TIs) are a striking example of materials in which topological invariants are manifested in robustness against perturbations. Their most prominent feature is the emergence of topological edge states with reduced…
Topological phases in quantum and classical systems have been of significant recent interest due to their fascinating physical properties. While a range of different mechanisms to induce topological order have been introduced, a quest for…
Topological phases of matter have garnered significant interest over the past two decades for two main reasons: their identification, via topological invariants, relies on the quantum geometry of the Bloch states, bringing attention to an…
Topologically protected one-way transportation of sound, mimicking the topological properties of the condensed matter, has received greatly attentions. Thus far, the topological phases and the topological edge states of sound are yielded in…
Strong light-matter interaction enriches topological photonics by dressing light with matter, which provides the possibility to realize tuneable topological devices with immunity to defects. Topological exciton polaritons, half-light…
Motivated by recent photoemission experiments on the surface of topological insulators we compute the spectrum of driven topological surface excitations in the presence of an external light source. We completely characterize the spectral…