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Register a new userDetermination of the effective transverse coherence of the neutron wave packet as employed in reflectivity investigations of condensed matter structures Part I: Measurements
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The primary purpose of this investigation is to determine the effective coherent extent of the neutron wave packet transverse to its mean propagation vector k, when it is prepared in a typical instrument used to study the structure of materials in thin film form via specular reflection. There are two principal reasons for doing so. One has to do with the fundamental physical interest in the characteristics of a free neutron as a quantum object while the other is of a more practical nature, relating to the understanding of how to interpret elastic scattering data when the neutron is employed as a probe of condensed matter structure on an atomic or nanometer scale. Knowing such a basic physical characteristic as the neutrons effective transverse coherence can dictate how to properly analyze specular reflectivity data obtained for material film structures possessing some amount of in-plane inhomogeneity. In this study we describe a means of measuring the effective transverse coherence length of the neutron wave packet by specular reflection from a series of diffraction gratings of different spacings. Complementary non-specular measurements of the widths of grating reflections were also performed which corroborate the specular results. (Part I principally describes measurements interpreted according to the theoretical picture presented in Part II.) Each grating was fabricated by lift-off photo-lithography patterning of a nickel film (approximately 1000 Angstroms thick) formed by physical vapor deposition on a flat silicon crystal surface. The grating periods ranged from 10 microns (5 microns Ni stripe, 5 microns intervening space) to several hundred microns. The transverse coherence length, modeled as the width of the wave packet, was determined from an analysis of the specular reflectivity curves of the set of gratings.
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In the analysis of neutron scattering measurements of condensed matter structure, it normally suffices to treat the incident and scattered neutron beams as if composed of incoherent distributions of plane waves with wavevectors of different magnitudes and directions which are taken to define an instrumental resolution. However, despite the wide-ranging applicability of this conventional treatment, there are cases in which the wave function of an individual neutron in the beam must be described more accurately by a spatially localized packet, in particular with respect to its transverse extent normal to its mean direction of propagation. One such case involves the creation of orbital angular momentum (OAM) states in a neutron via interaction with a material device of a given size. It is shown in the work reported here that there exist two distinct measures of coherence of special significance and utility for describing neutron beams in scattering studies of materials in general. One measure corresponds to the coherent superposition of basis functions and their wavevectors which constitute each individual neutron packet state function whereas the other measure can be associated with an incoherent distribution of mean wavevectors of the individual neutron packets in a beam. Both the distribution of the mean wavevectors of individual packets in the beam as well as the wavevector components of the superposition of basis functions within an individual packet can contribute to the conventional notion of instrumental resolution. However, it is the transverse spatial extent of packet wavefronts alone that determines the area within which a coherent scattering process can occur in the first place. This picture is shown to be consistent with standard quantum theory. It is also demonstrated that these two measures of coherence can be distinguished from one another experimentally.
The electronic density of states (DOS) quantifies the distribution of the energy levels that can be occupied by electrons in a quasiparticle picture, and is central to modern electronic structure theory. It also underpins the computation and interpretation of experimentally observable material properties such as optical absorption and electrical conductivity. We discuss the challenges inherent in the construction of a machine-learning (ML) framework aimed at predicting the DOS as a combination of local contributions that depend in turn on the geometric configuration of neighbours around each atom, using quasiparticle energy levels from density functional theory as training data. We present a challenging case study that includes configurations of silicon spanning a broad set of thermodynamic conditions, ranging from bulk structures to clusters, and from semiconducting to metallic behavior. We compare different approaches to represent the DOS, and the accuracy of predicting quantities such as the Fermi level, the DOS at the Fermi level, or the band energy, either directly or as a side-product of the evaluation of the DOS. The performance of the model depends crucially on the smoothening of the DOS, and there is a tradeoff to be made between the systematic error associated with the smoothening and the error in the ML model for a specific structure. We demonstrate the usefulness of this approach by computing the density of states of a large amorphous silicon sample, for which it would be prohibitively expensive to compute the DOS by direct electronic structure calculations, and show how the atom-centred decomposition of the DOS that is obtained through our model can be used to extract physical insights into the connections between structural and electronic features.
What is the difference between space and time? is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einsteins theory of relativity time and space combine into Minkowski spacetime. Here, we firstly propose Minkowski fermions in 2+1 dimensional Minkowski spacetime which have two space-like and one time-like momentum axes. These quasiparticles can be further classified as Klein-Gordon fermions and Dirac-Minkowski fermions according to the linearly and quadratically dispersing excitations. Realization of Dirac-Minkowski quasiparticles requires systems with particular topological nodal-line band degeneracies, such as hyperbolic nodal lines or coplanar band crossings. With the help of first-principles calculations we find that novel massless Dirac-Minkowski fermions are realized in a metastable bulk boron allotrope, Pnnm-B16.
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The density of two-dimensional Ag adatom gases on W(110) is determined by monitoring local electron reflectivity using low energy electron microscopy (LEEM). This method of adatom concentration measurement can detect changes in adatom density at least as small as 10$^{-3}$ ML for a $mu$m size region of the surface. Using this technique at high temperatures, we measure the sublimation rates of Ag adatoms on W(110). At lower temperatures, where Ag adatoms condense into monolayer islands, we determine the temperature dependence of the density of adatoms coexisting with this condensed phase and compare it with previous estimates.
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