Related papers: Continuous bulk and interface description of topol…
We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear…
Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
We demonstrate that topological insulators exhibit an intrinsic interfacial instability that amplifies small interface fluctuations, resulting in chaotic behavior during interface growth. This mechanism is fundamentally different from…
Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of…
We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omnipresent in the topological insulators literature. Using explicit…
Topological insulators (TIs) are a class of materials which are insulating in their bulk form yet, upon introduction of an a boundary or edge, e.g. by abruptly terminating the material, may exhibit spontaneous current along their boundary.…
Topological insulators (TIs) are materials that are insulating in the bulk but have zero band gap surface states with linear dispersion and are protected by time reversal symmetry. These unique characteristics could pave the way for many…
Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects or local disorder, and can even survive some…
In two dimensions, interacting Floquet topological phases may arise even in the absence of any protecting symmetry, exhibiting chiral edge transport that is robust to local perturbations. We explore a similar class of Floquet topological…
We apply ideas from $C^*$-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
Seeking the criterion for diagnosing topological phases in real materials has been one of the major tasks in topological physics. Currently, bulk-boundary correspondence based on spectral measurements of in gap topological boundary states…
Electronic topological insulators are one of the breakthroughs of the 21st century condensed matter physics. So far, the search for a light counterpart of an electronic topological insulator has remained elusive. This is due to the…
Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states…
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…
This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
Three dimensional (3D) topological insulators are quantum materials with a spin-orbit induced bulk insulating gap that exhibit quantum-Hall-like phenomena in the absence of applied magnetic fields. The proposed applications of topological…
Topological insulators are novel macroscopic quantum-mechanical phase of matter, which hold promise for realizing some of the most exotic particles in physics as well as application towards spintronics and quantum computation. In all the…