Menger's Theorem in bidirected graphs

Bidirected graphs are a generalisation of directed graphs that arises in the study of undirected graphs with perfect matchings. Menger's famous theorem - the minimum size of a set separating two vertex sets $X$ and $Y$ is the same as the maximum number of disjoint paths connecting them - is generally not true in bidirected graphs. We introduce a sufficient condition for $X$ and $Y$ which yields a version of Menger's Theorem in bidirected graphs that in particular implies its directed counterpart.Comment: 23 pages, 6 figure

Dark interlayer plasmons in colloidal gold nanoparticle bi- and few-layers

We demonstrate the excitation of dark plasmon modes with linearly polarized light at normal incidence in self-assembled layers of gold nanoparticles. Because of field retardation, the incident light field induces plasmonic dipoles that are parallel within each layer but antiparallel between the layers, resulting in a vanishing net dipole moment. Using microabsorbance spectroscopy we measured a pronounced absorbance peak and reflectance dip at 1.5 eV for bi- and trilayers of gold nanoparticles with a diameter of 46 nm and 2 nm interparticle gap size. The excitations were identified as dark interlayer plasmons by finite-difference time-domain simulations. The dark plasmon modes are predicted to evolve into standing waves when further increasing the layer number, which leads to 90% transmittance of the incident light through the nanoparticle film. Our approach is easy to implement and paves the way for large-area coatings with tunable plasmon resonance

Dark plasmon modes for efficient hot electron generation in multilayers of gold nanoparticles

The excitation of dark plasmons, i.e., coupled plasmon modes with a vanishing net dipole, is expected to favor Landau damping over radiative damping. Dark plasmon excitation might, therefore, lead to an increased absorption of energy within gold nanoparticles, resulting in a strong generation of hot electrons compared to the generation via bright plasmons. We performed transient-absorption spectroscopy on gold nanoparticle films to assess the initial electronic temperature before thermalization. We observe a significant increase in the electron–phonon coupling time when dark plasmon modes are excited in these films. The results indicate an efficient energy absorption due to the suppressed radiative decay of dark plasmon modes and a subsequent energy transformation into hot electrons

Direct optical excitation of dark plasmons for hot electron generation

An ideal plasmonic system for hot-electron generation allows the optical excitation of plasmons, limits radiation losses, exhibits strong non-radiative electron damping, and is made from scalable and cost-effective materials. Here we demonstrate the optical excitation of dark interlayer plasmons in bilayers of colloidal gold nanoparticles. This excitation is created by an antiparallel orientation of the dipole moments in the nanoparticle layers; it is expected to exhibit strongly reduced radiative damping. Despite the vanishing dipole moment, an incoming electromagnetic wave that is propagating normal to the surface will excite the dark mode due to field retardation. We observe a strong peak in the absorption spectrum of a colloidal gold bilayer (nanoparticle diameter = 46 nm); this peak is absent for a nanoparticle monolayer. The full width at half maximum of the dark mode is 230 meV for an ideal nanoparticle crystal and 320 meV for the structure produced by self-assembly out of solution. The position and width of the dark plasmon are efficiently tailored by the interparticle distance within the layer, nanoparticle size and layer number. We present time-resolved pump and probe experiments of hot-electron generation by bright and dark bilayer nanoparticle modes

Structural order in plasmonic superlattices

The assembly of plasmonic nanoparticles into ordered 2D- and 3D-superlattices could pave the way towards new tailored materials for plasmonic sensing, photocatalysis and manipulation of light on the nanoscale. The properties of such materials strongly depend on their geometry, and accordingly straightforward protocols to obtain precise plasmonic superlattices are highly desirable. Here, we synthesize large areas of crystalline mono-, bi- and multilayers of gold nanoparticles >20nm with a small number of defects. The superlattices can be described as hexagonal crystals with standard deviations of the lattice parameter below 1%. The periodic arrangement within the superlattices leads to new well-defined collective plasmon-polariton modes. The general level of achieved superlattice quality will be of benefit for a broad range of applications, ranging from fundamental studies of light-matter interaction to optical metamaterials and substrates for surface-enhanced spectroscopies. Superlattices of nanoparticles promise new properties emerging from the periodic order. Here, the authors describe the synthesis of superlattices of plasmonic gold nanoparticles with high crystallinity and demonstrate how new plasmon-polariton modes appear in the structures

A test of the extreme value type I assumption in the bus engine replacement model

This note tests the assumption of dynamic discrete choice models that underlying utility shocks have an extreme value type I distribution. We find that extreme value type I shocks cannot be rejected in most specifications of the Rust (1987) bus engine replacement model

Plasmonic bimetallic two-dimensional supercrystals for H2 generation

Sunlight-driven H-2 generation is a central technology to tackle our impending carbon-based energy collapse. Colloidal photocatalysts consisting of plasmonic and catalytic nanoparticles are promising for H-2 production at solar irradiances, but their performance is hindered by absorption and multiscattering events. Here we present a two-dimensional bimetallic catalyst by incorporating platinum nanoparticles into a well-defined supercrystal of gold nanoparticles. The bimetallic supercrystal exhibited an H-2 generation rate of 139mmolg(cat)(-1)h(-1) via formic acid dehydrogenation under visible light illumination and solar irradiance. This configuration makes it possible to study the interaction between the two metallic materials and the influence of this in catalysis. We observe a correlation between the intensity of the electric field in the hotspots and the boosted catalytic activity of platinum nanoparticles, while identifying a minor role of heat and gold-to-platinum charge transfer in the enhancement. Our results demonstrate the benefits of two-dimensional configurations with optimized architecture for liquid-phase photocatalysis

Impact of substrate on tip-enhanced Raman spectroscopy: A comparison between field-distribution simulations and graphene measurements

Tip-enhanced Raman spectroscopy (TERS) has reached nanometer spatial resolution for measurements performed at ambient conditions and subnanometer resolution at ultrahigh vacuum. Super-resolution (beyond the tip apex diameter) TERS has been obtained mostly in the gap mode configuration, where a conductive substrate localizes the electric fields. Here we present experimental and theoretical TERS to explore the field distribution responsible for spectral enhancement. We use gold tips of 40 +/- 10 nm apex diameter to measure TERS on graphene, a spatially delocalized two-dimensional sample, sitting on different substrates: (i) glass, (ii) a thin layer of gold and (iii) a surface covered with 12 nm diameter gold spheres, for which 6 nm resolution is achieved at ambient conditions. The super-resolution is due to the field configuration resulting from the coupled tip-sample-substrate system, exhibiting a nontrivial spatial surface distribution. The field distribution and the symmetry selection rules are different for nongap versus gap mode configurations. This influences the overall enhancement which depends on the Raman mode symmetry and substrate structure