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Non-trivial linking invariant encodes robust information of topological matter. It has been recently shown that the linking and winding of complex eigenenergy strings can classify one-dimensional non-Hermitian topological matter. However, in higher dimensions, bundles of linked strings can emerge such that every string is mutually linked with all the other strings. To the best of our knowledge, a non-Hermitian Hopf bundle has not been experimentally clarified. Here, we attempt to explore the non-Hermitian Hopf bundle by visualizing the global linking structure of spinor strings in the momentum space of a two-dimensional electric circuit. By exploiting the flexibility of reconfigurable couplings between circuit nodes, we study the non-Hermitian topological phase transition by exploring the intricate structure of the Hopf bundle. Furthermore, we find that the higher-order skin effect in real space is accompanied by the linking of spinor strings in momentum space, revealing bulk-boundary correspondence between the two domains. all: The authors employ topolectric circuits to realize a non-Hermitian topological Hopf bundle state of matter, which allows them to observe the emergence of phases that are unique to non-Hermitian systems. The proposed non-Hermitian Hopf bundle platform and visualization methodology pave the way for designing new topologically robust non-Hermitian phases of matter. [ABSTRACT FROM AUTHOR]

Berry curvature, the counterpart of the magnetic field in the momentum space, plays a vital role in the transport of electrons in condensed matter physics. It also lays the foundation for the emerging field of topological physics. In the three-dimensional systems, much attention has been paid to Weyl points, which serve as sources and drains of Berry curvature. Here, we demonstrate a toroidal moment of Berry curvature with flux approaching to π in judiciously engineered metamaterials. The Berry curvature exhibits a vortex-like configuration without any source and drain in the momentum space. Experimentally, the presence of Berry curvature toroid is confirmed by the observation of conical-frustum shaped domain-wall states at the interfaces formed by two metamaterials with opposite toroidal moments. The appearance of toroidal multipolar moments in electrodynamics interrogates the question for their existence in Berry curvature, which can be seen as the "magnetic field" in the momentum space. Here, the authors observe 3D vortex distributions in the Berry curvature within a photonic metamaterial. [ABSTRACT FROM AUTHOR]

Multistep plasmonic nanostructures can induce the deep modulation of electromagnetic-field interactions on the nanoscale for positioning hotspots, and this generation of enhanced fields is important in many optical applications. In this article, a new strategy is proposed for fabricating a plasmonic doublestacked nanocone (DSC) nanostructure. In the DSC structure, a tunable plasmonic hybrid mode proceeds from the strong coupling of the plasmonic resonance of a fundamental cavity mode with a localized surface plasmon gap mode. In the nanostructure, the far-field response is deeply modulated and the hottest spots can be effectively positioned on the top surface of the DSC nanostructure. A controllable and cost-effective mask-reconfiguration technique for manufacturing the multiscale nanostructure is developed, which guarantees the generation of the introduced crucial stage on the DSC nanostructure. To evaluate the features of the plasmonic resonance, the DSC nanostructure is used as a surface-enhanced Raman scattering (SERS) substrate for detecting 4-mercaptopyridine molecules under specific excitation conditions. Its good performance, with an average measured SERS enhancement factor as high as 10, demonstrates its strong plasmonic-mode hybridization and extreme field enhancement. [ABSTRACT FROM AUTHOR]