We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold. The frequency and the size of the gaps depend on the local order rather than on the symmetry or the global long range order. Good agreement between theory and experiment is obtained in the microwave regime. Calculations show that the approach can be scaled up to optical frequencies even in the presence of absorption.PACS numbers: 42.70.Qs Photonic band gap (PBG) is a spectral gap in which electromagnetic waves cannot propagate in any direction [1]. Recently, two promising routes have been discovered that may lead to PBG in the IR͞optical frequencies: (i) microfabrication [2] and (ii) inverse-opal and related techniques [3]. Both methods seek to create some predefined artificial structure with an interconnected array of high dielectrics. Here we propose an alternate route. Instead of emphasizing the structure, we focus on the building blocks. The building blocks we propose are spheres with a dielectric core, a metal coating, and an outer insulating layer. With multiple coatings of variable thicknesses, these coated spheres have continuously tunable scattering cross sections and resonances. In analogy with semiconductor physics, we have designable "photonic atoms" which have continuously tunable properties. Depending on how we assemble these spheres together, we can choose the crystal structure which in turn can be changed by external fields [4]. In this paper, we show by physical argument and by explicit calculation and experimentation that any periodic structure formed from such spheres can exhibit photonic band gaps. This contrasts with the conventional PBG systems where the global symmetry and the structure factors are equally important, which in turn lead to added difficulties in their fabrication.In order to handle the calculation involving spherical scatterers with metallic coating, we developed a band structure code based on the multiple scattering technique (MST) [5]. We checked our results against photonic band structures calculated using the finite-difference time domain (FDTD) method, where the convergence has been carefully monitored [6]. The test case is the photonic band structure of ideal metal spheres arranged in the diamond structure with a filling ratio f 0.31, embedded in a medium with e 2.1. This is a demanding test case since the metal spheres touch at f 0.34. With our code, we obtain a gap͞midgap frequency of 0.56 (with angular momentum up to l 7), which is in excellent agreement with that of FDTD [6]. Our result lies between their finest grid value of 0.53 and the extrapolated value of 0.56. The transmission spectra reported below are computed with the layer-MST formalism of Stefanou-Yannopapas-Modinos [7]. The agreement between the band structure code and the transmission code is excellent.Since metallic elements are invo...

Electrochemical carbon dioxide reduction reaction (CO2RR) is an efficient strategy to relieve global environmental and energy issues by converting excess CO2 from the atmosphere to value‐added products. Atomically dispersed metal‐nitrogen‐doped carbon (M‐N‐C) materials are superior catalysts for electrocatalytic CO2RR because of the 100% atomic utilization, unsaturated coordination configuration, relatively uniform active sites, and well‐defined and adjustable structure of active centers. However, the electrochemical CO2RR is a great challenge due to the process involving proton‐coupled multi‐electron transfer with a high energy barrier, which leads to unsatisfactory selectivity to the targeted product, especially for C2 products (e.g., C2H4 and C2H5OH). Here, the authors systematically summarize effective means, including reasonable selection of isolated metal sites, regulation of the coordination environment of isolated metal atoms, and fabrication of dimetallic single‐atom sites for attaining optimal geometric and electronic structures of M‐N‐C materials and further correlate these structures with catalytic selectivity to various C1 (e.g., CO and CH4) and C2 products in the CO2RR. Moreover, constructive strategies to further optimize M‐N‐C materials for electrocatalytic CO2RR are provided. Finally, the challenges and future research directions of the application of M‐N‐C materials for electrocatalytic CO2RR are proposed.

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