Related papers: Determining topological order from a local ground …
We show how quantum oscillation measurements of surface states in an insulator may allow to diagnose a strong topological insulator and distinguish it from its weak or topologically trivial counterpart. The criterion is defined by the…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…
When time-reversal symmetry is weakly broken and interactions are neglected, the surface of a $Z_{2}$ topological insulator supports a half-quantized Hall conductivity $\sigma_{S} = e^{2}/(2h)$. A surface Hall conductivity in an insulator…
Topological states of matter are robust quantum phases, characterised by propagating or localised edge states in an insulating bulk. Topological boundary states can be triggered by various mechanisms, for example by strong spin-orbit…
We propose a new method to numerically compute the $\mathbb{Z}_2$ indices for disordered topological insulators in Kitaev's periodic table. All of the $\mathbb{Z}_2$ indices are known to be derived from the index formulae which are…
Existing proximity effects stem from systems with a local order parameter, such as a local magnetic moment or a local superconducting pairing amplitude. Here, we demonstrate that despite lacking a local order parameter, topological phases…
The bulk-edge correspondence is a condensed matter theorem that relates the conductance of a Hall insulator in a half-plane to that of its (straight) boundary. In this work, we extend this result to domains with curved boundaries. Under…
A hallmark of certain topology, including the Chern number, is the obstruction to constructing exponentially localized Wannier functions in the bulk bands. Conversely, other types of topology do not necessarily impose Wannier obstructions.…
Quantum Hall systems host chiral edge states extending along the one-dimensional boundary of any two-dimensional sample. In solid state materials, the edge states serve as perfectly robust transport channels that produce a quantised Hall…
We propose a $\mathbb{Z}_{2}$ classification of Abelian time-reversal fractional topological insulators in terms of the composite fermions picture. We consider the standard toy model where spin up and down electrons are subjected to…
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
Utilizing Bott index vectors formulated through a series of polynomials of position operators under open boundary conditions, we establish a universal, rigorous, and complete correspondence between the Bott index vector and topological…
Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI)…
Localization of the helical edge states in quantum spin Hall insulators requires breaking time reversal invariance. In experiments this is naturally implemented by applying a weak magnetic field B. We propse a model based on scattering…
Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal insulator transition and the integral and fractional quantum Hall effects. In this paper, we investigate the role of disorder in the…
We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak…
We have studied the tachyonic excitations in the junction of two topological insulators in the presence of an external magnetic field. The Landau levels, evaluated from an effective two-dimensional model for tachyons, and from the junction…
Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…
This note gives an overview of the mathematical framework underlying topological insulators, highlighting the connection to K-theory and vector bundles. We see ``real'' and ``quaternionic'' vector bundles arise naturally in the presence of…