The coefficient of surface stiffness for a pinned interface

We derive nonperturbatively — within the meanfield version of the Landau-Ginzburg-Wilson theory — the expressions for the constrained order parameter, for the coefficient of surface stiffness, and for the effective interface potential of a fluctuating interface in the presence of a flat substrate. The derived expressions display the typical dependence on the distancel between the interface and the substrate; the exponentially decaying contributions are multiplied by polynomials inl. We show that the expressions for the coefficient of surface stiffness and for the effective interface potential have identical form as those proposed recently by Jin and Fisher (Phys. Rev.B 47, 7365 (1993)).Dedicated to Herbert Wagner on the occasion of his 60th birthday     

Comparative study of the nature of chemical bonding of corrugated graphene on Ru(0001) and Rh(111) by electronic structure calculations

Recently, atomic resolved scanning tunneling microscopy investigations revealed that, depending on the substrate (Ni(111), Ru(0001), Ir(111), Pt(111), Rh(111)), graphene overlayer might present regular corrugation patterns, with periodically repeated units of a few nanometers. Variations of the interactions at the interface and the modulation of the local electronic properties are associated with the exact atomic arrangement of the carbon pairs with respect to the metal atoms of the substrate. Better understanding of the atomic structure and of the chemical bonding between graphene and the underlying transition metal is motivated by the fundamental scientific relevance of such systems, but it is also crucial in the perspective of possible applications. With the present work, we propose model systems for the two interfaces showing the most pronounced corrugation patterns, i.e. graphene/Ru(0001) and graphene/Rh(111). Our goal is to understand the nature of the interactions by means of electronic structure calculations based on Density Functional Theory. Our simulations qualitatively reproduce very well experimental results such as the STM topographies and the electrostatic potential maps, and quantitatively provide the closest agreement that has been published so far. The detailed analysis of the electronic structure at the interface highlights similarities and differences by changing the supporting transition metal. Our results point to a fundamental role of the hybridization between the π orbitals of graphene with the d band of the metal in determining the specific corrugation of the adsorbed monolayer. It is shown that differences in the response of the graphene electronic structure to the interaction with the metal can hinder the hybridization and lead to substantially different structures.     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

Effects of surface corrugation on the molecular rotational dependence of H2 dissociative adsorption dynamics on Cu(100)

We investigate and discuss how surface corrugation affects the molecular rotational dependence of H₂ dissociative adsorption dynamics on Cu(100) by performing six-dimensional (6D) quantum dynamics calculations. We calculate the dissociative adsorption probability as a function of the initial rotational state J and the normal energy E_norm of incident molecules, and compare with the dissociative adsorption results obtained by four-dimensional (4D) quantum dynamics calculations where the surface is treated as flat. In our calculation, for the case of normal incidence, the increase in dissociative adsorption probability with increasing E_norm and the non-monotonic behavior of dissociative adsorption probability with respect to J are suppressed on a corrugated surface as compared to that on a flat surface.     

The two-dimensional anharmonic oscillator: Vibration-rotation constants of fulminic acid,HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν₅, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v₅, l₅), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q_5x, Q_5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle (～170°) with a maximum at the linear configuration about 2 cm^?1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants.We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.     

Prebreakdown excitation of crystals at double multiphoton resonance: I. Probabilities of interband transitions

Expressions for the probabilities of l-photon transitions (for arbitrary l) between the upper valence band v and lower conduction band c at two-photon resonance on the adjacent transition between the band c and the upper conduction band c ₁ are obtained by means of the S transformation of the electron-photon Hamiltonian. The effects of electron band spectrum transformation and photon reemission are taken into account.     

Reentrant wetting transition of a rough wall

A 2D model describing depinning of an interface from a rough, self-affine substrate, is studied by transfer matrix methods. The phase diagram is determined for several values of the roughness exponent, ζs, of the attractive wall. For all ζs > 0 the following scenario is observed. In first place, in contrast to the case of a flat wall (ζs = 0), for wall attraction energies between zero and a ζs-dependent positive value, the substrate is always wet. Furthermore, in a small range of attraction energies, a dewetting transition first occurs as T increases, followed by a wetting one. This unusual reentrance phenomenon seems to be a peculiar feature of self-affine roughness, and does not occur, e.g., for periodically corrugated substrates.     

Effective Hamiltonian for polyatomic linear molecules

The leading terms of an effective Hamiltonian for a linear molecule in a given vibrational state are presented up to κ¹⁰T_v order of magnitude, whereby higher-order l-dependent terms such as $\text{H}\text{?}{}_{12.0}$, $\text{H}\text{?}{}_{8.0}$, and $\text{H}\text{?}{}_{8.2}$ have been neglected because in spectroscopic application they are of minor importance. This Hamiltonian therefore includes all those l-type interactions which could contribute to the fitting procedure, within a vibrational state where one or more bending vibrations are excited.     

On standing wave solutions to the Schrödinger equation

The standing wave solution to the Schrödinger equation defined in terms of the standing wave Green's function for the full Hamiltonian is discussed. This solution is compared with the more usual standing wave solution. The former is shown to be one-half the sum of usual ingoing and outgoing wave solutions obeying Lippmann-Schwinger equations. Partial wave elements of the two solutions as well as of the two reaction (K) matrices are found to be related by a simple normalization factor, viz. cos²δ_l, where δ_l is the lth partial wave phase shift. Thus, either of the two standing wave solutions can be used to obtain the correct K matrix element, tan δ_l, since in each case it is the asymptotic ratio of the irregular to the regular solution.     

Impact parameter expansion of πN scattering amplitudes at intermediate energies

Impact parameter transforms of isospin even no-flip πN-amplitudes and of the overlap function are calculated from the new CERN phase shifts. The results are compared with different models.—The approximate equality of the partial wave and the impact transform forbq=(l+ 1/2) is valid for smalll and not for largel as frequently assumed. The “optical potential” has a repulsive core in the real part and rather flat tails beyond 0.5 fermi in the real and imaginary parts.     

Role of the substrate thickness for the structural properties of organic-organic heterostructures

F₁₆CuPc deposited on pentacene is characterized by the coexistence of two different configurations: F₁₆CuPc is found in the standing up phase (“s-configuration”) on top of pentacene terraces and in a lying down phase (“l-configuration”) at pentacene step edges. By combining AFM and grazing incidence X-ray diffraction we show that the ratio between F₁₆CuPc in l- and s-configurations increases with thickness of the pentacene substrate film, demonstrating the role of the pentacene steps as nucleation centers for the F₁₆CuPc l-configuration. Experiments performed with ultra-thin pentacene thicknesses disclose that the F₁₆CuPc l-configuration does not grow on top of the first and second pentacene layers, pointing to the action of long-range interactions with the substrate.     

Iodine adlayer structures on Au(111) as discerned by atomic-resolution scanning tunnelling microscopy: relation to iodide electrochemical adsorption

Coverage-dependent adlayer structures of iodine on Au(111) in air or organic solvents obtained by using a high-precision “beetle” — type scanning tunnelling microscope are reported in comparison with those obtained under potential control in aqueous electrochemical environments. The well-known (√3 × √3)R30° structure (Θ_I = 0.33) was only observed at the electrochemical interface at low potentials. Instead, two higher coverage adlattices are evident from the present STM images. The first comprises a (5 × √3) structure (Θ_I = 0.40), with a pair of iodine rows compressed by 20% in the R30° substrate direction. The second high-coverage phase (Θ_I ≈ 0.44) consists of a hexagonal iodine overlayer compressed and rotated a few degrees from the R30° direction, giving rise to a long-range (~ 20 Å) corrugation in the STM image. The virtues of quantitative atomic-resolution STM for deducing such complex adiayer structures are pointed out.     

Elastic deformation of Ti films during alternating bending

The effect of the state of stress at a film-substrate interface on the elastic deformation of Ti films is studied during alternating bending. The Al substrate compliance is shown to cause coherent deformation of the film-substrate system, resulting in the corrugation of a Ti film and the appearance of a wavelike film-substrate interface. Fatigue tests lead to the formation of a periodic distribution of normal and tangential stresses along the interface, and this distribution favors periodic film corrugation. The corrugation of a Ti film on a Ti substrate occurs randomly in local film separation areas and is caused by defects accumulated at the interface.     

X-ray study of c-axis parameters in disordered stage II Agχ TiS2

X-ray measurements have been performed on disordered Stage II Ag_χ TiS₂ crystals with χ = 0.18 and 0.19. The c-axis structure was determined using the 00.l reflections for 4 ?l? 29. A principal result is that the intercalation of Ag⁺ between S layers produces unequal TiS distances in the adjacent TiS₂. The charge transfer to the Ti layer produces an expanded TiS distance adjacent to the Ag layer. The TiS distance away from the Ag ions is accordingly contracted. This effective (indirect) repulsive interaction between Ag⁺ and Ti may provide a mechanism for staging in these materials by keeping the Ag layers as far apart as possible.     

Spin splitting of two-dimensional states in the conduction band of asymmetric heterostructures: Contribution from the atomically sharp interface

The effect of an atomically sharp impenetrable interface on the spin splitting of the spectrum of two-dimensional electrons in heterostructures based on (001) III–V has been analyzed. To this end, the single-band Hamiltonian Γ₆ for envelope functions is supplemented by a general boundary condition taking into account the possibility of the existence of Tamm states. This boundary condition also takes into account the spin-orbit interaction, the asymmetry of a quantum well, and the noncentrosymmetricity of the crystal and contains the single phenomenological length R characterizing the structure of the interface at atomic scales. The model of a quasi-triangular well created by the field F has been considered. After the unitary transformation to zero boundary conditions, the modified Hamiltonian contains an interface contribution from which the two-dimensional spin Hamiltonian is obtained through averaging over the fast motion along the normal. In the absence of magnetic field B, this contribution is the sum of the Dresselhaus and Bychkov-Rashba terms with the constants renormalized owing to the interface contribution. In the field B containing the quantizing component B _z , the off-diagonal (in cubic axes) components of the g factor tensor are linear functions of |B _z | and the number of the Landau level N. The results are in qualitative agreement with the experimental data.     

Interface effect on structural and electronic properties of graphdiyne adsorbed on SiO_2 and h-BN substrates:A first-principles study

We use the first-principles calculation method to study the interface effect on the structure and electronic properties of graphdiyne adsorbed on the conventional substrates of rough SiO2 and flat h-BN. For the SiO2 substrate, we consider all possible surface terminations, including Si termination with dangling bond, Si terminations with full and partial hydrogenation, and oxygen terminations with dimerization and hydrogenation. We find that graphdiyne can maintain a flat geometry when absorbed on both h-BN and SiO2 substrates except for the Si termination with partial hydrogenation(Si-H) SiO2 substrate. A lack of surface corrugation in graphdiyne on the substrates, which may help maintain its electronic band character, is due to the weak Van der Waals interaction between graphdiyne and the substrate. Si-H SiO2 should be avoided in applications since a covalent type bonding between graphdiyne and SiO2 will totally vary the band structure of graphdiyne.Interestingly, the oxygen termination with dimerization SiO2 substrate has spontaneous p-type doping on graphdiyne via interlayer charge transfer even in the absence of extrinsic impurities in the substrate. Our result may provide a stimulus for future experiments to unveil its potential in electronic device applications.     

Hydrodynamic interaction between two spheres

We evaluate the hydrodynamic interaction tensors for two spheres of unequal size and for general mixed slip-stick boundary conditions. A method of reflections leads to a series expansion for the diffusion tensors in powers of the inverse distance l^?1 between sphere centers and explicit results are derived through terms of order l^?7. It turns out that the series expansion for the diffusion tensors converges much more rapidly than that for the friction tensors.     

Topologic distance in the Lucena network

The Lucena network (LN) is the dual of a multifractal partition of the square. We analyzethe relation between the typical topologic distance l and the number ofvertices Nof the LN. The multifractal partition has one parameter ρ which controls thegeometrical asymmetry of the multifractal. In the limit of ρ → 1 the blocks of thepartition are squared, the connections amont the blocks are short range, the LN is moreregular and the relation l ∝ √N is observed. For the limit ρ → 0 the blocks arestrongly asymmetric, long range connections appear, and the topologic distance followsl ∝(log?N)^α, a weak smallworld phenomenon. For any network size we calculate analytically the size of the minimumdistance l_min (ρ → 0) and the maximaldistance l_max (ρ → 1). The distance in theweak small world regime is calculated using the number of vertices inside a radius oflength land taking into account the network average connectivity and the exponent α.