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A general and simple semi-analytic theory of multilayer dielectric gratings is presented. It extends a previous work [J. Opt. Soc. Am. A 41 , 252 (2024)] that assumes symmetric grating profile and Littrow mounting to gratings of asymmetric profiles in off-Littrow mounting.

van der Waals heterostructures constitute a new class of artificial materials formed by stacking atomically thin planar crystals. We demonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. In our samples, this interplay between short-and long-wavelength effects resulted in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality. This picture is confirmed by our observation of fractional quantum Hall states at ±5/3 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.

This paper proposes a method for locating small multi-layer inclusions, addressing the challenge of accurately identifying the position and properties of such inclusions within layered materials. The difficulty lies in the complex nature of multi-layered structures, where traditional methods often fail to provide precise results. A mathematical model for multiple-layered inclusions is developed using the Laplace system to tackle this. The solution is then derived through asymptotic analysis and layer-potential techniques. The uniqueness of the recovery process is confirmed by applying the unique continuation theorem, ensuring the method’s reliability for precise identification of small inclusions in layered media.

Field-tunable bandgap in bilayer graphene The electronic bandgap of a material refers to an energy region where electrons are not 'allowed' to reside because of quantum mechanical considerations related to the symmetries and atomic constituents of the underlying crystal structure. It is a fundamental property of semiconductors and insulators and determines their electrical and optical response, which is why it is a crucial consideration in modern device physics and technologies. Ideally, the bandgap would be tunable by electric fields, which would allow great flexibility in device design and functionality. Until now electrical tunability has proved elusive, but now Zhang et al . demonstrate such a tunable bandgap in a bilayer-graphene-based device, spanning a spectral range from zero to mid-infrared. The ability to electrically control the bandgap, a fundamental property of semiconductors and insulators that determines electrical and optical response, is highly desirable for device design and functionality. Experiments now demonstrate versatile control of the bandgap in bilayer graphene-based devices by use of electric fields. The electronic bandgap is an intrinsic property of semiconductors and insulators that largely determines their transport and optical properties. As such, it has a central role in modern device physics and technology and governs the operation of semiconductor devices such as p–n junctions, transistors, photodiodes and lasers 1 . A tunable bandgap would be highly desirable because it would allow great flexibility in design and optimization of such devices, in particular if it could be tuned by applying a variable external electric field. However, in conventional materials, the bandgap is fixed by their crystalline structure, preventing such bandgap control. Here we demonstrate the realization of a widely tunable electronic bandgap in electrically gated bilayer graphene. Using a dual-gate bilayer graphene field-effect transistor (FET) 2 and infrared microspectroscopy 3 , 4 , 5 , we demonstrate a gate-controlled, continuously tunable bandgap of up to 250 meV. Our technique avoids uncontrolled chemical doping 6 , 7 , 8 and provides direct evidence of a widely tunable bandgap—spanning a spectral range from zero to mid-infrared—that has eluded previous attempts 2 , 9 . Combined with the remarkable electrical transport properties of such systems, this electrostatic bandgap control suggests novel nanoelectronic and nanophotonic device applications based on graphene.

Consider the multivariate nonparametric regression model. It is shown that estimators based on sparsely connected deep neural networks with ReLU activation function and properly chosen network architecture achieve theminimax rates of convergence (up to log n-factors) under a general composition assumption on the regression function. The framework includes many well-studied structural constraints such as (generalized) additive models. While there is a lot of flexibility in the network architecture, the tuning parameter is the sparsity of the network. Specifically, we consider large networks with number of potential network parameters exceeding the sample size. The analysis gives some insights into why multilayer feedforward neural networks perform well in practice. Interestingly, for ReLU activation function the depth (number of layers) of the neural network architectures plays an important role, and our theory suggests that for nonparametric regression, scaling the network depth with the sample size is natural. It is also shown that under the composition assumption wavelet estimators can only achieve suboptimal rates.

In this study, double‐multilayer monochromators that generate intense, high‐energy, pink X‐ray beams are designed, installed and evaluated at the SPring‐8 medium‐length (215 m) bending‐magnet beamline BL20B2 for imaging applications. Two pairs of W/B4C multilayer mirrors are designed to utilize photon energies of 110 keV and 40 keV with bandwidths of 0.8% and 4.8%, respectively, which are more than 100 times larger when compared with the Si double‐crystal monochromator (DCM) with a bandwidth of less than 0.01%. At an experimental hutch located 210 m away from the source, a large and uniform beam of size 14 mm (V) × 300 mm (H) [21 mm (V) × 300 mm (H)] was generated with a high flux density of 1.6 × 109 photons s−1 mm−2 (6.9 × 1010 photons s−1 mm−2) at 110 keV (40 keV), which marked a 300 (190) times increase in the photon flux when compared with a DCM with Si 511 (111) diffraction. The intense pink beams facilitate advanced X‐ray imaging for large‐sized objects such as fossils, rocks, organs and electronic devices with high speed and high spatial resolution. Double‐multilayer monochromators for high‐energy and large‐field X‐ray imaging applications are designed, installed and evaluated at the SPring‐8 medium‐length (215 m) bending‐magnet beamline BL20B2.

In this work a multilayer barrier paperboard was produced in a roll-to-roll process by slot-die coating of nanocellulose (microfibrillated cellulose or carboxymethylated cellulose nanofibrils) followed by extrusion coating of biodegradable thermoplastics (polylactic acid, polybutylene adipate terephthalate and polybutylene succinate). Hyperplaty kaolin pigments were blended in different ratios into nanocellulose to tailor the barrier properties of the multilayer structure and to study their influence on adhesion to the thermoplastic top layer. Influence of a plasticizer (glycerol) on flexibility and barrier performance of the multilayer structure was also examined. Water vapor permeance for the multilayer paperboard was below that of control single-layer thermoplastic materials, and oxygen permeance of the coated structure was similar or lower than that of pure nanocellulose films. Glycerol as a plasticizer further lowered the oxygen permeance and kaolin addition improved the adhesion at the nanocellulose/thermoplastic interface. The results provide insight into the role played by nanocelluloses, thermoplastics, pigments, and plasticizers on the barrier properties when these elements are processed together into multilayer structures, and paves the way for industrial production of sustainable packaging.

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n  = 0 and displacement field D  = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D , we observed a Chern insulator state with C  = −5 and two other states with C  = −3 at a magnetic field of around 1 T. At high D and n , we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering. Pentalayer graphene in the rhombohedral stacking order exhibits rich phases including a correlated insulator, isospin-polarized metals and Chern insulators. These findings demonstrate electron-correlated and topological states in crystalline 2D materials without the need for a moiré superlattice.

Optoelectronic effects differentiating absorption of right and left circularly polarized photons in thin films of chiral materials are typically prohibitively small for their direct photocurrent observation. Chiral metasurfaces increase the electronic sensitivity to circular polarization, but their out-of-plane architecture entails manufacturing and performance trade-offs. Here, we show that nanoporous thin films of chiral nanoparticles enable high sensitivity to circular polarization due to light-induced polarization-dependent ion accumulation at nanoparticle interfaces. Self-assembled multilayers of gold nanoparticles modified with l - phenylalanine generate a photocurrent under right-handed circularly polarized light as high as 2.41 times higher than under left-handed circularly polarized light. The strong plasmonic coupling between the multiple nanoparticles producing planar chiroplasmonic modes facilitates the ejection of electrons, whose entrapment at the membrane–electrolyte interface is promoted by a thick layer of enantiopure phenylalanine. Demonstrated detection of light ellipticity with equal sensitivity at all incident angles mimics phenomenological aspects of polarization vision in marine animals. The simplicity of self-assembly and sensitivity of polarization detection found in optoionic membranes opens the door to a family of miniaturized fluidic devices for chiral photonics. Chiral gold nanoparticles coated with enantiomerically pure phenylalanine were assembled into nanoporous membranes, whose ionic conductivity depends on the handedness of the incident circularly polarized light.