Related papers: Controlled topological phases and bulk-edge corres…
The bulk-edge correspondence for topological quantum liquids states that the spectrum of the reduced density matrix of a large subregion reproduces the thermal spectrum of a physical edge. This correspondence suggests an intricate…
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…
The bulk-edge correspondence is one of the most important ingredients in the theory of topological phases of matter. While the bulk-edge correspondence is applicable for Hermitian junction systems where two subsystems with independent…
We propose a unified framework, dubbed topological word, for the complete non-Abelian bulk-boundary correspondence in multigap non-Abelian topological insulators. Composed by an ordered sequence of letters, each a non-Abelian charge…
It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional…
The bulk-boundary correspondence, which relates topological properties of a material in the bulk to the presence of robust modes localized on the edge, is at the core of the now mature field of topological wave physics. More recently, it…
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…
We analyze the topological $\mathbb{Z}_2$ invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological $\mathbb{Z}_2$ invariant counts the parity of…
We demonstrate that the presence of a localized state at the corner of an insulating domain is not always a predictor of a certain non-trivial higher-order topological invariant, even though they appear to co-exist in the same Hamiltonian…
The role of polarization in the topology of quantum emitter chains is investigated theoretically, whereby "polarization" refers to the transition dipole moments of the emitters. We show that, if the chain is zigzag-shaped, different…
Symmetry-protected topological (SPT) phases in insulators and superconductors are known for their robust edge modes, linked to bulk invariants through the bulk-boundary correspondence. While this principle traditionally applies to gapped…
The bulk-edge correspondence principle, a cornerstone of topological physics, ensures that first-order topological systems host robust chiral edge states in two dimension. This was later extended to higher-order phases, where second-order…
We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on…
The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for…
The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in…
The topological pumping [1-3] is revisited from a view point of the bulk-edge correspondence. Shift of the center of mass (CM) as a pumped charge is explicitly given by the Berry connection in time direction. We show that observed pumping…
The interface between two materials described by spectrally gapped Hamiltonians is expected to host an in-gap interface mode, whenever a certain topological invariant changes across the interface. We provide a precise statement of this…
Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems…
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…
In this Letter, we discuss two general classes of apparent violations of the bulk-edge correspondence principle for uniform topological photonic materials, associated with the asymptotic behavior of the surface modes for diverging…