Dielectric Screening by 2D Substrates

Two-dimensional (2D) materials are increasingly being used as active components in nanoscale devices. Many interesting properties of 2D materials stem from the reduced and highly non-local electronic screening in two dimensions. While electronic screening within 2D materials has been studied extensively, the question still remains of how 2D substrates screen charge perturbations or electronic excitations adjacent to them. Thickness-dependent dielectric screening properties have recently been studied using electrostatic force microscopy (EFM) experiments. However, it was suggested that some of the thickness-dependent trends were due to extrinsic effects. Similarly, Kelvin probe measurements (KPM) indicate that charge fluctuations are reduced when BN slabs are placed on SiO$_2$, but it is unclear if this effect is due to intrinsic screening from BN. In this work, we use first principles calculations to study the fully non-local dielectric screening properties of 2D material substrates. Our simulations give results in good qualitative agreement with those from EFM experiments, for hexagonal boron nitride (BN), graphene and MoS$_2$, indicating that the experimentally observed thickness-dependent screening effects are intrinsic to the 2D materials. We further investigate explicitly the role of BN in lowering charge potential fluctuations arising from charge impurities on an underlying SiO$_2$ substrate, as observed in the KPM experiments. 2D material substrates can also dramatically change the HOMO-LUMO gaps of adsorbates, especially for small molecules, such as benzene. We propose a reliable and very quick method to predict the HOMO-LUMO gap of small physisorbed molecules on 2D and 3D substrates, using only the band gap of the substrate and the gas phase gap of the molecule.Comment: 24 pages, 5 figures, Supplementary Informatio

Scaling and Universality in the Counterion-Condensation Transition at Charged Cylinders

We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions (3D), correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. In two dimensions (2D), we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical temperature, which is also found to be universal and in accordance with the mean-field prediction.Comment: 31 pages, 16 figure

Overcoming the Challenges Associated with Image-based Mapping of Small Bodies in Preparation for the OSIRIS-REx Mission to (101955) Bennu

The OSIRIS-REx Asteroid Sample Return Mission is the third mission in NASA's New Frontiers Program and is the first U.S. mission to return samples from an asteroid to Earth. The most important decision ahead of the OSIRIS-REx team is the selection of a prime sample-site on the surface of asteroid (101955) Bennu. Mission success hinges on identifying a site that is safe and has regolith that can readily be ingested by the spacecraft's sampling mechanism. To inform this mission-critical decision, the surface of Bennu is mapped using the OSIRIS-REx Camera Suite and the images are used to develop several foundational data products. Acquiring the necessary inputs to these data products requires observational strategies that are defined specifically to overcome the challenges associated with mapping a small irregular body. We present these strategies in the context of assessing candidate sample-sites at Bennu according to a framework of decisions regarding the relative safety, sampleability, and scientific value across the asteroid's surface. To create data products that aid these assessments, we describe the best practices developed by the OSIRIS-REx team for image-based mapping of irregular small bodies. We emphasize the importance of using 3D shape models and the ability to work in body-fixed rectangular coordinates when dealing with planetary surfaces that cannot be uniquely addressed by body-fixed latitude and longitude.Comment: 31 pages, 10 figures, 2 table

The visibility based Tapered Gridded Estimator (TGE) for the redshifted 21-cm power spectrum

We present the improved visibility based Tapered Gridded Estimator (TGE) for the power spectrum of the diffuse sky signal. The visibilities are gridded to reduce the computation, and tapered through a convolution to suppress the contribution from the outer regions of the telescope's field of view. The TGE also internally estimates the noise bias, and subtracts this out to give an unbiased estimate of the power spectrum. An earlier version of the 2D TGE for the angular power spectrum $C_{\ell}$ is improved and then extended to obtain the 3D TGE for the power spectrum $P({\bf k})$ of the 21-cm brightness temperature fluctuations. Analytic formulas are also presented for predicting the variance of the binned power spectrum. The estimator and its variance predictions are validated using simulations of $150 \, {\rm MHz}$ GMRT observations. We find that the estimator accurately recovers the input model for the 1D Spherical Power Spectrum $P(k)$ and the 2D Cylindrical Power Spectrum $P(k_\perp,k_\parallel)$, and the predicted variance is also in reasonably good agreement with the simulations.Comment: 19 pages, 13 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnrasl.oxfordjournals.org