Magneto-Optics of Exciton Rydberg States in a Monolayer Semiconductor

We report 65 tesla magneto-absorption spectroscopy of exciton Rydberg states in the archetypal monolayer semiconductor WSe$_2$. The strongly field-dependent and distinct energy shifts of the 2s, 3s, and 4s excited neutral excitons permits their unambiguous identification and allows for quantitative comparison with leading theoretical models. Both the sizes (via low-field diamagnetic shifts) and the energies of the $ns$ exciton states agree remarkably well with detailed numerical simulations using the non-hydrogenic screened Keldysh potential for 2D semiconductors. Moreover, at the highest magnetic fields the nearly-linear diamagnetic shifts of the weakly-bound 3s and 4s excitons provide a direct experimental measure of the exciton's reduced mass, $m_r = 0.20 \pm 0.01~m_0$.Comment: To appear in Phys. Rev. Lett. Updated version (25 jan 2018) now includes detailed supplemental discussion of Landau levels, Rydberg exciton energies, exciton mass, Dirac Hamiltonian, nonparabolicity, and dielectric effect

Polarization-Sensitive Optical Responses from Natural Layered Hydrated Sodium Sulfosalt Gerstleyite

Multi-element layered materials have gained substantial attention in the context of achieving the customized light-matter interactions at subwavelength scale via stoichiometric engineering, which is crucial for the realization of miniaturized polarization-sensitive optoelectronic and nanophotonic devices. Herein, naturally occurring hydrated sodium sulfosalt gerstleyite is introduced as one new multi-element van der Waals (vdW) layered material. The mechanically exfoliated thin gerstleyite flakes are demonstrated to exhibit polarization-sensitive anisotropic linear and nonlinear optical responses including angle-resolved Raman scattering, anomalous wavelength-dependent linear dichroism transition, birefringence effect, and polarization-dependent third-harmonic generation (THG). Furthermore, the third-order nonlinear susceptibility of gerstleyite crystal is estimated by the probed flake thickness-dependent THG response. We envisage that our findings in the context of polarization-sensitive light-matter interactions in the exfoliated hydrated sulfosalt layers will be a valuable addition to the vdW layered material family and will have many implications in compact waveplates, on-chip photodetectors, optical sensors and switches, integrated photonic circuits, and nonlinear signal processing applications

Naturally Occurring Layered Mineral Franckeite with Anisotropic Raman Scattering and Third-Harmonic Generation Responses

Vertically stacked van der Waals (vdW) heterostructures have introduced a unique way to engineer optical and electronic responses in multifunctional photonic and quantum devices. However, the technical challenges associated with the artificially fabricated vertical heterostructures have emerged as a bottleneck to restrict their proficient utilization, which emphasizes the necessity of exploring naturally occurring vdW heterostructures. As one type of naturally occurring vdW heterostructures, franckeite has recently attracted significant interest in optoelectronic applications, but the understanding of light-matter interactions in such layered mineral is still very limited especially in the nonlinear optical regime. Herein, the anisotropic Raman scattering and third-harmonic generation (THG) from mechanically exfoliated franckeite thin flakes are investigated. The observed highly anisotropic Raman modes and THG emission patterns originate from the low-symmetry crystal structure of franckeite induced by the lattice incommensurability between two constituent stacked layers. The thickness-dependent anisotropic THG response is further analyzed to retrieve the third-order nonlinear susceptibility for franckeite crystal. The results discussed herein not only provide new insights in engineering the nonlinear light-matter interactions in natural vdW heterostructures, but also develop a testbed for designing future miniaturized quantum photonics devices and circuits based on such heterostructures

The inverse electromagnetic scattering problem in a piecewise homogeneous medium

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].Comment: 19 pages, 2 figures, submitted for publicatio

Inference of gene regulatory networks from genome-wide knockout fitness data

Motivation: Genome-wide fitness is an emerging type of high-throughput biological data generated for individual organisms by creating libraries of knockouts, subjecting them to broad ranges of environmental conditions, and measuring the resulting clone-specific fitnesses. Since fitness is an organism-scale measure of gene regulatory network behaviour, it may offer certain advantages when insights into such phenotypical and functional features are of primary interest over individual gene expression. Previous works have shown that genome-wide fitness data can be used to uncover novel gene regulatory interactions, when compared with results of more conventional gene expression analysis. Yet, to date, few algorithms have been proposed for systematically using genome-wide mutant fitness data for gene regulatory network inference. Results: In this article, we describe a model and propose an inference algorithm for using fitness data from knockout libraries to identify underlying gene regulatory networks. Unlike most prior methods, the presented approach captures not only structural, but also dynamical and non-linear nature of biomolecular systems involved. A state–space model with non-linear basis is used for dynamically describing gene regulatory networks. Network structure is then elucidated by estimating unknown model parameters. Unscented Kalman filter is used to cope with the non-linearities introduced in the model, which also enables the algorithm to run in on-line mode for practical use. Here, we demonstrate that the algorithm provides satisfying results for both synthetic data as well as empirical measurements of GAL network in yeast Saccharomyces cerevisiae and TyrR–LiuR network in bacteria Shewanella oneidensis

Investigating the impact of anatase on the dissolution of boehmite

The dissolution of boehmite in synthetic Bayer liquors is inhibited in the presence of anatase. It has been suggested both by us and others (e.g. Loan et al., 2005) that dissolved titanate adsorbs onto the surface of the boehmite limiting its dissolution. This manuscript reports on digestion, X-ray diffraction (XRD) and transmission electron microscopy (TEM) investigations of boehmite solids partially dissolved in synthetic Bayer liquor in the presence of anatase. Energy filtered transmission electron microscopy (EFTEM) is used to obtain elemental distribution maps, which support the adsorption hypothesis and show enrichment of titanium on the boehmite crystals. Interestingly, the aluminium also becomes associated with some of the Ti-rich particles