scholarly journals Exact higher-order bulk-boundary correspondence of corner-localized states

2021 ◽  
Vol 104 (19) ◽  
Author(s):  
Minwoo Jung ◽  
Yang Yu ◽  
Gennady Shvets
Keyword(s):  
Higher Order ◽  
Localized States ◽  
Boundary Correspondence

scholarly journals A fractional corner anomaly reveals higher-order topology

Science ◽  
2020 ◽  
Vol 368 (6495) ◽  
pp. 1114-1118 ◽  
Author(s):  
Christopher W. Peterson ◽  
Tianhe Li ◽  
Wladimir A. Benalcazar ◽  
Taylor L. Hughes ◽  
Gaurav Bahl
Keyword(s):  
Charge Density ◽  
Higher Order ◽  
Order Topology ◽  
Two Dimensional ◽  
Spectral Measurements ◽  
Fractional Charge ◽  
Boundary Correspondence ◽  
Rotationally Symmetric ◽  
Topological Crystalline Insulators ◽  
Gap States

Spectral measurements of boundary-localized topological modes are commonly used to identify topological insulators. For high-order insulators, these modes appear at boundaries of higher codimension, such as the corners of a two-dimensional material. Unfortunately, this spectroscopic approach is only viable if the energies of the topological modes lie within the bulk bandgap, which is not required for many topological crystalline insulators. The key topological feature in these insulators is instead fractional charge density arising from filled bulk bands, but measurements of such charge distributions have not been accessible to date. We experimentally measure boundary-localized fractional charge density in rotationally symmetric two-dimensional metamaterials and find one-fourth and one-third fractionalization. We then introduce a topological indicator that allows for the unambiguous identification of higher-order topology, even without in-gap states, and we demonstrate the associated higher-order bulk-boundary correspondence.

scholarly journals Quantum superposition demonstrated higher-order topological bound states in the continuum

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Yao Wang ◽  
Bi-Ye Xie ◽  
Yong-Heng Lu ◽  
Yi-Jun Chang ◽  
Hong-Fei Wang ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Bound States ◽  
Topological Insulators ◽  
Higher Order ◽  
Conclusive Evidence ◽  
Localized States ◽  
Quantum Superposition ◽  
Boundary States ◽  
Superposition States ◽  
The Continuum

AbstractHigher-order topological insulators, as newly found non-trivial materials and structures, possess topological phases beyond the conventional bulk-boundary correspondence. In previous studies, in-gap boundary states such as the corner states were regarded as conclusive evidence for the emergence of higher-order topological insulators. Here, we present an experimental observation of a photonic higher-order topological insulator with corner states embedded into the bulk spectrum, denoted as the higher-order topological bound states in the continuum. Especially, we propose and experimentally demonstrate a new way to identify topological corner states by exciting them separately from the bulk states with photonic quantum superposition states. Our results extend the topological bound states in the continuum into higher-order cases, providing an unprecedented mechanism to achieve robust and localized states in a bulk spectrum. More importantly, our experiments exhibit the advantage of using the time evolution of quantum superposition states to identify topological corner modes, which may shed light on future exploration between quantum dynamics and higher-order topological photonics.

scholarly journals Nonlinear second-order photonic topological insulators

2021 ◽  
Author(s):  
Marco S. Kirsch ◽  
Yiqi Zhang ◽  
Mark Kremer ◽  
Lukas J. Maczewsky ◽  
Sergey K. Ivanov ◽  
...  
Keyword(s):  
Topological Insulators ◽  
Higher Order ◽  
Topological Phase ◽  
Topological Properties ◽  
Linear Evolution ◽  
New Class ◽  
On Demand ◽  
Boundary Correspondence ◽  
Topological States ◽  
The Impact

AbstractHigher-order topological insulators are a novel topological phase beyond the framework of conventional bulk–boundary correspondence1,2. In these peculiar systems, the topologically non-trivial boundary modes are characterized by a co-dimension of at least two3,4. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems5,6, the flourishing field of experimental higher-order topological insulator research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. Here we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.

Vectorial solitons, higher-order localized states and compound states in a single-mirror feedback system

2004 ◽  
Author(s):  
Matthias Pesch ◽  
Edgar Große Westhoff ◽  
Thorsten Ackemann ◽  
Wulfhard Lange
Keyword(s):  
Feedback System ◽  
Higher Order ◽  
Localized States

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

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