Periodic Surface Potential Research Articles

Ferrotronics for the creation of band gaps in graphene

We experimentally demonstrate a simple graphene/ferrolectric device, termed ferrotronic (electronic effect from ferroelectric) device in which the band structure of single-layer graphene is modified. The device architecture consists of graphene deposited on a ferroelectric substrate which encodes a periodic surface potential achieved through domain engineering. This structure takes advantage of the nature of conduction through graphene to modulate the Fermi velocity of the charge carriers by the variations in surface potential, leading to the emergence of energy minibands and a band gap at the superlattice Brillouin zone boundary. Our work represents a simple route to building circuits whose functionality is controlled by the underlying substrate.

Discrete Laplacian in a half‐space with a periodic surface potential I: Resolvent expansions, scattering matrix, and wave operators

AbstractWe present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half‐space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we prove the continuity of the scattering matrix, and we establish new formulas for the wave operators. Along the way, our analysis puts into evidence a surprising relation between some properties of the potential, like the parity of its period, and the behaviour of the integral kernel of the wave operators.

Atomistic mechanisms for frictional energy dissipation during continuous sliding

After more than a century of detailed investigations into sliding friction, we have not arrived yet at a basic understanding of energy dissipation, even for the simple geometry of a rigid slider moving over a perfectly periodic counter surface. In this article, we use a first-principles-based analysis to establish the atomistic mechanisms of frictional energy dissipation for a rigid object that moves continuously in the periodic surface potential landscape of a solid with vibrational degrees of freedom. We identify two mechanisms that can be viewed as (i) the continuous pumping of energy into the resonant modes, if these exist, and (ii) the destructive interference of the force contributions introduced by all excited phonon modes. These mechanisms act already in a purely dynamic system that includes independent, non-interacting phonon modes, and they manifest irreversibility as a kind of “dynamical stochastization”. In contrast to wide-spread views, we show that the transformation of mechanical energy into heat, that always takes place in real systems due to the coupling between phonon modes, can play only a minor role in the appearance of friction, if any. This insight into the microscopic mechanisms of energy dissipation opens a new, direct way towards true control over friction.

Quantum motion of hydrogen on Ni(100) surfaces

Vibration modes of hydrogen atoms on Ni(100) are studied. The number of observed energy losses as well as their full width at half maximum (FWHM) are incompatible with the classical model of localized vibrations. Number and energy of modes agree, however, well with a previously published quantum-mechanical treatment of the motion of hydrogen in the periodic surface potential of Ni(100). For the dilute surface phase of hydrogen, the FWHM is a factor of 4 larger than expected from the dispersion of the bands. The effect is attributed to rapid tunneling of vibrationally excited hydrogen into empty neighboring sites.

Analytical study of AC electroosmotic mixing in 2-dimensional microchannel with time periodic surface potential.

This work reported an analytic study of AC electroosmotic flows with a view to control the degree of mixing in a rectangular microchannel. Only with spatially non-uniform zeta potential distribution, fluid particles travel back and forth along a vortical flow field developed inside a microchannel. Although complex patterns of electroosmotic vortical flows can be obtained by various types of non-uniform zeta potential distributions, fluid particles always follow regular paths due to a laminar flow limit. To further facilitate the mixing of sample fluid, we propose a scheme that the zeta potential distribution was temporally non-uniform as well. General solutions for both the double layer potential distribution and the AC electroosmotic flow field are analytically determined by solving the unsteady Stokes equation with an electrostatic body force. As an illustrative example, we consider a case where two different types of non-uniform zeta potential distributions alternate with each other and the effects of both the AC frequency and the frequency of the alternation of the two zeta potential distributions on flow characteristics are examined using the Poincaré sections. Conclusively, one can either enhance or prevent mixing compared to a static electroosmotic flow, which is in line with previously demonstrated experimental works. Thus, the results presented would be an effective mean for controllable electroosmotic flow in a microfluidic platform.

Energy splitting of image states induced by the surface potential corrugation of InAs(111)A

By means of scanning tunneling spectroscopy (STS) we study the electronic structure of the III-V semiconductor surface InAs(111)A in the field emission regime (above the vacuum level). At high sample bias voltages (approaching +10 V), a series of well defined resonances are identified as the typical Stark shifted image states that are commonly found on metallic surfaces in the form of field emission resonances (FER). At lower bias voltages, a more complex situation arises. Up to three double peaks are identified as the first three FERs that are split due to their interaction with the periodic surface potential. The high corrugation of this potential is also quantified by means of density functional theory (DFT) calculations. Another sharp resonance not belonging to the FER series is associated with an unoccupied surface state.

Phase equilibrium in argon films stabilized by homogeneous surfaces and thermodynamics of two-stage melting transition

Freezing of gases adsorbed on open surfaces (e.g., graphite) and in narrow pores is a widespread phenomenon which is a subject of a large number of publications. Modeling of the gas/liquid-solid transition is usually accomplished with a molecular simulation technique. However, quantitative analysis of the gas/liquid-solid coexistence and thermodynamic properties of the solid layer still encounters serious difficulties. This is mainly due to the effect of simulation box size on the lattice constant. Since the lattice constant is a function of loading and temperature, once the ordering transition has occurred, the simulation box size must be corrected in the course of simulation according to the Gibbs-Duhem equation. A significant problem is also associated with accurate prediction of the two-dimensional liquid-solid coexistence because of a small difference in densities of coexisting phases. The aim of this study is thermodynamic analysis of the two-dimensional phase coexistence in systems involving crystal-like free of defects layers in narrow slit pores. A special attention was paid to the determination of triple point temperatures. It is shown that intrinsic properties of argon monolayer adsorbed on the graphite surface are similar to those of isolated monolayer accommodated in the slit pore having width of two argon collision diameters. Analysis of the latter system is shown to be clearer and less time-consuming than the former one, which has allowed for explanation of the experimentally observed two-stage melting transition of argon monolayer on graphite without invoking the periodic surface potential modulation and orientational transition.

Direct observation of substrate induced exciton in carbon nanotube

We have successfully measured the electroluminescence spectra of a single-walled carbon nanotube (CNT) grown to serpentine shape on quartz substrate. We observe two emission peaks: One locates at 0.85 eV and is identified as the usual E11 exciton peak, and the other locates at slightly higher energy of 0.94 eV with similar symmetrical line shape and comparable intensity. However, the extra peak is substantially wider and it broadens with increasing current at unusually faster speed. We show that the extra peak is not from interband transitions, and ascribe it to a type of exciton induced by the formation of substrate-CNT superlattice. The periodic surface potential of the substrate modulates the CNT band structure, causes degeneracy lifting and band flattering at the Brillouin zone, and generates the higher energy exciton. For confirmation, a similar device is fabricated using amorphous SiO2 substrate to avoid the formation of the superlattice. Indeed, the extra emission peak disappears.

The role of chemical interactions and epitaxy during nucleation of organic crystals on crystalline substrates

A tandem strategy to control polymorphism through epitaxial relationships with crystalline substrates reveals the importance of chemical interactions at the nucleation surface compared with the periodic surface potential associated with epitaxy.

2D MATTER WAVES GUIDED IN VAN DER WAALS POTENTIALS OF DIELECTRIC SURFACES

The dipolar interaction between neutral atoms and non-resonant surfaces results in attractive potentials.We describe here techniques to probe these interactions, particulary focussing in mechanisms to selectively prepare adsorption quantum states. The control of the external degrees of freedom of atoms very close to a surface allows one, in the one hand, to get values for the parameters of the potentials between neutral atoms and solid surfaces and, on the other hand, to develop schemes to explore matter behavior at low dimensionality. As an application for the 2D confined atomic matter-wave we consider Bloch oscillation for atoms in a periodic surface potential.

Theory of surface-potential-mediated photorefractivelike effects in liquid crystals

We make a phenomenological model of optical two-beam interaction in a model planar liquid crystal cell. The liquid crystal is subject to homeotropic anchoring at the cell walls, is surrounded by thin photosensitive layers, and is subject to a variable potential across the cell. These systems are often known as liquid crystal photorefractive systems. The interference between the two obliquely incident beams causes a time-independent periodic modulation in electric field intensity in the direction transverse to the cell normal. Our model includes this field phenomenologically by supposing an effect on the electric potential at the cell walls. The transverse periodic surface potential causes spatially periodic departures from a pure homeotropic texture. The texture modulation acts as a grating for the incident light. The incident light is both directly transmitted and also subject to diffraction. The lowest order diffracted beams correspond to energy exchange between the beams. We find that the degree of energy exchange can be strongly sensitive to the mean angle of incidence, the angle between the beams, and the imposed potential across the cell. We use the model to speculate about what factors optimize nonlinear optical interaction in liquid crystalline photorefractive systems.

Force measurement with a scanning tunneling microscope

The scanning tunneling microscope STM has proven its unique abilities in imaging surfaces up to atomic resolution. Soon after its invention by Binnig and Rohrer it was realized that, due to its close proximity to the surface atoms the STM tip often influences and modifies the surface. This disadvantage however was used positively by modifying substrate surfaces in a controlled way. Eigler et al.1 showed that even single atoms can be positioned on selected adsorption sites proving the startling possibilities to build up man-designed functional nanostructures atom by atom. The manipulation process itself is a subject of fundamental experiments with single atoms. The data recorded during the positioning with the microscopes tip yields information whether the interaction is attractive or repulsive2 and about the atoms path on the surface.3,4 The nature of the tip-atom interaction for metal atoms was determined recently as a chemical force, dependant only on the tip-atom distance.5 Recent insights into single atom processes on crystal surfaces include friction measurements with atomically sharp cantilever6 and the dynamics of single atom switching.7 The force required to move a single atom across a crystal surface however has not been measured yet and we show here a simple way to measure forces with a STM. A formula is presented and tested with simulated manipulation curves. Atomic manipulation can be described within a simple model where the surface is assumed to have a continuous sinusoidal potential with the amplitude of the diffusion barrier.3 We describe here the tip with a Morse potential and let the atom reside in the local minimum of the combined tip and surface potential. The scheme used here is not dependant on the used potential, other potentials or results from firstprinciple calculations can be used too. The atom moves on a two dimensional surface and the tip is assumed to be spherical. With these assumptions one can realistically describe atomic movements and tip height curves once the tip-atom force and the diffusion barrier are known. A simulation starts by placing the tip above the atom and the height is adjusted with closed feedback loop until the current set point is reached. The local potential minimum of the combined potentials is determined and the atom is shifted to it. Again the tip height is adjusted to reach the set point value of the current. These feedback loop cycles are repeated until the atom stabilizes only then the tip is shifted laterally. Figure 1 shows a description of the potential model where the atom always resides in a local potential minimum of the combined potentials of tip and surface.3 In this equilibrium position the tipatom force is counterbalanced by the surface forces expressed by the migration barrier U0. With this description topography curves or manipulation curves at constant current can be calculated.8 The reverse, namely the tip-atom interaction forces can be determined too. They require experimental manipulation curves. In such case first the atoms position is determined and then the tip-atom interaction force can be calculated. Hereby one uses that the projected lateral force component Flat=Ftip cos needs to be equal to the surfaces force Fsurface. By using an approximate potential for the surface one can follow a simpler way and the force can be determined from a single formula shown in the following. Figure 2 shows simulated tip height or manipulation curves for a quasi-one-dimensional periodic surface potential. Experimental values for the height are typically 4 A and the amplitudes range is 0.1 A.2 The tip moves over the atom and changes thereby the lateral force component which is pulling the atom across the surface plane. Once the lateral force component exceeds the counterforces from the surface the atom will jump to the next local potential minimum. The recorded tip height shows a characteristic shape which can

Quantum surface diffusion of vibrationally excited molecular dimers

We consider the thermally activated quantum diffusion of a molecular dimer in a periodic surface potential by means of a time-dependent wave packet method. We show that the potential energy surface resulting from the interplay of intradimer and dimer-surface interactions can lead to resonant states and predict high tunneling probabilities at specific, below barrier, energies that depend also on the initial vibrational state of the dimer. For soft molecular bonds, we show that the chaotic dynamical regime of classical dimers is mirrored, in the quantum case, by the tunneling induced mixing of vibrational states. The knowledge of the transmission coefficient is used to formulate an approximate description of quantum thermal diffusion by defining an effective temperature-dependent activation energy that can be compared to the classical case.

Spectral analysis of the generalized surface Maryland model

The d-dimensional discrete Schrodinger operator whose potential is sup- ported on the subspace Z d2 of Z d is considered: H = Ha + VM ,w hereHa = H0 + Va, H0 is the d-dimensional discrete Laplacian, Va is a constant potential, Va(x )= aδ(x1), x =( x1 ,x 2), x1 ∈ Z d1 , x2 ∈ Z d2 , d1 + d2 = d ,a ndVM (x )= gδ(x1 )t anπ(α · x2 + ω )w ithα ∈ R d2 , ω ∈ (0, 1). It is proved that if the com- ponents of α are rationally independent, i.e., the surface potential is quasiperiodic, then the spectrum of H on the interval (−d, d) (coinciding with the spectrum of the discrete Laplacian) is purely absolutely continuous, and the associated generalized eigenfunctions have the form of the sum of the incident wave and waves reflected by the surface potential and propagating into the bulk of Z d . If, in addition, α satisfies a certain Diophantine condition, then the remaining part R (−d, d) of the spectrum is pure point, dense, and of multiplicity one, and the associated eigenfunctions decay exponentially in both x1 and x2 (localized surface states). Also, the case of a rational α = p/q for d1 = d2 = 1 (i.e., the case of a periodic surface potential) is discussed. In this case the entire spectrum is purely absolutely continuous, and besides the bulk waves there are also surface waves whose amplitude decays exponentially as |x1 |→∞ but does not decay in x2. The part of the spectrum corresponding to the surface states consists of q separated bands. For large q, the bands outside of (−d, d )a re exponentially small in q, and converge in a natural sense to the pure point spectrum of the quasiperiodic case with Diophantine α's.

Localization of a Gaussian polymer in a weak periodic surface potential disturbed by a single defect

Using the results of the recently studied problem of adsorption of a Gaussian polymer in a weak periodic surface potential we study the influence of a single rod like defect on the polymer being localized in the periodic surface potential. We have found that the polymer will be localized at the defect under condition u > u c, where uc is the localization threshold in the periodic potential, for any infinitesimal strength of the interaction with defect. We predict that the concentration of monomers of the localized polymer decays exponentially as a function of the distance to the defect and is modulated with the period of the surface potential.

Planar nematic anchoring due to a periodic surface potential

A polyimide-coated substrate is rubbed periodically with the stylus of an atomic-force microscope. The effective polar and azimuthal anchoring strength coefficients for planar anchoring are determined as a function of the spatial separation L of rub lines. Both anchoring coefficients are found to decrease monotonically with L, apparently leveling off at nonzero values for L≳2 μm. The observed behavior is discussed in terms of a combination of intrinsic anchoring strength in the rubbed regions and a surface memory effect.

Adsorption and phase transitions in a two-siteassociating Lennard-Jones fluid confined to energeticallyheterogeneous slit-like pores; application of the density functionalmethod

A density functional approach is used to study adsorption and phasebehaviour of the two-bonding-site associating Lennard-Jones (LJ)fluid in slit-like pores with energetically heterogeneous walls.Phase behaviour of strongly and weakly associating, polymerizingfluid in the pores with a periodic surface potential, characterizedby different strengths and the spacings between adjacent minima, aswell as different pore widths is discussed. A comparison of theresults obtained for strongly and weakly associating fluidselucidates the role of bonding between fluid species in thepore-filling mechanism. An interplay between layering transitions,the formation of an intermediate `bridge' phase and the finalcapillary condensation in the pores with energetically corrugatedwalls is discussed in detail.

Absolutely continuous spectrum and scattering in the surface Maryland model

We study the discrete Schrödinger operator H in 𝐙 d with the surface quasi periodic potential V(x)=gδ(x 1 )tanπ(α·x 2 +ω), where x=(x 1 ,x 2 ),x 1 ∈𝐙 d 1 ,x 2 ∈𝐙 d 2 ,α∈𝐑 d 2 ,ω∈[0,1). We first discuss a proof of the pure absolute continuity of the spectrum of H on the interval [-d,d] (the spectrum of the discrete laplacian) in the case where the components of α are rationally independent. Then we show that in this case the generalized eigenfunctions have the form of the “volume” waves, i.e. of the sum of the incident plane wave and reflected from the hyper-plane 𝐙 d 1 waves, the form that is well known in the scattering theory for decaying potential. These eigenfunctions are orthogonal, complete and verify a natural analogue of the Lippmann-Schwinger equation. We find the wave operators and the scattering matrix in this case. We discuss also the case of rational α=p/q’s, p,q∈ℕ for d 1 =d 2 =1, i.e. of a periodic surface potential. In this case besides the volume waves there are also the surface waves, whose amplitude decays exponentially as |x 1 |→∞. For large q corresponding part of the absolutely continuos spectrum consists of q exponentially narrow bands, lying all except one outside the interval [-2,2], and converging in a natural sense as q→∞ to the dense point spectrum found before in [13] for the irrational diophantine α’s.

Diffraction of correlated electron pairs from crystal surfaces

The spectra of the internal energy distribution of correlated electron pairs, ejected from W(0 0 1), Fe(1 1 0) and Cu(0 0 1) following the impact of a low-energy electron, show characteristic structure that can be associated with the diffraction of two-electron quasi-particles from the periodic surface potential. In this combined theoretical and experimental work we show that the positions of these features in momentum space are determined by the amount of change of the center-of-mass wave vector of the pairs with respect to the surface reciprocal lattice vector. This corresponds to a two-particle Bragg diffraction. The relative intensities of the peaks and the shapes of the peaks depend mainly on the internal correlation of the electron pair, i.e. on the strength of the electronic interaction.

Ordered Growth of Substituted Phthalocyanine Thin Films: Hexadecafluorophthalocyaninatozinc on Alkali Halide (100) and Microstructured Si Surfaces

Physical vapor deposition of hexadecafluorophthalocyaninatozinc (F16PcZn) is performed under UHV conditions from monolayer coverages to an average thickness of about 20 nm on the (100) surfaces of NaCl, KCl, and KBr and on quartz glass as well as on microstructured interdigitated electrode arrays on amorphous SiO2. UV−vis absorption spectroscopy indicates stacks of cofacial parallel molecules for thin films on SiO2 and NaCl, whereas a component typical for a head-to-tail arrangement of molecules is detected on KCl and KBr. Atomic force microscopy shows well-defined crystals oriented in a defined azimuth angle relative to the substrate lattice on KCl and KBr, indicating a growth in molecular square lattices parallel to the substrate surface which is confirmed by molecular mechanics and periodic surface potential calculations. Plateaus of molecules predominantly standing upright on the surface are seen for the films on NaCl and SiO2 which is confirmed by the relative intensity of optical absorptions and by the electrical conductivity changes observed during growth on SiO2. The temperature dependence of the electrical conductivity of films on SiO2 yields an increase of the thermal activation energy around 200 °C corresponding to a loss in spectral fine structure as reported earlier [J. Phys. Chem. B 1999, 103, 3078]. A clear correlation is seen between film structure and electrical as well as optical properties of molecular semiconductor thin films.