Related papers: Microlocal analysis of the bulk-edge correspondenc…

We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped…

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects.…

Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge…

We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…

We analyze continuous partial differential models of topological insulators in the form of systems of Dirac equations. We describe the bulk and interface topological properties of the materials by means of indices of Fredholm operators…

The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…

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…

Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…

I analyze electron transport through a Y-junction formed by helical edge states of a two-dimensional topological insulator (2DTI), focusing on the strongly interacting regime. An experimentally motivated device geometry and a…

Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological…

We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase…

This paper analyzes Floquet topological insulators resulting from the time-harmonic irradiation of electromagnetic waves on two dimensional materials such as graphene. We analyze the bulk and edge topologies of approximations to the…

Most natural and artificial materials have crystalline structures from which abundant topological phases emerge [1-6]. The bulk-edge correspondence, widely-adopted in experiments to determine the band topology from edge properties, however,…

Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one…

The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current…

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…

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…

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…

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact…

We study the open system dynamics and steady states of two dimensional Floquet topological insulators: systems in which a topological Floquet-Bloch spectrum is induced by an external periodic drive. We solve for the bulk and edge state…