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Bare silicon dimers on hydrogen-terminated Si(100) have two dangling bonds. These are atomically localized regions of high state density near to and within the bulk silicon band gap. We studied bare silicon dimers as monomeric units. Silicon dimer wires are much more stable than wires composed of individual dangling bonds. Dimer wires composed of 1 to 5 dimers were intentionally fabricated and characterised by STM techniques combined with density functional theory to provide detailed insights into geometric and electronic structure. Structural and dynamic qualities displayed by short wires were shown to be similar to the characteristics of a relatively long 37 dimer wire. Rather than adding two states into the band gap, experiment and theory reveal that each dimer adds one empty state into the gap and one filled state into the valence bands. Coupling among these states provides a conduction pathway with small bulk coupling., Comment: 14 pages, 5 figures

In scanning tunneling microscopy of molecules, an insulating buffer layer is often introduced to reduce interactions between adsorbed molecules and the substrate. Focusing on tunneling through the molecule's electronic transport gap, we demonstrate that the buffer itself strongly influences the wave function of the tunneling electron at the molecule. This is exemplified for an adsorbed platinum phthalocyanine molecule by varying the composition and thickness of the buffer. We find that, in particular, the buffer's lattice parameter is crucial. By expanding the wave function of the tunneling electron in molecular orbitals (MOs), we illustrate how one can strongly vary the relative weights of different MOs, such as the highest occupied MO versus some low-lying MOs with few nodal surfaces. The set of MOs with significant weight are important for processes used to manipulate the state of the molecule by a tunneling electron, such as molecular luminescence. The choice of buffer therefore provides an important tool for manipulating these processes., Comment: 30 pages, 5 figures

Using scanning tunneling microscopy (STM), we experimentally and theoretically investigate isolated platinum phthalocyanine (PtPc) molecules adsorbed on atomically thin NaCl(100) vapor deposited on Au(111). We obtain good agreement between theory and constant-height STM topography. We examine why strong distortions of STM images occur as a function of distance between molecule and STM tip. The images of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) exhibit, for increasing distance, significant radial expansion due to electron propagation in the vacuum. Additionally, the imaged angular dependence is substantially distorted. The LUMO image has substantial intensity along the molecular diagonals where PtPc has no atoms. In the electronic transport gap the image differs drastically from HOMO and LUMO, even at energies very close to these orbitals. As the tunneling becomes increasingly off-resonant, the eight angular lobes of the HOMO or of the degenerate LUMOs diminish and reveal four lobes with maxima along the molecular axes, where both, HOMO and LUMO have little or no weight. These images are strongly influenced by low-lying PtPc orbitals that have simple angular structures.

The alkali halides are ionic compounds. Each alkali atom donates an electron to a halogen atom, leading to ions with full shells. The valence band is mainly located on halogen atoms, while, in a traditional picture, the conduction band is mainly located on alkali atoms. Scanning tunnelling microscopy of NaCl at 4 K actually shows that the conduction band is located on Cl$^-$ because the strong Madelung potential reverses the order of the Na$^+$ 3s and Cl$^-$ 4s levels. We verify this reversal is true for both atomically thin and bulk NaCl, and discuss implications for II-VI and I-VII compounds.

We report on scanning tunneling microscopy (STM) topographs of individual metal phthalocyanines (MPc) on a thin salt (NaCl) film on a gold substrate, at tunneling energies within the molecule's electronic transport gap. Theoretical models of increasing complexity are discussed. The calculations for MPcs adsorbed on a thin NaCl layer on Au(111) demonstrate that the STM pattern rotates with the molecule's orientations - in excellent agreement with the experimental data. Thus, even the STM topography obtained for energies in the transport gap represent the structure of a one atom thick molecule. It is shown that the electronic states inside the transport gap can be rather accurately approximated by linear combinations of bound molecular orbitals (MOs). The gap states include not only the frontier orbitals but also surprisingly large contributions from energetically much lower MOs. These results will be essential for understanding processes, such as exciton creation, which can be induced by electrons tunneling through the transport gap of a molecule.

Spreadsheets are one of the most popular data analysis tools, wherein users can express computation as formulae alongside data. The ensuing dependencies are tracked as formula graphs. Efficiently querying and maintaining these formula graphs is critical for interactivity across multiple settings. Unfortunately, formula graphs are often large and complex such that querying and maintaining them is time-consuming, reducing interactivity. We propose TACO, a framework for efficiently compressing formula graphs, thereby reducing the time for querying and maintenance. The efficiency of TACO stems from a key spreadsheet property: tabular locality, which means that cells close to each other are likely to have similar formula structures. We leverage four such tabular locality-based patterns and develop algorithms for compressing formula graphs using these patterns, directly querying the compressed graph without decompression, and incrementally maintaining the graph during updates. We integrate TACO into an open-source spreadsheet system and show that TACO can significantly reduce formula graph sizes. For querying formula graphs, the speedups of TACO over a baseline implemented in our framework and a commercial spreadsheet system are up to 34,972x and 632x, respectively.

We report the observation of the existence of a possible universal limit for valence parton distributions that should exist once partonic degrees of freedom are relevant for high energy scattering from strongly interacting bound systems like a nucleon, meson or a few nucleon system at very short distances. Our observation is based on the notion that the Bjorken x weighted valence parton distribution function has a peak, $x_p$, that characterizes the average momentum fraction carried out by the valence quarks in the system. Within the residual mean-field model of the valence quark distribution we found that $x_p$ has an upper limit: $x_p \leq {1\over 2(n_V-1)}$, where $n_V$ is the number of valence quarks which can be considered in the cluster embedded in the strongly interacting environment of the bound system. The existence of such a limit imposes a new constraint on choosing the starting resolution scale $Q_0$ for PDFs. Our prediction for the nucleon is that $x_p\mid_{Q\to Q_0}\le{1\over 4}$, which is in agreement with all the available valence PDFs that employ the standard approach for selecting starting $Q_0$. We also demonstrate how the existence of this limit can be used to check the onset of quark-clusters in short range nucleon correlations in nuclei., Comment: Main article 9 pages with 5 figures

We study fluctuations in plasmonic electroluminescence at the single-atom limit profiting from the precision of a low-temperature scanning tunneling microscope. First, we investigate the influence of a controlled single-atom transfer on the plasmonic properties of the junction. Next, we form a well-defined atomic contact of several quanta of conductance. In contact, we observe changes of the electroluminescence intensity that can be assigned to spontaneous modifications of electronic conductance, plasmonic excitation and optical antenna properties all originating from minute atomic rearrangements at or near the contact. The observations are relevant for the understanding of processes leading to spontaneous intensity variations in plasmon-enhanced atomic-scale spectroscopies.

We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark-quark interactions that generate the high $x$ tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, $x_p$, of the peak of $xq_V(x)$ distribution of the valence quark and the effective mass of the residual system, $m_R$, in the form: $x_{p} \approx {1\over 4} (1-{m_R\over m_N})$ at starting $Q^2$. This relation explains the difference in the peak positions for d- and u- quarks through the expected difference of residual masses for valence d- and u- quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u- quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions., Comment: 45 pages and 13 figures

Light sources on the scale of single molecules can be addressed and characterized on their proper sub-nanometer scale by scanning tunneling microscopy induced luminescence (STML). Such a source can be driven by defined short charge pulses while the luminescence is detected with sub-nanosecond resolution. We introduce an approach to concurrently image the molecular emitter, which is based on an individual defect, with its local environment along with its luminescence dynamics at a resolution of a billion frames per second. The observed dynamics can be assigned to the single electron capture occurring in the low-nanosecond regime. While the emitter's location on the surface remains fixed, the scanning of the tip modifies the energy landscape for charge injection to the defect. The principle of measurement is extendable to fundamental processes beyond charge transfer like exciton diffusion.

The constituent counting ruling (CCR) has been found to hold for numerous hard, exclusive processes. It predicts the differential cross section at high energies and fixed $\cos \theta_{c.m.}$ should follow $\frac{d \sigma}{dt} \sim \frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in the reaction. Here we provide an in-depth analysis of the reaction $\gamma p \rightarrow \omega p$ at $\theta_{c.m.}\sim 90^\circ$ using CLAS data with an energy range of $s = 5 - 8$ GeV$^2$, where the CCR has been shown to work in other reactions. We argue for a stringent method to select data to test the CCR and utilize a Taylor-series expansion to take advantage of data from nearby angle bins in our analysis. Na\"{i}vely, this reaction would have $n=9$ (or $n=10$ if the photon is in a $q\bar{q}$ state) and we would expect a scaling of $\sim s^{-7}$ ($s^{-8}$). Instead, a scaling of $s^{-(9.08 \pm 0.11)}$ was observed. Explanations for this apparent failure of the na\"{i}ve CCR assumptions are examined., Comment: 6 pages, 8 figures

Examining the evolution of the maximum of valence quark distribution weighted by Bjorken x, $h(x,t)\equiv xq_V(x,t)$, we observe that $h(x,t)$ at the peak should become a one parameter function; $h(x_p,t)=\Phi(x_p(t))$, where $x_p$ is the position of the peak and $t= \log{Q^2}$. This observation is used to derive a new model independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in $x_p$ to the QCD evolution equation through the $x_p$-derivative of the logarithm of the function $\Phi(x_p(t))$. A numerical analysis of this relation using empirical PDFs results in a observation of the exponential form of the $\Phi(x_p(t)) = h(x_p,t) = Ce^{D x_p(t)}$ for leading to next-to-next leading order approximations of PDFs for the all $Q^2$ range covering four orders in magnitude. The exponent, $D$, of the observed "height-position" correlation function converges with the increase of the order of approximation. This result holds for all PDF sets considered. A similar relation is observed also for pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed "height - position" correlation is used also to indicate that no finite number exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed $Q^2$., Comment: 6 pages and 7 figures

We present a new approach for the calculation of the valence quark distributions in the nucleon based on the scenario in which the spectrum of the valence quarks at x>0.05 is generated through three main mechanisms: interaction of valence quarks with the mean field generated by the residual nucleon system, two and three quark short range interactions through gluon exchanges. In the current report we present the first phase of the project in which we develop a non-perturbative model for valence quark interaction in the mean field of the nucleonic interior to describe their distribution in the moderate x region (0.05 < x < 0.4). The short range quark-quark interaction effects in our approach generate the high x tail of valence quark distributions. The presented non-perturbative model is based on the picture in which three relativistic valence quarks occupy the nucleon core at distances of $\le 0.5$ Fm while interacting in the mean field generated by the residual nucleon system. The calculations are based on the assumption of the a factorization of the internal interaction of short-range three valence quarks with the long-range interaction of these quarks with the residual system. The theoretical approach is based on effective light-front diagrammatic approach which allows us to introduce the valence quark and residual system wave functions in a consistent way The parameters of these wave functions are fixed by the position of the peak of the xf_q(x) distribution of valence quarks at Q_0 corresponding to the charm-quark mass. With few parameters we achieved a very reasonable description of the up and down valence quark distributions in the moderate x region (x < 0.4), where one expects the mean field dynamics to dominate. The model, however, systematically underestimates the high $x$ region where enhanced contributions from partonic short-range correlations are expected., Comment: 5 pages, 3 figures, Proceedings for Light Cone 2019 - QCD on the light cone: from hadrons to heavy ions

We extensively characterize the electronic structure of ultra-narrow graphene nanoribbons (GNRs) with armchair edges and zig-zag termini that have 5 carbon atoms across their width (5-AGNRs), as synthesised on Au(111). Scanning tunnelling spectroscopy measurements on the ribbons, recorded on both the metallic substrate and a decoupling NaCl layer, show well-defined dispersive bands and in-gap states. In combination with theoretical calculations, we show how these in-gap states are topological in nature and localised at the zig-zag termini of the nanoribbons. Besides rationalising the driving force behind the topological class selection of 5-AGNRs, we also uncover the length-dependent behaviour of these end states which transition from singly occupied spin-split states to a closed-shell form as the ribbons become shorter. Finally, we demonstrate the magnetic character of the end states via transport experiments in a model two-terminal device structure in which the ribbons are suspended between the scanning probe and the substrate that both act as leads.

A hallmark of quantum control is the ability to manipulate quantum emission at the nanoscale. Through scanning tunneling microscopy induced luminescence (STML) we are able to generate plasmonic light originating from inelastic tunneling processes that occur in a few-nanometer thick molecular film of C$_{60}$ deposited on Ag(111). Single photon emission, not of excitonic origin, occurs with a 1/$e$ lifetime of a tenth of a nanosecond or less, as shown through Hanbury Brown and Twiss photon intensity interferometry. We have performed tight-binding calculations of the electronic structure for the combined Ag-C$_{60}$-tip system and obtained good agreement with experiment. The tunneling happens through electric field induced split-off states below the C$_{60}$ LUMO band, which leads to a Coulomb blockade effect and single photon emission. The use of split-off states is shown to be a general technique that has special relevance for narrowband materials with a large bandgap.

Photon statistics is a powerful tool for characterizing the emission dynamics of nanoscopic systems and their photophysics. Recent advances that combine correlation spectroscopy with scanning tunneling microscopy-induced luminescence (STML) have allowed measuring the emission dynamics from individual molecules and defects demonstrating their nature as single photon emitters. The application of correlation spectroscopy to the analysis of the dynamics of a well-characterized adsorbate system in ultrahigh vacuum remained to be shown. Here we combine single photon time correlations with STML to measure the dynamics of individual $H_2$ molecules between a gold tip and a Au(111) surface. An adsorbed $H_2$ molecule performs recurrent excursions below the tip apex. We use the fact that the presence of the $H_2$ molecule in the junction modifies plasmon emission to study the adsorbate dynamics. Using the $H_2$ molecule as a chopper for STM-induced optical emission intensity we demonstrate bunching in the plasmonic photon train in a single measurement over six orders of magnitude in the time domain (from microseconds to seconds) that takes only a few seconds. Our findings illustrate the power of using photon statistics to measure the diffusion dynamics of adsorbates with STML., Comment: 17 pages, 5 figures

Generating correlated photon pairs at the nanoscale is a prerequisite to creating highly integrated optoelectronic circuits that perform quantum computing tasks based on heralded single-photons. Here we demonstrate fulfilling this requirement with a generic tip-surface metal junction. When the junction is luminescing under DC bias, inelastic tunneling events of single electrons produce a photon stream in the visible spectrum whose super-bunching index is 17 when measured with a 53 picosecond instrumental resolution limit. These photon bunches contain true photon pairs of plasmonic origin, distinct from accidental photon coincidences. The effect is electrically rather than optically driven - completely absent are pulsed lasers, down-conversions, and four-wave mixing schemes. This discovery has immediate and profound implications for quantum optics and cryptography, notwithstanding its fundamental importance to basic science and its ushering in of heralded photon experiments on the nanometer scale.

Excitons and their constituent charge carriers play the central role in electroluminescence mechanisms determining the ultimate performance of organic optoelectronic devices. The involved processes and their dynamics are often studied with time-resolved techniques limited by spatial averaging that obscures the properties of individual electron-hole pairs. Here we overcome this limit and characterize single charge and exciton dynamics at the nanoscale by using time-resolved scanning tunnelling microscopy-induced luminescence (TR-STML) stimulated with nanosecond voltage pulses. We use isolated defects in C$_{60}$ thin films as a model system into which we inject single charges and investigate the formation dynamics of a single exciton. Tuneable hole and electron injection rates are obtained from a kinetic model that reproduces the measured electroluminescent transients. These findings demonstrate that TR-STML can track dynamics at the quantum limit of single charge injection and can be extended to other systems and materials important for nanophotonic devices.