Electronic structure of triangular, hexagonal and round graphene flakes near the Fermi level

The electronic shell structure of triangular, hexagonal and round graphene quantum dots (flakes) near the Fermi level has been studied using a tight-binding method. The results show that close to the Fermi level the shell structure of a triangular flake is that of free massless particles, and that triangles with an armchair edge show an additional sequence of levels ("ghost states"). These levels result from the graphene band structure and the plane wave solution of the wave equation, and they are absent for triangles with an zigzag edge. All zigzag triangles exhibit a prominent edge state at the Fermi level, and few low-energy conduction electron states occur both in triangular and hexagonal flakes due to symmetry reasons. Armchair triangles can be used as building blocks for other types of flakes that support the ghost states. Edge roughness has only a small effect on the level structure of the triangular flakes, but the effect is considerably enhanced in the other types of flakes. In round flakes, the states near the Fermi level depend strongly on the flake radius, and they are always localized on the zigzag parts of the edge

Rectangular quantum dots in high magnetic fields

We use density-functional methods to study the effects of an external magnetic field on two-dimensional quantum dots with a rectangular hard-wall confining potential. The increasing magnetic field leads to spin polarization and formation of a highly inhomogeneous maximum-density droplet at the predicted magnetic field strength. At higher fields, we find an oscillating behavior in the electron density and in the magnetization of the dot. We identify a rich variety of phenomena behind the periodicity and analyze the complicated many-electron dynamics, which is shown to be highly dependent on the shape of the quantum dot.Comment: 6 pages, 6 figures, submitted to Phys. Rev.

Electronic structure of rectangular quantum dots

We study the ground state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the deformation, and at realistic sizes the non-interacting picture determines the general behavior. However, close to the degenerate points where Hund's rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR

High-resolution Local Gravity Model of the South Pole of the Moon from GRAIL Extended Mission Data

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6deg by 1/6deg (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40deg. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models

Using models of the ocean's mean dynamic topography to identify errors in coastal geodetic levelling

Identifying errors (blunders and systematic errors) in coastal geodetic levelling networks has often been problematic. This is because (1) mean sea level (MSL) at tide gauges cannot be directly compared to height differences from levelling because the geoid/quasigeoid and MSL are not parallel, being separated by the ocean’s mean dynamic topography (MDT) and (2) the lack of redundancy at the edge of the levelling network. This paper sets out a methodology to independently identify blunders and/or systematic errors (over long distances) in geodetic levelling using MDT models to account for the separation between the geoid/quasigeoid and MSL at tide gauges. This method is then tested in a case study using an oceanographic MDT model, MSL observations, GNSS data and a quasigeoid model. The results are significant because the errors found could not be detected by standard levelling misclosure checks alone, with supplementary data from an MDT model, with cross-validation from GNSS-quasigeoid allowing their detection. In addition, it appears that an oceanographic-only MDT is as effective as GNSS and a quasigeoid model for detecting levelling errors, which could be particularly useful for countries with coastal levelling errors in their levelling networks that cannot be identified by conventional levelling closure checks

Electronic resonance states in metallic nanowires during the breaking process simulated with the ultimate jellium model

We investigate the elongation and breaking process of metallic nanowires using the ultimate jellium model in self-consistent density-functional calculations of the electron structure. In this model the positive background charge deforms to follow the electron density and the energy minimization determines the shape of the system. However, we restrict the shape of the wires by assuming rotational invariance about the wire axis. First we study the stability of infinite wires and show that the quantum mechanical shell-structure stabilizes the uniform cylindrical geometry at given magic radii. Next, we focus on finite nanowires supported by leads modeled by freezing the shape of a uniform wire outside the constriction volume. We calculate the conductance during the elongation process using the adiabatic approximation and the WKB transmission formula. We also observe the correlated oscillations of the elongation force. In different stages of the elongation process two kinds of electronic structures appear: one with extended states throughout the wire and one with an atom-cluster like unit in the constriction and with well localized states. We discuss the origin of these structures.Comment: 11 pages, 8 figure

Development of a Synthetic Earth Gravity Model by 3D mass optimisation based on forward modelling

Several previous Synthetic Earth Gravity Model (SEGM) simulations are based on existing information about the Earth’s internal mass distribution. However, currently available information is insufficient to model the Earth’s anomalous gravity field on a global scale. The low-frequency information is missing when modelling only topography, bathymetry and crust (including the Mohorovičić discontinuity), but the inclusion of information on the mantle and core does not seem to significantly improve this situation. This paper presents a method to determine a more realistic SEGM by considering simulated 3D mass distributions within the upper mantle as a proxy for all unmodelled masses within the Earth.The aim is to improve an initial SEGM based on forward gravity modelling of the topography, bathymetry and crust such that the missing low-frequency information is now included. The simulated 3D mass distribution has been derived through an interactive and iterative mass model optimisation algorithm, which minimises geoid height differences with respect to a degree-360 spherical harmonic expansion of the EGM2008 global external gravity field model. We present the developed optimisation algorithm by applying it to the development of a global SEGM that gives a reasonably close fit to EGM2008, and certainly closer than a SEGM based only on the topography, bathymetry and crust

Airborne geoid determination

Airborne geoid mapping techniques may provide the opportunity to improve the geoid over vast areas of the Earth, such as polar areas, tropical jungles and mountainous areas, and provide an accurate "seam-less" geoid model across most coastal regions. Determination of the geoid by airborne methods relies on the development of airborne gravimetry, which in turn is dependent on developments in kinematic GPS. Routine accuracy of airborne gravimetry are now at the 2 mGal level, which may translate into 5-10 cm geoid accuracy on regional scales. The error behaviour of airborne gravimetry is well-suited for geoid determination, with high-frequency survey and downward continuation noise being offset by the low-pass gravity to geoid filtering operation. In the paper the basic principles of airborne geoid determination are outlined, and examples of results of recent airborne gravity and geoid surveys in the North Sea and Greenland are given