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We utilize a combined computational-experimental approach to examine the influence of indium nanoparticle (NP) array distributions on deep-ultraviolet (UV) plasmon resonances. For photon energies < 5.7 eV, analysis of ellipsometric spectra reveals an increase in silicon reflectance induced by indium NP arrays on silicon. For various energies in the range 5.7–7.0 eV, a decrease in reflectance is induced by the NP arrays. Similar trends in reflectance are predicted from finite-difference time-domain (FDTD) simulations using NP size distributions extracted from atomic-force micrographs as input. In addition, in the energy range of 7.4–9.2 eV, the FDTD simulations reveal reflectance minima, characteristic of localized surface plasmon resonances. Electron energy-loss spectroscopy collected from individual indium NPs reveals the presence of LSPR at ≈ 8 eV, further supporting the promise of indium NP arrays on silicon for deep-UV plasmonics. 

We construct a broad class of bounded potentials of the one-dimensional Schroedinger operator that have the same spectral structure as periodic finite-gap potentials, but that are neither periodic nor quasi-periodic. Such potentials, which we call primitive, are non-uniquely parametrized by a pair of positive Hoelder continuous functions defined on the allowed bands. Primitive potentials are constructed as solutions of a system of singular integral equations, which can be efficiently solved numerically. Simulations show that these potentials can have a disordered structure. Primitive potentials generate a broad class of bounded non-vanishing solutions of the KdV hierarchy, and we interpret them as an example of integrable turbulence in the framework of the KdV equation. 

The history of the growth of continental crust is uncertain, and several different models that involve a gradual, decelerating, or stepwise process have been proposed1,2,3,4. Even more uncertain is the timing and the secular trend of the emergence of most landmasses above the sea (subaerial landmasses), with estimates ranging from about one billion to three billion years ago5,6,7. The area of emerged crust influences global climate feedbacks and the supply of nutrients to the oceans8, and therefore connects Earth’s crustal evolution to surface environmental conditions9,10,11. Here we use the triple-oxygen-isotope composition of shales from all continents, spanning 3.7 billion years, to provide constraints on the emergence of continents over time. Our measurements show a stepwise total decrease of 0.08 per mille in the average triple-oxygen-isotope value of shales across the Archaean–Proterozoic boundary. We suggest that our data are best explained by a shift in the nature of water–rock interactions, from near-coastal in the Archaean era to predominantly continental in the Proterozoic, accompanied by a decrease in average surface temperatures. We propose that this shift may have coincided with the onset of a modern hydrological cycle owing to the rapid emergence of continental crust with near-modern average elevation and aerial extent roughly 2.5 billion years ago.