On the structure of signed Selmer groups

Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclotomic extension of $F$. Generalizing Kobayashi plus/minus Selmer groups for elliptic curves, B\"uy\"ukboduk and Lei have defined modified Selmer groups, called signed Selmer groups, for certain non-ordinary $\mathrm{Gal} \overline{F}/F)$-representations. In particular, their construction applies to abelian varieties defined over $F$ with good supersingular reduction at primes of $F$ dividing $p$. Assuming that these Selmer groups are cotorsion $\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-modules, we show that they have no proper sub-$\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-module of finite index. We deduce from this a number of arithmetic applications. On studying the Euler-Poincar\'e characteristic of these Selmer groups, we obtain an explicit formula on the size of the Bloch-Kato Selmer group attached to these representations. Furthermore, for two such representations that are isomorphic modulo $p$, we compare the Iwasawa-invariants of their signed Selmer groups

On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions

Let $F$ be a number field unramified at an odd prime $p$ and $F_\infty$ be the $\mathbf{Z}_p$-cyclotomic extension of $F$. Let $A$ be an abelian variety defined over $F$ with good supersingular reduction at all primes of $F$ above $p$. B\"uy\"ukboduk and the first named author have defined modified Selmer groups associated to $A$ over $F_\infty$. Assuming that the Pontryagin dual of these Selmer groups are torsion $\mathbf{Z}_p[[\mathrm{Gal}(F_\infty/F)]]$-modules, we give an explicit sufficient condition for the rank of the Mordell-Weil group $A(F_n)$ to be bounded as $n$ varies

Large area Al₂O₃–Au raspberry-like nanoclusters from iterative block-copolymer self-assembly

In the field of functional nanomaterials, core–satellite nanoclusters have recently elicited great interest due to their unique optoelectronic properties. However, core–satellite synthetic routes to date are hampered by delicate and multistep reaction conditions and no practical method has been reported for the ordering of these structures onto a surface monolayer. Herein we show a reproducible and simplified thin film process to fabricate bimetallic raspberry nanoclusters using block copolymer (BCP) lithography. The fabricated inorganic raspberry nanoclusters consisted of a ∼36 nm alumina core decorated with ∼15 nm Au satellites after infusing multilayer BCP nanopatterns. A series of cylindrical BCPs with different molecular weights allowed us to dial in specific nanodot periodicities (from 30 to 80 nm). Highly ordered BCP nanopatterns were then selectively infiltrated with alumina and Au species to develop multi-level bimetallic raspberry features. Microscopy and X-ray reflectivity analysis were used at each fabrication step to gain further mechanistic insights and understand the infiltration process. Furthermore, grazing-incidence small-angle X-ray scattering studies of infiltrated films confirmed the excellent order and vertical orientation over wafer scale areas of Al2O3/Au raspberry nanoclusters. We believe our work demonstrates a robust strategy towards designing hybrid nanoclusters since BCP blocks can be infiltrated with various low cost salt-based precursors. The highly controlled nanocluster strategy disclosed here could have wide ranging uses, in particular for metasurface and optical based sensor applications

High refractive index in low metal content nanoplasmonic surfaces from self-assembled block copolymer thin films

Materials with a high and tunable refractive index are attractive for nanophotonic applications. In this contribution, we propose a straightforward fabrication technique of high-refractive index surfaces based on self-assembled nanostructured block copolymer thin films. The selective and customizable metal incorporation within out-of-plane polymer lamellae produces azimuthally isotropic metallic nanostructures of defined geometries, which were analysed using microscopy and small-angle X-ray scattering techniques. Variable-angle spectroscopic ellipsometry was used to relate the geometrical parameters of the metallic features and the resulting refractive index of the patterned surfaces. In particular, nanostructured gold patterns with a high degree of homogeneity and a gold content as low as 16 vol% reach a refractive index value of more than 3 in the visible domain. Our study thus demonstrates a new route for the preparation of high refractive index surfaces with a low metal content for optical applications

Les triterp\ue8nes des latex d\u27Euphorbia. Contribution \ue0 une \ue9tude chimio-syst\ue9matique du genre Euphorbia

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Spontaneous and field-induced mesomorphism of a silyl-terminated bent-core liquid crystal as determined from second-harmonic generation and resonant X-ray scattering

The polarity and structure of the phases of a liquid crystal constituted by thiophene-based bent-core molecules is investigated by means of optical second-harmonic generation (SHG), and resonant and conventional X-ray diffraction. The material studied is representative of a wide family of mesogens that contain silyl groups at the ends of the chains. These bulky terminal groups have been reported to give rise to smectic phases showing ferroelectric switching. However, the analysis of the SHG signal before and after application of electric fields has allowed us to establish unambiguously that the reported ferroelectricity is not intrinsic to the material but stabilized by the cell substrates once an electric field has been applied. In addition, the results obtained from resonant X-ray diffraction indicate that virgin samples have antiferroelectric undulated synclinic smectic structures

Hierarchical self-assembly of nanoparticles for optical metamaterials

Hierarchical self-assembly arranges nanostructures at different length scales. It gradually becomes an effective method of fabricating artificial metamaterials from composite nanostructures tailored for a particular response. Hierarchical self-assembly overcomes shortcomings of "top-down" methods by significantly reducing fabrication time and making it possible to form bulk materials. Here we report an application of hierarchical self-assembly of metal nanoparticles for the creation of the first isotropic optical metamaterial with strong artificial magnetism in blue light. We have used colloidal self-assembly to create artificial "nanomolecules" that generate the desired magnetic response and microfluidic self-assembly to produce a bulk metastructure. We demonstrate that the magnetic response of the final material is accurately described by an isotropic magnetic permeability that satisfies the principle of locality. Our approach unlocks the fabrication of large volumes of composite nanomaterials. Moreover, the spatial disorder inherent to this "bottom-up" method holds the key to solving the non-locality problem. The technique can be readily extended to the future generations of low-loss optical metamaterials made of dielectric nano-blocks to bypass the limitations of optical losses associated with plasmonic resonances in noble metals.Initiative d'excellence de l'Université de Bordeau