Interactions Mediated by Surface States: From Pairs and Trios to Adchains and Ordered Overlayers

Since metallic surface states on (111) noble metals are free-electron like, their propagators can be evaluated analytically. Since they are well-screened, one can use simple tight-binding formalism to study their effects. The needed phase shifts can be extracted from experiment. Hence, one can now make quantitative predictions of these slowly-decaying, oscillatory indirect interactions. For the (isotropic!) pair interactions (which decay as the inverse square of adatom-adatom separation), remarkable agreement has been obtained with experiments by two groups. We have extended the formalism to consider the full indirect ("triple") interaction of 3 adsorbates, which is the sum of the 3 constituent pair interactions plus the non-pairwise "trio" contribution, which tends to decay with the 5/2 power of perimeter. Here, we concentrate on interactions due to ordered overlayers and to linear defects, relating the latter to the interactions of (nx1) ordered overlayers and to the constituent pair interactions. We compare with experimental studies of interactions of adatoms with adchains and of consequent 1D motion of adatoms trapped between two such parallel chains. We discuss implications for step-step interactions (on vicinal surfaces), with attention to the modification of the surface state itself for small terrace widths.Comment: 4 pages, Proceedings of 14th International Conference on Crystal Growth, Grenoble, France, 9-13 August 2004; to be published in J. Crystal Growth (2005

Thermal transport in SiC nanostructures

SiC is a robust semiconductor material considered ideal for high-power application due to its material stability and large bulk thermal conductivity defined by the very fast phonons. In this paper, however, we show that both material-interface scattering and total-internal reflection significantly limit the SiC-nanostructure phonon transport and hence the heat dissipation in a typical device. For simplicity we focus on planar SiC nanostructures and calculate the thermal transport both parallel to the layers in a substrate/SiC/oxide heterostructure and across a SiC/metal gate or contact. We find that the phonon-interface scattering produces a heterostructure thermal conductivity significantly smaller than what is predicted in a traditional heat-transport calculation. We also document that the high-temperature heat flow across the metal/SiC interface is limited by total-internal reflection effects and maximizes with a small difference in the metal/SiC sound velocities.Comment: 15 pages, 4 figure

An analysis of van der Waals density functional components: Binding and corrugation of benzene and C60 on boron nitride and graphene

The adsorption of benzene and C60 on graphene and boron nitride (BN) is studied using density functional theory with the non-local correlation functional vdW-DF. By comparing these systems we can systematically investigate their adsorption nature and differences between the two functional versions vdW-DF1 and vdW-DF2. The bigger size of the C60 molecule makes it bind stronger to the surface than benzene, yet the interface between the molecules and the sheets are similar in nature. The binding separation is more sensitive to the exchange variant used in vdW-DF than to the correlation version. This result is related to the exchange and correlation components of the potential energy curve (PEC). We show that a moderate dipole forms for C60 on graphene, unlike for the other adsorption systems. We find that the corrugation is very sensitive to the variant or version of vdW-DF used, in particular the exchange. Further, we show that this sensitivity arise indirectly through the shift in binding separation caused by changing vdW-DF variant. Based on our results, we suggest a concerted theory-experiment approach to assess the exchange and correlation contributions to physisorption. Using DFT calculations, the corrugation can be linked to the optimal separation, allowing us to extract the exchange-correlation part of the adsorption energy. Molecules with same interfaces to the surface, but different geometries, can in turn cast light on the role of van der Waals forces.Comment: 16 page

Phonon Knudsen flow in nanostructured semiconductor systems

We determine the size effect on the lattice thermal conductivity of nanoscale wire and multilayer structures formed in and by some typical semiconductor materials, using the Boltzmann transport equation and focusing on the Knudsen flow effect. For both types of nanostructured systems we find that the phonon transport is reduced significantly below the bulk value by boundary scattering off interface defects and/or interface modes. The Knudsen flow effects are important for almost all types of semiconductor nanostructures but we find them most pronounced in Si and SiC systems due to the very large phonon mean-free paths. We apply and test our wire thermal-transport results to recent measurements on Si nanowires. We further investigate and predict size effects in typical multilayered SiC nanostructures, for example, a doped-SiC/SiC/SiO$_2$ layered structure that could define the transport channel in a nanosize transistor. Here the phonon-interface scattering produces a heterostructure thermal conductivity smaller than what is predicted in a traditional heat-transport calculation, suggesting a breakdown of the traditional Fourier analysis even at room temperatures. Finally, we show that the effective thermal transport in a SiC/SiO$_2$ heterostructure is sensitive to the oxide depth and could thus be used as an in-situ probe of the SiC oxidation progress.Comment: 29 pages, 9 figures. (Submitted to Journal of Applied Physics

An exchange functional that tests the robustness of the plasmon description of the van der Waals density functional

Is the plasmon description within the non-local correlation of the van der Waals density functional by Dion and coworkers (vdW-DF1) robust enough to describe all exchange-correlation components? To address this question, we design an exchange functional, termed LV-PW86r based on this plasmon description as well as recent analysis on exchange in the large $s$-regime. In the regime with reduced gradients $s=|\nabla n|/2n k_{\rm F}(n)$ smaller than $\approx 2.5$, dominating the non-local correlation part of the binding energy, the enhancement factor $F_x(s)$ closely resembles the Langreth-Vosko screened exchange. In the $s$-regime beyond, dominated by exchange, $F_x(s)$ passes smoothly over to the revised Perdew-Wang-86 form. Our tests indicate that vdW-DF1(LV-PW86r) produces accurate separations and binding energies of the S22 data set of molecular dimers as well as accurate lattice constants of layered materials and tightly-bound solids. These results suggest that vdW-DF1 has a good plasmon description in the low-to-moderate $s$-regime

Signatures of van der Waals binding: a coupling-constant scaling analysis

The van der Waals (vdW) density functional (vdW-DF) method [ROPP 78, 066501 (2015)] describes dispersion or vdW binding by tracking the effects of an electrodynamic coupling among pairs of electrons and their associated exchange-correlation holes. This is done in a nonlocal-correlation energy term $E_c^{nl}$, which permits density functional theory calculation in the Kohn-Sham scheme. However, to map the nature of vdW forces in the fully interacting materials system, it is necessary to compensate for associated kinetic-correlation energy effects. Here we present a coupling-constant scaling analysis that also permits us to compute the kinetic-correlation energy $T_c^{nl}$ that is specific to the vdW-DF account of nonlocal correlations. We thus provide a spatially-resolved analysis of the total nonlocal-correlation binding, including vdW forces, in both covalently and non-covalently bonded systems. We find that kinetic-correlation energy effects play a significant role in the account of vdW or dispersion interactions among molecules. We also find that the signatures that we reveal in our full-interaction mapping are typically given by the spatial variation in the $E_c^{nl}$ binding contributions, at least in a qualitative discussion. Furthermore, our full mapping shows that the total nonlocal-correlation binding is concentrated to pockets in the sparse electron distribution located between the material fragments.Comment: 15 pages, 8 figure

Finite-temperature properties of non-magnetic transition metals: Comparison of the performance of constraint-based semi and nonlocal functionals

We assess the performance of nonempirical, truly nonlocal and semi-local functionals with regard to structural and thermal properties of $3d$, $4d$, and $5d$ non-magnetic transition metals. We focus on constraint-based functionals and consider the new consistent-exchange van der Waals density functional version vdW-DF-cx [Phys. Rev. B 89, 035412 (2014)], the semi-local PBE [Phys. Rev. Lett. 77, 3865 (1996)] and PBEsol functionals [Phys. Rev. Lett. 100, 136406 (2008)] as well as the AM05 meta-functional [Phys. Rev. B 72, 085108 (2005)]. Using the quasi-harmonic approximation structural parameters, elastic response, and thermal expansion at finite temperatures are computed and compared to experimental data. We also compute cohesive energies explicitly including zero-point vibrations. It is shown that overall vdW-DF-cx provides an accurate description of thermal properties and retains a level of transferability and accuracy that is comparable to or better than some of the best constraint-based semi-local functionals. Especially, with regard to the cohesive energies the consistent inclusion of spin polarization effects in the atoms turns out to be crucial and it is important to use the rigorous spin-vdW-DF-cx formulation [Phys. Rev. Lett. 115, 136402 (2015)]. This demonstrates that vdW-DF-cx has general-purpose character and can be used to study systems that have both sparse and dense electron distributions.Comment: 10 pages, 5 figure

Rings sliding on a honeycomb network: Adsorption contours, interactions, and assembly of benzene on Cu(111)

Using a van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92, 246401 (2004)], we perform ab initio calculations for the adsorption energy of benzene (Bz) on Cu(111) as a function of lateral position and height. We find that the vdW-DF inclusion of nonlocal correlations (responsible for dispersive interactions) changes the relative stability of eight binding-position options and increases the binding energy by over an order of magnitude, achieving good agreement with experiment. The admolecules can move almost freely along a honeycomb web of "corridors" passing between fcc and hcp hollow sites via bridge sites. Our diffusion barriers (for dilute and two condensed adsorbate phases) are consistent with experimental observations. Further vdW-DF calculations suggest that the more compact (hexagonal) Bz-overlayer phase, with lattice constant a = 6.74 \AA, is due to direct Bz-Bz vdW attraction, which extends to ~8 \AA. We attribute the second, sparser hexagonal Bz phase, with a = 10.24 \AA, to indirect electronic interactions mediated by the metallic surface state on Cu(111). To support this claim, we use a formal Harris-functional approach to evaluate nonperturbationally the asymptotic form of this indirect interaction. Thus, we can account well for benzene self-organization on Cu(111).Comment: 13 pages, 7 figures, 3 tables, submitted for publication Accepted for publication in Phys. Rev. B. This version contains improved notation (with corresponding relabeling of figures), very small corrections to some tabulated values, and corrections concerning lattice lengths and subsequent discussion of commensurability of unit-cell dimension

Stacking and band structure of van der Waals bonded graphane multilayers

We use density functional theory and the van der Waals density functional (vdW-DF) method to determine the binding separation in bilayer and bulk graphane and study the changes in electronic band structure that arise with the multilayer formation. The calculated binding separation (distance between center-of-mass planes) and binding energy are 4.5-5.0 {\AA} (4.5-4.8 {\AA}) and 75-102 meV/cell (93-127 meV/cell) in the bilayer (bulk), depending on the choice of vdW-DF version. We obtain the corresponding band diagrams using calculations in the ordinary generalized gradient approximation for the geometries specified by our vdW-DF results, so probing the indirect effect of vdW forces on electron behavior. We find significant band-gap modifications by up to -1.2 eV (+4.0 eV) in various regions of the Brillouin zone, produced by the bilayer (bulk) formation.Comment: 11 pages, 7 figures, 2 tables, accepted for publication in Phys. Rev.