Probing topological protection using a designer surface plasmon structure.

Xihang Shi,Zhaoju Yang,John D. Joannopoulos,Hongyi Xu,Ling Lu,Zhen Gao,Marin Soljačić,Yidong Chong,Xiao Lin,Baile Zhang,Hongsheng Chen,Fei Gao

doi:10.1038/ncomms11619

Abstract

Topological photonic states, inspired by robust chiral edge states in topological insulators, have recently been demonstrated in a few photonic systems, including an array of coupled on-chip ring resonators at communication wavelengths. However, the intrinsic difference between electrons and photons determines that the ‘topological protection' in time-reversal-invariant photonic systems does not share the same robustness as its counterpart in electronic topological insulators. Here in a designer surface plasmon platform consisting of tunable metallic sub-wavelength structures, we construct photonic topological edge states and probe their robustness against a variety of defect classes, including some common time-reversal-invariant photonic defects that can break the topological protection, but do not exist in electronic topological insulators. This is also an experimental realization of anomalous Floquet topological edge states, whose topological phase cannot be predicted by the usual Chern number topological invariants.

Highlights

The ideal elastic limit is the upper bound to the stress and elastic strain a material can withstand
The observed onset of yielding in bulk MGs2 is known to be controlled by the relatively easy propagation of shear bands[4,5], which is the dominant mode of plastic deformation at temperatures well below the glass transition temperature (Tg)
In the amorphous structure there are internal ‘defects’ or inherently more fertile sites for shear transformations, and their coordinated organization/evolution can lead to the formation of shear bands[4,5,6]. This is analogous to the case of crystalline metals: normally there are pre-existing dislocations and easy sources for dislocation nucleation; in their absence yielding can be delayed so much that the elastic limit can be pushed towards the ‘theoretical strength’, which is at least an order of magnitude higher than the commonly observed apparent σy

Summary

Introduction

The ideal elastic limit is the upper bound to the stress and elastic strain a material can withstand. In the amorphous structure there are internal ‘defects’ or inherently more fertile sites for shear transformations, and their coordinated organization/evolution can lead to the formation of shear bands[4,5,6] This is analogous to the case of crystalline metals: normally there are pre-existing dislocations and easy sources for dislocation nucleation; in their absence yielding can be delayed so much that the elastic limit can be pushed towards the ‘theoretical strength’, which is at least an order of magnitude higher than the commonly observed apparent σy. It is well known that small volume single crystalline samples, such as whiskers[7], nanowires[8] and nanopillars[9], offer the opportunity to observe ultrahigh strength and large elastic strains close to the theoretical limit[10] This is because only for such micro- and nano-scale samples can pristine crystals be made to minimize those defects that are inevitable in their bulk counterpart, such that nucleation of fresh defects is often required for yielding. The in situ transmission electron microscopy (TEM) tensile tests using ‘window-frame’ rather than free-standing samples, are complicated by confinements/constraints and the lack of quantitative stress–strain curves[13,22]

Methods

Results

Conclusion