Edge-following topological states

The $K$-theoretic bulk-edge correspondence for topological insulators

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 sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real $C^*$-algebras and $KKO$-theory must be used.

Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structures

This paper summarizes and extends the authors' work on the bifurcation of topologically protected edge states in continuous two-dimensional honeycomb structures. We consider a family of Schrödinger Hamiltonians consisting of a bulk honeycomb potential and a perturbing edge potential. The edge potential interpolates between two different periodic structures via a domain wall. We begin by reviewing our recent bifurcation theory of edge states for continuous two-dimensional honeycomb structures. The topologically protected bifurcation of edge states is seeded by the zero-energy eigenstate of a on…

具有奇时间反演对称性的拓扑绝缘体的绝对连续边谱

Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry

该研究证明受奇时间反演对称性保护的非平凡二维拓扑绝缘体具有绝对连续边谱，借助Wold分解的时间反演对称版本分离出其弹道边缘模，为相关拓扑绝缘体的边缘态性质提供了理论证明。

沿弯曲界面的拓扑边缘谱

Topological edge spectrum along curved interfaces

本文研究拓扑绝缘体边界几何形状对导电性的影响，证明边界将平面分成两个含任意大球区域时必为导体，而可嵌入条带内的拓扑绝缘体则未必存在导电边界模式。

Magnetic slowdown of topological edge states

We study the propagation of wavepackets along curved interfaces between topological, magnetic materials. Our Hamiltonian is a massive Dirac operator with a magnetic potential. We construct semiclassical wavepackets propagating along the curved interface as adiabatic modulations of straight edge states under constant magnetic fields. While in the magnetic-free case, the wavepackets propagate coherently at speed one, here they experience slowdown, dispersion, and Aharonov - Bohm effects. Several numerical simulations illustrate our results.

Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors

Identifying entanglement-based order parameters characterizing topological systems, in particular topological superconductors and topological insulators, has remained a major challenge for the physics of quantum matter in the last two decades. Here we show that the end-to-end, long-distance, bipartite squashed entanglement between the edges of a many-body system, defined in terms of the edge-to-edge quantum conditional mutual information, is the natural nonlocal order parameter for topological superconductors in one dimension as well as in quasi one-dimensional geometries. For the Kitaev chain…