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We numerically demonstrate a practical means of systematically controlling topological transport on the surface of a three dimensional topological insulator, by introducing strong disorder in a layer of depth $d$ extending inward from the…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…
Topological edge states arise at the interface of two topologically-distinct structures and have two distinct features: they are localized and robust against symmetry protecting disorder. On the other hand, conventional transport in one…
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this…
One of the most striking features of quantum mechanics is the appearance of phases of matter with topological origins. These phases result in remarkably robust macroscopic phenomena such as the edge modes in integer quantum Hall systems,…
The dynamics of the magnetic field in a superconducting phase is described by an effective massive bosonic field theory. If the superconductor is confined in a domain M with boundary \partial M, the boundary conditions of the…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…
Topological insulators provide great potentials to control diffusion phenomena as well as waves. Here, we show that the direction of thermal diffusion can be selected by the contributions of the topologically protected edge modes via the…
The past decade has witnessed a booming development of topological photonics, which revolutionizes the methodology for controlling the behavior of light. A gigantic achievement is to engineer robust confined modes localized at interfaces…
A review is given of recent work on topology changing solutions to the first order form of general relativity. These solutions have metrics which are smooth everywhere, invertible almost everywhere, and have bounded curvature. The…
This paper proposes a quantitative description of the low energy edge states at the interface between two-dimensional topological insulators. They are modeled by continuous Hamiltonians as systems of Dirac equations that are amenable to a…
Edge states emerge in diverse areas of science, offering new opportunities for the development of novel electronic or optoelectronic devices, sound and light propagation controls in acoustics and photonics. Previous experiments on edge…
We investigate the formation of the one-dimensional channels on the topological surface under the gate electrode. The energy dispersion of these channels is almost linear in the momentum with the velocity sensitively depending on the…
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…
The study of topological states in electronic structures, which allows robust transport properties against impurities and defects, has been recently extended to the realm of elasticity. This work shows that nontrivial topological flexural…
We argue that symmetry-broken phases proximate in phase space to symmetry-protected topological phases can exhibit dynamical signatures of topological physics. This dynamical, symmetry-protected "topological" regime is characterized by…
We derive the universal real time $U(1)$ topological gauge field action for mixed quantum states of weakly correlated fermions in all dimensions, and demonstrate its independence of the underlying equilibrium or non-equilibrium nature of…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
We use the bulk Hamiltonian for a three-dimensional topological insulator such as $\rm Bi_2 Se_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the…