Related papers: Coarse geometry and its applications in solid stat…
The spin polarization of topological surface states is of high interest for possible applications in spintronics. At present, the only technique capable to measure the surface state spin texture is spin and angle resolved photoemission…
The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or…
We investigate states on the surface of strong and weak topological insulators and superconductors that have been gapped by a symmetry breaking term. The surface of a strong 3D topological insulator gapped by a magnetic material is well…
John Roe \cite{Roe lectures} introduced coarse structures for arbitrary sets $X$ by considering subsets of $X\times X$. That definition, while natural for analysts, is a bit more difficult to digest for topologists and geometers. In this…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
Information processing devices operating in the quantum mechanical regime strongly rely on the quantum coherence of charge carriers. Studies of electronic dephasing in conventional metallic and semiconductor systems have not only paved the…
Topological crystalline insulators (TCIs) possess metallic surface states protected by crystalline symmetry, which are a versatile platform for exploring topological phenomena and potential applications. However, progress in this field has…
We study topological states of matter in quasicrystals, which do not rely on crystalline orders. In the absence of a bandstructure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a…
We review the contributions of surface science methods to discover and improve 3D topological insulator materials, while illustrating with examples from our own work. In particular, we demonstrate that spin-polarized angular-resolved…
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two- or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes…
We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
Recently, correlated physics such as superconductivity and insulator at commensurate fractional electron fillings has been discovered in several different systems with Moire superlattice and narrow electron bands near charge neutrality.…
Topological insulators are states of matter distinguished by the presence of symmetry protected metallic boundary states. These edge modes have been characterised in terms of transport and spectroscopic measurements, but a thermodynamic…
Capillary forces are involved in a variety of natural phenomena, ranging from droplet breakup to the physics of clouds. The forces from surface tension can also be exploited in industrial application provided the length scales involved are…
Topological insulating phases are primarily associated with condensed-matter systems, which typically feature short-range interactions. Nevertheless, many realizations of quantum matter can exhibit long-range interactions, and it is still…