Abstract: Friedel's law states that the modulus of the Fourier transform of real functions is centrosymmetric, while the phase is antisymmetric. As a consequence of this, elastic scattering of plane-wave photons or electrons within the first-order Born-approximation, as well as Fraunhofer diffraction on any aperture, is bound to result in centrosymmetric diffraction patterns. Friedel's law, however, does not apply for vortex beams, and centrosymmetry in general is not present in their diffraction patterns. In this work we extend Friedel's law for vortex beams by showing that the diffraction patterns of vortex beams with opposite topological charge, scattered on the same two-dimensional potential, always are centrosymmetric to one another, regardless of the symmetry of the scattering object. We verify our statement by means of numerical simulations and experimental data. Our research provides deeper understanding in vortex-beam diffraction and can be used to design new experiments to measure the topological charge of vortex beams with diffraction gratings or to study general vortex-beam diffraction.

Abstract: We show numerically that a harmonically trapped and coherently Rabi-coupled three-component Bose-Einstein condensate can host unconventional vortex lattices in its rotating ground state. The discovered lattices incorporate square and zig-zag patterns, vortex dimers and chains, and doubly quantized vortices, and they can be quantitatively classified in terms of a skyrmionic topological index, which takes into account the multicomponent nature of the system. The exotic ground-state lattices arise due to the intricate interplay of the repulsive density-density interactions and the Rabi couplings as well as the ubiquitous phase frustration between the components. In the frustrated state, domain walls in the relative phases can persist between some components even at strong Rabi coupling, while vanishing between others. Consequently, in this limit the three-component condensate effectively approaches a two-component condensate with only density-density interactions. At intermediate Rabi coupling strengths, however, we face unique vortex physics that occurs neither in the two-component counterpart nor in the purely density-density-coupled three-component system.

Abstract: Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow variations in the single-particle density of states driven by the size quantization. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size coherent effects, overlooked previously. The many-body physics is revealed here in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. The single-particle energy spectrum for the transverse dimensions is tightly bound, whereas for the longitudinal direction it resembles a quasi-free dispersion. This results in the formation of a series of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subband, and the aggregate condensate contains both BCS and BEC-like components.

Abstract: We investigate topological aspects of subnanometer electron vortex beams upon elastic propagation through atomic scattering potentials. Two main aspects can be distinguished: (i) significantly reduced delocalization compared to a similar nonvortex beam if the beam centers on an atomic column and (ii) site symmetry dependent splitting of higher-order vortex beams. Furthermore, the results provide insight into the complex vortex line fabric within the elastically scattered wave containing characteristic vortex loops predominantly attached to atomic columns and characteristic twists of vortex lines around atomic columns. DOI: 10.1103/PhysRevA.87.033834

Abstract: Electron vortex beams have been predicted to enable atomic scale magnetic information measurement, via transfer of orbital angular momentum. Research so far has focused on developing production techniques and applications of these beams. However, methods to measure the outgoing orbital angular momentum distribution are also a crucial requirement towards this goal. Here, we use a method to obtain the orbital angular momentum decomposition of an electron beam, using a multipinhole interferometer. We demonstrate both its ability to accurately measure orbital angular momentum distribution, and its experimental limitations when used in a transmission electron microscope.

Abstract: We numerically study the vortex-vortex interaction in multicomponent homogeneous Bose-Einstein condensates within the realm of the Gross-Pitaevskii theory. We provide strong evidence that pairwise vortex interaction captures the underlying mechanisms which determine the geometric configuration of the vortices, such as different lattices in many-vortex states, as well as the bound vortex states with two (dimer) or three (trimer) vortices. Specifically, we discuss and apply our theoretical approach to investigate intra- and intercomponent vortex-vortex interactions in two- and three-component Bose-Einstein condensates, thereby shedding light on the formation of the exotic vortex configurations. These results correlate with current experimental efforts in multicomponent Bose-Einstein condensates and the understanding of the role of vortex interactions in multiband superconductors.

Abstract: Recent theoretical and experimental developments in the field of electron-vortex-beam physics have raised questions about what exactly this novelty in the field of electron microscopy (and other fields, such as particle physics) really provides. An important part of the answer to these questions lies in scattering theory. The present investigation explores various aspects of inelastic quantum scattering theory for cylindrically symmetric beams with orbital angular momentum. The model system of Coulomb scattering on a hydrogen atom provides the setting to address various open questions: How is momentum transferred? Do vortex beams selectively excite atoms, and how can one employ vortex beams to detect magnetic transitions? The analytical approach presented here provides answers to these questions. OAM transfer is possible, but not through selective excitation; rather, by pre- and postselection one can filter out the relevant contributions to a specific signal.

Abstract: Controlling the morphology of organolead halide perovskite crystals is crucial to a fundamental understanding of the materials and to tune their properties for device applications. Here, we report a facile solution-based method for morphology-controlled synthesis of rod-like and plate-like organolead halide perovskite nanocrystals using binary capping agents. The morphology control is likely due to an interplay between surface binding kinetics of the two capping agents at different crystal facets. By high-resolution scanning transmission electron microscopy, we show that the obtained nanocrystals are monocrystalline. Moreover, long photoluminescence decay times of the nanocrystals indicate long charge diffusion lengths and low trap/defect densities. Our results pave the way for large-scale solution synthesis of organolead halide perovskite nanocrystals with controlled morphology for future device applications.

Abstract: In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the ul-component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.

Abstract: An important issue in biodiversity valuation is gaining a better understanding of how biodiversity conservation affects economic activities and human welfare. Quantifying the economic benefits of biodiversity for human well-being is not straightforward. Here, we expand the ecosystem service cascade by (i) attributing a methodology to the different steps of the cascade to assess the effects of changes in functional group diversity on economic activities; (ii) including multiple attributes for defining functional diversity and (iii) integrating a dynamic ecological model simulating complex interactions and feedbacks between species with an economic model assessing the effects of changes in functional group diversity for gross revenues. The stepwise methodological framework integrates a production function approach with a market price-based approach in order to investigate the indirect use value of functional group diversity based on the ecological role of species in the ecosystem. The methodology is applied to estimate the relationship between the gross economic value of Chinook salmon (Pacific Northwest, United States) and the diversity of freshwater macroinvertebrates. The results of our analysis emphasize the importance of biological diversity for sustaining ecosystem goods and services. The analysis provides a tractable framework for quantitatively exploring the economic consequences of changes in functional group diversity.

Abstract: In spite of global actions, biodiversity is declining at an alarming rate. Despite the need for objectively comparable monetary standards to include biodiversity arguments in policymaking, research on the relationship between species diversity and its valuation from a societal perspective is still scarce. In this paper, a methodological framework for the valuation of natural predators based on their ecological role in the agroecosystem is introduced. The framework integrates a dynamic ecological model simulating interactions between species with an economic model, thereby quantifying the effect of reduced numbers of natural predators on the net farm income. The model attributes an objective monetary value to increased species diversity through the changes in the provisioning of a marketable good. Results indicate that the loss of three predators could decrease net farm income with 88.86 ha− 1 to 2186.5 ha− 1. For the pear production sector in Flanders in 2011, this constitutes to an indirect use value of 0,68 million for one predator and 16.63 million for the presence of three predators. The aim is to provide a justification for the argument for biodiversity conservation, based on the ecological function of species, through the delivery of comparable monetary standards.

Abstract: Integrated ecosystem management is challenging due to many, often conflicting, targets and limited resources to allocate. A valuable and straightforward approach is to integrate an ecosystem services assessment in a cost-effectiveness analysis as method to evaluate and compare the cost-effectiveness of several management scenarios to reach one or more objectives and take into account the potential effects on other ecosystem functions and services. Nevertheless, this method is not commonly used in ecosystem management evaluation but can provide an alternative for the frequently used but often contested cost-benefit analysis (which requires the step of assigning a monetary value to each benefit). The aim of this study is to apply the cost-effectiveness analysis in combination with an ecosystem services assessment on a real case-study (comparing alternative management strategies for estuaries) to derive lessons learned to go from theory to practice. The application of this method for the case-study reveals many remaining challenges such as data availability and knowledge to assess ecosystem effects of management measures. Nevertheless, the analysis demonstrates that this method can be used for making a more integrated evaluation and supporting better-informed management decisions.