Surface Local Density Of States Research Articles

WAVES ON A METAL SURFACE AND QUANTUM CORRALS

Electrons occupying surface states on the close-packed faces of noble metals form a two-dimensional (2-d) nearly free electron gas. Because this system is accessible to the scanning tunneling microscope (STM), it provides a unique opportunity to study the local properties of low-dimensional electrons. On Cu (111) we have observed standing wave patterns in the surface local density of states due to the quantum mechanical interference of surface state electrons scattering off of step edges and adsorbates. We find that Fe adatoms strongly scatter the surface state and, as a result, are good building blocks for constructing atomic-scale barriers (“quantum corrals”) to confine the surface state electrons. The barriers are constructed by individually positioning Fe adatoms using the tip of a cold (4 K) STM. Tunneling spectroscopy performed inside of the corrals reveals discrete resonances, consistent with size quantization. A more quantitative understanding is obtained by accounting for the multiple scattering of surface state electrons with the corrals’ constituent adatoms. This scattering is characterized by a complex phase shift which can be extracted from the electronic density pattern inside a quantum corral.

Multiband approach to surface resonances

The matching formalism, which has been introduced recently [W Jaskólski, Phys Rev, 45, 4398 (1991)], is used to find image-induced resonances of the (111) surface of Al,Cu, and Ag. The method is applied within a multiband pseudopotential model. The resonances are identified with the maxima of the local surface density of states. The crystal-derived localized surface states are also found. The applicability of the method and the usefulness of the pseudopotential model are discussed.

Theory of tip-surface gap dependence in laser-assisted scanning tunneling microscopy

Nonlinear characteristics of laser-assisted tunneling in the context of scanning tunneling microscopy (STM) are investigated by combining Bardeen's formalism and the WKB approximation. Atomic-scale images of the second-order nonlinear response calculated for graphite are dependent on the tip-sample distance. At small distance, this response is proportional to the square of the derivative of the surface local density of states (LDOS), giving trigonal images peaking atop A sites. However, at large distance, the images are proportional to the square of the LDOS, giving trigonal images of B sites. The present formalism can also predict atomic-scale STM images induced by laser irradiating other surfaces such as silicon.

Generalized expression for the tunneling current in scanning tunneling microscopy.

We present an analytical method for treating the tunneling current between a tip and a sample in scanning tunneling microscopy (STM) that goes beyond the independent-electrode (Bardeen) approximation and is valid for smaller tip-to-surface separations. The extremity of the tip is represented by a single spherical potential well. This well is strongly coupled to neighboring tip atoms, as well as the sample electrode, both of which we leave in a general form. The wave function for the entire system is obtained by a matching procedure, from which the total current is determined. If the current is associated with s-derived tip orbitals, the result is comparable in simplicity with that of J. Tersoff and D. Hamann [Phys. Rev. B 31, 805 (1985)]. The low-bias tunnel conductance is proportional to the local density of states (LDOS) of the surface, but renormalized to include multiple reflections to all orders: \ensuremath{\sigma}\ensuremath{\propto}${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$(${\mathbf{r}}_{0}$,${\mathit{E}}_{\mathit{F}}$)/D, where D depends on both the tip and sample electronic structures and on the tip position ${\mathbf{r}}_{0}$. This effect includes the modification of the surface LDOS due to the presence of the tip. A compact expression is also obtained for orbitals of higher angular momenta: p and d states. The current then depends on the gradients of the surface spectral density, and not on the LDOS, and also has a characteristic denominator. We discuss the significance of this effect, both in the interpretation of STM images and related spectroscopies.

Local density of states for transition-metal interfaces.

We have calculated the interface local density of states (LDOS) for the three transition metals V, Nb, and Ta, using a tight-binding Slater-Koster description and the Green's-function-matching method, together with quickly converging algorithms, to compute the transfer matrices. We obtain the surface LDOS as a byproduct. The calculation turns out to be an almost trivial computational problem. The method proves to be a very useful tool to analyze experimental results and to check models as a function of the value of the tight-binding parameters either of the bulk or at the interface itself or as a function of different geometrical situations. It is also a solid basis on which other problems depending on a proper description of the local density of states can be worked out. We analyze in detail the Nb/Ta, Nb/V, and Ta/V interfaces in the [100] direction. We find that some of the properties found in surfaces could also be found at interfaces. In particular, we find that the V side of some interfaces could show magnetism on the atomic layer in contact with the foreign medium as the (100) surface does for this metal.

Effect of tip atomic structure on scanning tunneling spectroscopy

Tunneling conductance in scanning tunneling spectroscopy of graphite is simulated by the first-principles electronic structure calculation. As models of tip, W 10[111], W 14[110], and Pt 10[111] clusters are adopted. Simulated tunneling spectra are influenced by the shape of tip apex and deviate from one obtained by the theory assuming the conductance proportional to the surface local density of states. A broader energy spectrum of tip levels reproduces well the experimental data.

Image induced surface resonance of clean (001) and (111) surface of aluminium

The effect of an image potential on the local surface density of states is investigated in the framework of a nearly free electron model by employing the matching Green function method. The influence of the image plane position on the shift and broadening of image induced surface resonance is discussed. Finally, results are compared to experimental data and other theoretical calculations.

Analysis of the structure of the surface local density of states at the Fermi level: an application of the surface Green function matching method

We use a tight-binding description of the bands of bulk vanadium to set a surface-band structure. We show that knowledge of the s–d charge transfer in the surface layer is very important to be able to reproduce the ferromagnetic behavior of the (100) vanadium surface. We use the surface Stoner criterion of Allan to determine the acceptable values for the s–d charge transfer. There is no full agreement between theory and experiment on the magnetic properties of (100) vanadium at present.

Surface effects in the electronic properties of YBa 2Cu 3O 7

The electronic structure of basal plane surfaces of the high- T c. superconducting material YBa 2Cu 3O 7 has been determined using a tight-binding Hamiltonian derived from a first-principle calculation of the bulk phase. The surface local density of states has been obtained for four different surface configurations, which differ for the yttrium and oxygen content. The results show that the presence and state of the surface have a strong influence on the distribution of single particle states. The nature of the surface induced modifications is detailed and the relevance of the results to the understanding of experimental data is shortly discussed.

Interaction of metastable noble-gas atoms with transition-metal surfaces: Resonance ionization and Auger neutralization.

Electron emission due to deexcitation of metastable noble-gas atoms occurs at transition-metal surfaces which are either clean or covered by atomic adsorbates via resonance ionization of the metastable atom and subsequent Auger neutralization. The resulting electron-energy distributions contain information on the local surface density of states. For analysis, the electron-energy distribution is approximated by a self-convolution function. The validity of this approximation is discussed in detail. The deconvolution of the experimental data yields an effective transition density function reflecting the main features of the electronic surface density of states. The deconvolution technique is described in the Appendix. Furthermore, results are presented on the angular distribution of electrons emitted by Auger neutralization as well as on the lowering of the ionization potential of meta- stable and ground-state noble-gas atoms at surfaces which provides information on the distance range where resonance ionization, Auger neutralization, and Auger deexcitation occur.

Theory of the scanning tunneling microscope.

The recent development of the “scanning tunneling microscope” (STM) by Binnig et al. [8.1–5] has made possible the direct real-space imaging of surface topography. In this technique, a metal tip is scanned along the surface while ad justing its height to maintain constant vacuum tunneling current. The result is essentially a contour map of the surface. This contribution reviews the the ory [8.6–8] of STM, with illustrative examples. Because the microscopic structure of the tip is unknown, the tip wave functions are modeled as s-wave functions in the present approach [8.6, 7]. This approximation works best for small effective tip size. The tunneling current is found to be proportional to the surface local density of states (at the Fermi level), evaluated at the position of the tip. The effective resolution is roughly [2A(R+d)]1/2, where R is the effective tip radius and d is the gap distance. When applied to the 2x1 and 3x1 reconstructions of the Au(l10) surface, the theory gives excellent agreement with experiment [8.4] if a 9 A tip radius is assumed. For dealing with more complex or aperiodic surfaces, a crude but convenient calculational technique based on atom charge superposition is introduced; it reproduces the Au(l10) results reasonably well. This method is used to test the structure-sensitivity of STM. The Au(l10) image is found to be rather insensitive to the position of atoms beyond the first atomic layer.

The effect of adsorption of various gas molecules on the EEEL Sof the (100) face of tungsten

The effect of adsorption on the EELS of the tungsten (100) surface plane, for loss energies in the range of 2–25 eV, is investigated for a series of adsorbates (i.e. O 2, N 2, NO, CO and H 2). Low-lying sharp structures observed in the energy loss spectra seem to be associated with prominent structures in the local surface density of states. A growth of a peak at a loss energy of about 7.5 eV, observed after exposing the surface to any one of the gases studied, is attributed to the breakdown of optic-like selection rules by the adsorption process. The effect of adsorption on the various surface plasmon peaks seems to be adsorbate-specific.

Itinerant electron surface magnetism

Although many experiments have been applied to study the surface magnetism, only a few give a direct and unambiguous answer to a so simple question as “what is the value of the surface magnetic moment”. Some examples of all these experiments are reviewed to show the main differences between two- and three-dimensional magnetism. Then we show that the magnetic moment can be enhanced near the surface in itinerant electron magnetism. This may be the case of He 3 atoms in confined geometries, or of transition metal surfaces or more generally when the local surface density of states at the Fermi level is much larger than the bulk one.

Density of states of a semi-infinite rare-earth metal with magnetic structure: A simple model

Using a simple tight-binding model and the transfer-matrix approach, we have calculated the spectral density of states (SDOS) of a rare-earth metal in the presence of a surface for different magnetic arrangements (such as ferromagnetic, antiferromagnetic, and conical orderings). The local density of states (LDOS) has also been calculated for some examples, integrating the SDOS over the Brillouin zone. The main effect observed deals with the absence of Van Hove's singularities in the surface LDOS, a fact that appears to be an intrinsic property of the surface. Finally the relaxation of the overlap parameters at the surface is discussed and some numerical examples are shown.

Electronic theory of surface segregation in CuNi alloys

A calculation of the surface composition of CuNi alloys based on their electronic properties is proposed. Without any adjustable parameters, the theory predicts a surface enrichment in Cu quite consistent with the experimental results. Bulk and surface local densities of states are also given.

The importance of asphericity of potential and charge transfer at a surface : ab initio self-consistent calculations for Ni(001)

Abstract Ab initio optimum local orbital calculations of the surface local density of states for Xi(001) are presented. The importance of the effect of asphericity of the potential at the surface is emphasized. Charge transfer is included self-consistently in the derivation of the potential. Orbital local densities of states for the bulk, surface and subsurface layers are discussed.

Surface electronic structure of antiferromagnetic chromium

The (001) surface electronic structure of chromium is investigated within the tight-binding approximation in the non-magnetic and in the antiferromagnetic states. The paramagnetic local surface density of states shows a large peak near the middle of the d band just below the Fermi level. This peak induces a large increase of the surface magnetic moment in the antiferromagnetic state. Comparison is made with experimental results. Discussion is made of possible influences of this magnetic moment on photoemission or on LEED experiments for (001) and (110) chromium surfaces.

Prediction and confirmation of two bands of surface resonances on the (100) plane of molybdenum

Two bands of surface resonances on the (100) face of molybdenum have been observed confirming the prediction of a previously published calculation. Angle-integrated photoemission spectra using unpolarized radiations 21.22 eV and 16.85 eV reveal two surface resonance peaks: 0.3 eV and 2.6 eV below the Fermi energy. The origin of the lower-lying resonance is discussed in terms of the previously published calculation of the k  and orbital-resolved surface local density of states.

Surface Resonances on the (100) Plane of Molybdenum

Surface resonances on Mo(100) have been confirmed and studied in detail experimentally by field-emission energy distributions and theoretically by a linear-combination-of-atomic-orbitals calculation of the ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$-resolved surface local density of states. The experimental results in conjunction with the calculations have provided evidence of band-structure effects in field-emission energy distributions. The calculated results have also explained the angle-resolved photoemission results on W(100) and provided a clear picture as to the origin of these resonances.

Calculation of the surface density of electronic states in lead

We present a tight-binding calculation of the local surface density of states for the (001) surface of lead. It is based on a simple phenomenological interpolation scheme which replaces the one-dimensional bulk density of states normal to the surface by a surface adapted curve. The integration over the two-dimensional Brillouin zone is performed numerically. The calculation explains qualitatively differences observed between experimental X-ray photoemission density of states and bulk-value calculations in both s-like and p-like bands.