Electron Propagation along Cu Nanowires Supported on a Cu(111

NANO LETTERS

Electron Propagation along Cu Nanowires Supported on a Cu(111) Surface

2008 Vol. 8, No. 9 2712-2717

Sergio Dı´az-Tendero,*,†,‡ Stefan Fo¨lsch,§ Fredrik E. Olsson,| Andrey G. Borisov,†,‡ and Jean-Pierre Gauyacq†,‡ CNRS, Laboratoire des Collisions Atomiques et Mole´culaires, UMR 8625, Batiment 351, 91405 Orsay Cedex, France, UniVersite´ Paris-Sud, Laboratoire des Collisions Atomiques et Mole´culaires, UMR 8625, Batiment 351, 91405 Orsay Cedex, France, Paul Drude Institut fu¨r Festko¨rperelektronik, HausVogteiplatz 5-7, 10117 Berlin, Germany, and Department of Applied Physics, Chalmers/Go¨teborg UniVersity, S-41296 Go¨teborg, Sweden Received April 11, 2008; Revised Manuscript Received June 12, 2008

ABSTRACT We present a joint experimental-theoretical study of the one-dimensional band of excited electronic states with sp character localized on Cu nanowires supported on a Cu(111) surface. Energy dispersion and lifetime of these states have been obtained, allowing the determination of the mean distance traveled by an excited electron along the nanowire before it escapes into the substrate. We show that a Cu nanowire supported on a Cu(111) surface can guide a one-dimensional electron flux over a short distance and thus can be considered as a possible component for nanoelectronics devices.

Atomic and molecular nanowires represent an ultimate limit of the miniaturization of electronic devices, where the properties of the system are governed by quantum mechanics. The central importance of nanowires for nanoscale electronics1 as well as the possibility of using them as gas sensors2 has led to a large number of studies over the last few years.3-7 Most of the research so far has been done on free-standing nanowires or nanowires bridging metallic leads, where the major phenomena controlling the electronic properties and conductivity are quite well understood.8 Recently, manipulation of adsorbed atoms and molecules with atomic precision offered by scanning tunneling microscopy (STM) allowed the creation of Pd, Au, and Cu atom chains aligned on a metal surface.9-14 It has been demonstrated that the unoccupied electronic states of the chain correspond to a onedimensional (1D) free-electron-like band quantized on the finite size object.10,11,13,15 This 1D band describes an electron propagating along the nanowire. It develops from the hybridization of excited electronic states of sp symmetry strongly polarized perpendicular to the surface and localized on the individual adatoms.15,13,16,17 Energetically the 1D band of nanowire localized states is located inside the surface projected band gap of the substrate. † CNRS, Laboratoire des Collisions Atomiques et Mole ´ culaires, UMR 8625. ‡ Universite ´ Paris-Sud, Laboratoire des Collisions Atomiques et Mole´culaires, UMR 8625. § Paul Drude Institut fu ¨ r Festko¨rperelektronik. | Department of Applied Physics, Chalmers/Go ¨ teborg University.

10.1021/nl801045b CCC: $40.75 Published on Web 08/01/2008

 2008 American Chemical Society

So far, only the energies and the local density of states (LDOS) distributions of the electronic states of atomic chains supported on a metal surface have been addressed experimentally and theoretically. It has been shown that the dispersion of the 1D sp band can be well-described with a tight-binding (TB) modeling only including the electronic states localized on the chain atoms.13-15 This is a remarkable result since one could expect an atom in the wire to be coupled in a similar way to its two neighbors in the wire and to its several neighbors in the substrate. It has been argued that owing to the projected band gap of the substrate, the nanowire-localized states are partly decoupled from the substrate leading to a lifetime increase, as already observed in several different systems.18-20 However, the quantitative study of the lifetimes of the electronic states of supported nanowires is still missing, despite its central importance: the lifetime determines how far an excited electron can propagate along the nanowire, i.e., whether an atomic wire on a metal surface can be considered as an almost independent entity or whether it is simply a protruding part of the substrate. The latter question is crucial for possible applications of metal-supported metallic nanowires for nanoscale electronics. In this Letter, we present a joint experimental-theoretical study of the energies and, most importantly, of the lifetimes of the electronic states of the excited 1D sp band of a Cu nanowire on a Cu(111) surface. The two sets of results are in quantitative agreement and we can precisely settle the question of electron propagation along the Cu supported wire:

Figure 2. Energy dispersion of the Cu nanowire localized sp band. The energy with respect to the Fermi level is shown as a function of the electron wave vector parallel to the wire (in atomic units: 1 au ) 1 a0-1). Black solid line with squares: present theoretical results for the wire/Cu(111) system. Blue dashed line with diamonds: present theoretical results with the effect of the STM bias included. Open circles: experimental data by Fo¨lsch et al.13 The insert shows schematically the Cu nanowire (red) supported on a Cu(111) surface (blue).

Figure 1. (a) Constant-current STM images of a Cu monomer, a dimer, and close-packed monatomic Cu/Cu(111) chains with the number N of atoms ranging from three to nine (from left to right). (b) Constant-current height profiles of the adatom and the assembled structures in (a) measured along the 〈110〉 chain direction; each attachment of a single atom results in a chain length increase by an increment of 2.5 Å. (c) Experimental dI/dV spectra probing the LDOS of close-packed Cu/Cu(111) chains (Cu-Cu spacing 2.55 Å) in the regime of unoccupied sample states with the STM tip located at constant height over the center of the nanostructure; the color-coding of the number N of atoms in the chain is indicated. The resonance peak observed for each chain is associated with the sp-derived chain-confined electronic ground state. The insert shows that the dI/dV peak magnitude scales with 1/N, consistent with the chain-delocalized character of the 1D state. All data were taken at 7 K: set point parameters prior to opening the feedback loop, 1 V, 1 nA; peak-to-peak amplitude and frequency of the lock-in modulation, 30 mV and 640 Hz.

the mean distance traveled by an electron along the nanowire before its escape into the substrate reaches 12 Å, i.e., basically five nanowire atoms. It indeed shows a partial decoupling of the nanowire from the substrate and allows one to introduce the concept of a short supported Cu wire. On the experimental side,21 we carried out scanning tunneling spectroscopy (STS) measurements at 7 K to characterize the confined states in monatomic Cu/Cu(111) chains assembled by atom manipulation under ultrahigh vacuum conditions. The constant-current STM images in Figure 1a illustrate the stepwise Cu chain assembly, starting Nano Lett., Vol. 8, No. 9, 2008

with a discrete Cu adatom (left) and finally yielding a nine atomic close-packed chain (right) by the successive attachment of single Cu atoms along the 〈110〉 in-plane direction22 (N denotes the number of atoms). Figure 1b summarizes height profiles of the adatom and the assembled chains shown in (a) measured along the 〈110〉 chain direction. It is evident that with each manipulation event the apparent chain length (represented by the half-width of the along-chain height profile) increases by an increment of about 2.5 Å, indicating that atoms within the chain reside on nearest-neighbor facecentered cubic (fcc) lattice sites of the substrate surface (the Cu-Cu spacing along 〈110〉 is a/
2 ) 2.55 Å, with the Cu lattice constant a ) 3.61 Å). Finally, Figure 1c shows resonance peaks in the bias-dependent differential tunneling conductance dI/dV (providing a measure of the electronic LDOS) obtained for Cu chains consisting of three to seven atoms. In each measurement, the STM tip was positioned at constant height over the chain center (the lateral tip positions are indicated by the vertical bars in (b), each corresponding to one of the color-coded height profiles). The resonances reflect the chain-confined lowest lying states characterized by a single-lobe squared wave function13 and show a downward shift in energy toward the Fermi level with increasing length. The measured energies are well reproduced within a simple tight-binding scheme.14 The insert in Figure 1c shows that the peak magnitude scales with 1/N which we interpret as an indication of the chain-delocalized character of the 1D state. The peak profiles further indicate a full width at half-maximum (fwhm) of about half an electronvolt showing a slight reduction with increasing chain length. 2713

lifetimes and wave functions are extracted from the timedependence of ψkz.23 The calculation of the total potential V “seen” by an excited electron follows an approach developed in our previous studies of individual Cu adatoms.16,24 In brief, V consists of several terms V ) Vs(x) + ∆Vwire(x, y, z) + Vopt(x, y)

Figure 3. Width of the quasi-stationary states of the 1D sp band localized on a Cu wire supported on a Cu(111) surface. Results are presented as a function of the electron wave vector parallel to the wire (in atomic units: 1 au ) 1 a0-1). Black solid line with squares: present theoretical results for the wire/Cu(111) system. Violet dashed line with diamonds: present theoretical results with the effect of the STM bias included. Symbols: present experimental results. The different colors of the symbols refer to the different numbers, N, of atoms in the chain (code given in the insert). The full circles present the results for the lowest lying (n ) 1) state confined in each chain, whereas the open symbols (squares and triangles) present higher lying confined states (n ) 2 and 3).

On the theoretical side, we studied a single infinite Cu wire, aligned along the 〈110〉 in-plane direction as sketched in the insert of Figure 2. The distance between the Cu nanowire and the topmost layer of surface atoms is 1.92 Å as obtained in the present study. We use a mixed approach where ab initio density functional theory (DFT) calculations of the ground-state properties of the system are followed by the wave packet propagation (WPP) study of the dynamics of an excited electron. For detailed descriptions of WPP we refer to refs 20, 23, and 24. The time-dependent Schro¨dinger equation for the wave function of the excited electron Ψ(x,y,z;t) is solved on a 3D mesh in Cartesian coordinates. Periodic Bloch boundary conditions are imposed: Ψ(x,y,z;t) ) eikzzψkz(x,y,z;t), where z is the coordinate along the wire (see Figure 2), and kz is the corresponding wave vector. The x-axis is normal to the surface and goes through the center of the Cu-wire atom placed at the coordinate origin. The time evolution of ψkz(x,y,z;t) is governed by the Hamiltonian Hkz Hkz ) -

[

) ] + V(x, y, z)

∂ 1 ∂2 ∂2 + ikz + + 2 ∂x2 ∂y2 ∂z

(

2

(1)

where V(x,y,z) is the total potential (see below). Provided an initial condition ψkz(x,y,z;t ) 0) ) ψ0, the time evolution is obtained via short time-propagation with the split-operator technique.25 The Fourier-grid pseudospectral method26 is used for the spatial derivatives entering the Hamiltonian. The nanowire localized quasi-stationary states appear as exponentially decaying resonances of the system. Their energies, 2714

(2)

Vs(x) is a one-dimensional representation of the Cu(111) surface potential obtained by Chulkov et al.27 on the basis of ab initio calculations. It is designed to describe the observed band gap, image states, and surface state energies j point. ∆Vwire(x,y,z) is the nanowire-induced potential. at the Γ An absorbing potential28 Vopt(x,y) is introduced at the x and y mesh boundaries to impose outgoing wave boundary conditions. The nanowire-induced potential, ∆Vwire, has been obtained from DFT calculations performed for the clean Cu(111) and Cu nanowire/Cu(111) systems (see also refs 16 and 24). We have used a plane-wave pseudopotential method within the local density approximation as implemented in the Vienna ab initio simulation package code.29 The core electrons of the Cu atoms were represented by a nonlocal pseudopotential VPP of Kleinman-Bylander type.30 The supercell geometry with four Cu layers has been used. For a Cu nanowire case the 4 × 1 surface unit cell has been used to minimize the interaction between the nanowire and its periodic images. The calculated nanowire-induced electron density, ∆n, and nanowire-induced one-electron exchange-correlation potential, ∆VXC are thus well localized along the x and y coordinates inside the calculation supercell. The nanowireinduced Hartree potential, ∆VH, is calculated in entire space by solving Poisson’s equation with ∆n as a source. This procedure ensures that the long-range behavior of ∆VH is free of periodicity effects and corresponds to the case of a single nanowire on the surface. Finally, ∆Vwire ) ∆VXC + ∆VH + VPP. In Figure 2 we show the calculated energy of the sp band of the Cu nanowire on the Cu(111) surface together with the experimental data. Results are presented as a function of the electron wave vector kz parallel to the wire. The parabolic shape of the band dispersion corresponds to the free-particle-like motion of the electron along the wire. An effective mass m* ) 0.5me (me is the free electron mass) is obtained from the theoretical WPP results, whereas an effective mass m* ) 0.68me has been extracted from STS measurements.13 The calculated energies of the sp band states appear systematically lower than the measured ones. We ascribe this discrepancy to the perturbation of the system induced by the STM tip. This conclusion is supported by calculations where an additional term USTM has been added to the total potential in eq 2 to model the STM junction. A capacitor model is used here.31 This representation of the applied voltage in dI/dV simulations gives a good description of the position of the sp resonance of the individual Cu adatom,16 as well as of the shifts of the surface state and image state thresholds observed in dI/dV data.32,33 To mimic the experimental STS situation, the bias U of the junction was set self-consistently equal to the energy of the nanowire Nano Lett., Vol. 8, No. 9, 2008

Figure 4. (a) Energies of different electronic states in the Cunanowire/Cu(111) system for kz ) 0. Energies are shown as a function of the electron momentum perpendicular to the wire ky. Vacuum is at zero energy. The 3D-propagating states are represented by the hatched area. The surface state is shown by the blue parabola. The horizontal line indicates the Cu(111) states degenerate with the nanowire-localized state. (b) Electron density of the quasistationary sp state of the Cu nanowire supported on Cu(111). The figure presents the logarithm of the electron density for kz ) 0. Results are shown in the (xy)-plane and the origin of coordinates is placed at one Cu atom of the wire (see Figure 2). The dark areas correspond to a large probability of presence of the electron and the color code is explained in the insert.

localized state (measured from the Fermi level). Since excited states above Fermi level are probed, the potential due to the STM tip is repulsive and lifts the energies of the nanowirelocalized states (so-called “Stark shift effect”). Thus, a much better agreement with experiment is reached. Because of their coupling to the continuum of the electronic states of the Cu substrate, the nanowire-localized states, as studied in the WPP approach, decay via oneelectron energy-conserving (resonant) transfer into the metal. Thus, for a given kz, the nanowire-localized state is a quasistationary state with a finite width Γ equal to the resonant decay rate and to the inverse of the lifetime τ: Γ ) 1/τ. The calculated and measured widths of the states of the 1D sp band are presented in Figure 3 as a function of the electron wave vector kz parallel to the wire. Let us discuss first the theoretical results obtained for the pure nanowire/surface system (no STM tip-induced electric field included). An average width of the order of 0.36 eV has been obtained, with only a slight dependence on kz for 0 < kz < 0.4 au (1 au ) 1 a0-1; a0, Bohr radius). The resonant decay rates obtained here are much larger than the many-body decay rate which is typically of the order of a few tens of meV for various excited states at surfaces.19,20 Thus, for the present system the lifetime of the sp band states is dominated by the one-electron process and is of the order of τ ∼ 2 fs; during this time an excited electron is trapped on the wire and propagates along it. Figure 3 also presents the sp-level width as extracted from the experimental measurements compared to the calculated decay rate. The color-coded full circles denote the fwhm values inferred from the spectra of the lowest lying state in Figure 1, whereas the colored empty symbols indicate fwhm values obtained for the second (squares, n ) 2) and third states (triangle, n ) 3) of chains with four (magenta), five (red), and six (orange)34 Cu atoms. With the typical line Nano Lett., Vol. 8, No. 9, 2008

widths involved, the peak broadening due to temperatureinduced Fermi broadening does not play a role at the present measurement temperature of 7 K. On the other hand, the experimental data concern finite-size chains, for which electron scattering at the end of the chain may lead to an extra decay process. Such an edge-induced broadening effect is consistent with the length-dependent trend in peak width apparent from the ground-state spectra in Figure 3, documenting an increased fwhm value at smaller chain length. End effects leading to extra decay processes were not addressed in the present calculations. However, for the comparison between experimental and theoretical results, the presence of the STM bias has to be taken into account, similarly to what was done for the energy comparison (Figure 2). Two independent effects are present: (i) The electric field of the STM junction induces an extra polarization of the electronic cloud. It pushes the sp electron toward the surface. Thus, the width of the sp-band is increased reflecting an increased coupling with the substrate. (ii) The experimental procedure for the level width measurement involves scanning the STM bias U and, thus, introduces an apparent increase of the width. Indeed, due to the Stark shift, the energy of the sp-resonance varies roughly linearly with U as has been obtained here: EU(kz) ∼ E(kz) + RU. E(kz) is the field-free energy measured with respect to the Fermi energy. The corresponding width can be simply evaluated for a resonant Lorentzian profile of the form A/[(U - EU(kz))2 + Γ2(kz)/4]. It can be reexpressed as: B/[(U - Eapp(kz))2 + Wapp2(kz)/4] where the apparent resonance energy and width are given respectively by Eapp(kz) ) E(kz)/(1 - R) and Wapp(kz) ) Γ(kz)/ (1 - R). Thus when the STM bias is scanned through a resonant profile, the energy position of the resonance changes continuously, resulting in an apparent change of the resonance width. In practice, effect (ii) reduces to defining the measured width Wapp(kz) from the calculated decay rate Γ(kz) as: Wapp(kz) ) Γ(kz)E′(kz)/E(kz), where E′(kz) is the calculated energy of the kz state in the presence of the STM bias (see Figure 2). Effect (i) turns out to be weaker than effect (ii). As seen in Figure 3, the theoretical prediction, including the STS bias effect, agrees very well with the experimental data. The agreement between the experimental and theoretical energies and widths (Figures 2 and 3) gives confidence in the present analysis. Let us now discuss the role played by the surface-projected band gap of Cu(111) in trapping excited states on the nanowire. Figure 4a illustrates the band gap stabilization effect (see also in refs 18-20). The energies of the electronic states of the system are schematically shown as functions of the electron momentum ky parallel to the surface and perpendicular to the wire. The band folding effect35 (exchange of a reciprocal lattice vector in the z-direction) is not relevant for the kz range considered here. The substrate states disperse parabolically with ky while the sp electron is localized in the y-direction so that the nanowire-localized sp-band states do not disperse with ky. The electron escape from the nanowire by an energy-conserving (resonant) transition into the substrate requires final electronic states in the substrate that have finite ky. Two escape pathways are 2715

Figure 5. Distance (in Å) traveled by the electron injected into the 1D sp band of a Cu wire. Results are presented as a function of the electron wave vector parallel to the wire (in atomic units: 1 au ) 1 a0-1).

possible: the intrinsic surface state, with a given ky, and the metal bulk states, with ky above a certain critical value. Decay with ky ∼ 0, i.e., close to the surface normal, is impossible. The latter is the “easiest” direction of the electron transfer, and so the band gap leads to the stabilization of the nanowirelocalized states. The projected band gap effect is further illustrated in Figure 4b, where the electronic density of the nanowirelocalized state is shown for kz ) 0. The spx hybridization results in a shift of the maximum of the electron density above the nanowire as has been already pointed out by different authors.13,15,16,36 The decay of the nanowire-localized state into the surface state continuum of Cu(111) appears as an outgoing flux of electrons along the surface. The decay into the bulk states is however less pronounced. Since an electron escape along the surface normal is impossible, the flux of electrons escaping into Cu(111) bulk appears as two symmetric branches oriented under a certain angle with respect to the surface normal. The oscillating behavior of the wave packet in the bulk reflects the periodicity of the atomic planes of Cu(111). It is noteworthy that electron transfer into the surface state is the dominating decay channel. One can stress that, although the electronic structure of the surface is locally perturbed by the atomic chain (this effect is introduced via the ∆Vwire term in eq 2), the projected band gap, i.e., the impossibility for an electron to escape into the metal close to the surface normal, is still present since it is a bulk property. Thus, the local perturbation induced by the atomic chain cannot modify the spectrum of electronic states available for electron transfer. We can now turn to the initial question on the nature of the wire. Provided the calculated energies and lifetimes of the different kz states, we can calculate the distance d traveled by an electron in the 1D sp band of the Cu nanowire. It is 2716

given by the product of the group velocity Vg and the lifetime d(kz) ) Vg(kz)τ(kz) ) Vg(kz)/Γ(kz), where Vg(kz) ) ∂E(kz)/∂kz. Figure 5 shows d as a function of the electron wave vector along the wire. The calculated travel distance d increases with kz and reaches d ∼ 12 Å, for kz ∼ 0.35 au. This distance corresponds approximately to five interatomic spacings along the wire (2.55 Å); i.e., an excited electron with kz ∼ 0.35 au covers the equivalent distance of four to five atoms along the wire before it escapes into the substrate. Thus, a Cu nanowire on the Cu(111) surface can guide a 1D electron flux over a short distance. In this respect it appears as an isolated entity and not as a part of the substrate metal. In summary, we have presented the results of a joint experimental-theoretical study of the energy and lifetime of the excited 1D sp band localized on an atomic Cu nanowire supported on Cu(111). By taking the STM bias into account in the calculation, an energy dispersion and a level width of the sp band are obtained which are in very good agreement with the STS data. We found that an electron injected into the sp band can travel a distance up to 12 Å before it escapes from the nanowire into the substrate. Thus, the system can be seen as a short 1D wire with possible applications in nanodevices. The presence of the surface-projected band gap plays an essential role in decoupling the nanowire from the substrate so that the wire behaves as a separate entity and not as a part of the substrate. This suggests that any metal surface with a surface-projected band gap in the relevant energy range is a good candidate for supporting metallic nanowires. Acknowledgment. S.D.-T. gratefully acknowledges a postdoctoral fellowship from the Spanish Ministerio de Educacio´n y Ciencia. References (1) Mirkin, C. A.; Ratner, M. A. Annu. ReV. Phys. Chem. 1992, 43, 719. (2) Favier, F.; Walter, E. C.; Zach, M. P.; Benter, T.; Renner, R. M. Science 2001, 293, 2227. (3) Yanson, A. I.; Yanson, I. K.; van Ruitenbeek, J. M. Nature 1999, 400, 144. (4) Nitzan, A. Annu. ReV. Phys. Chem. 2001, 52, 681. (5) Joachim, C.; Gimzewski, J. K.; Aviram, A. Nature 2000, 408, 541. (6) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384. (7) Di Ventra, M.; Pantelides, S. T.; Lang, N. D. Phys. ReV. Lett. 2000, 84, 979. (8) For an overview of the field see: Introducing Molecular Electronics; Cuniberti, G., Fagas, G., Richter, K., Eds.; Lecture Notes in Physics 680; Springer Verlag: Berlin, 2005, and references therein. (9) Nilius, N.; Wallis, T. M.; Ho, W. Science 2002, 297, 1853. (10) Wallis, T. M.; Nilius, N.; Ho, W. Phys. ReV. Lett. 2002, 89, 236802. (11) Nilius, N.; Wallis, T. M.; Ho, W. Appl. Phys. A: Mater. Sci. Process. 2005, 80, 951. (12) Nilius, N.; Wallis, T. M.; Ho, W. J. Phys. Chem. B 2005, 109, 20657. (13) Fo¨lsch, S.; Hyldgaard, P.; Koch, R.; Ploog, K. H. Phys. ReV. Lett. 2004, 92, 056803. (14) Lagoute, J.; Liu, X.; Fo¨lsch, S. Phys. ReV. B 2006, 74, 125410. (15) Persson, M. Phys. ReV. B 2004, 70, 205420. (16) Olsson, F. E.; Persson, M.; Borisov, A. G.; Gauyacq, J. P.; Lagoute, J.; Fo¨lsch, S. Phys. ReV. Lett. 2004, 93, 206803. (17) Stepanyuk, V. S.; Klavsyuk, A. N.; Niebergall, L.; Bruno, P. Phys. ReV. B 2005, 72, 153407. (18) Borisov, A. G.; Kazansky, A. K.; Gauyacq, J. P. Surf. Sci. 1999, 430, 165. (19) Borisov, A. G.; Gauyacq, J. P.; Kazansky, A. K.; Chulkov, E. V.; Silkin, V. M.; Echenique, P. M. Phys. ReV. Lett. 2001, 86, 488. (20) Chulkov, E. V.; Borisov, A. G.; Gauyacq, J. P.; Sa´nchez-Portal, D.; Silkin, V. M.; Zhukov, V. P.; Echenique, P. M. Chem. ReV. 2006, 106, 4160. Nano Lett., Vol. 8, No. 9, 2008

(21) Technical details on the sample preparation and other experimental procedures are given in refs 13 and 14. (22) Single Cu/Cu(111) adatoms can be manipulated at low temperature along arbitrary lateral directions by reducing the tip-to-surface height to about 1.5 Å, sweeping the tip at constant height (with the feedback loop turned off) across the adatom position, and finally retracting the tip. The current response sampled during the constant-height sweep indicates a sliding motion of the atom and thereby an attractive tip/ adatom interaction, which is a common finding in atom manipulation in the case of metal-on-metal systems. (23) Borisov, A. G.; Kazansky, A. K.; Gauyacq, J. P. Phys. ReV. B 1999, 59, 10935. (24) Olsson, F. E.; Borisov, A. G.; Gauyacq, J. P. Surf. Sci. 2006, 600, 2184. (25) Feit, M. D., Jr.; Steiger, A. J. Comput. Phys. 1982, 47, 412. (26) Kosloff, R. J. Phys. Chem. 1988, 92, 2087. (27) Chulkov, E. V.; Silkin, V. M.; Echenique, P. M. Surf. Sci. 1999, 437, 330. (28) Neuhauser, D.; Baer, M. J. Chem. Phys. 1989, 91, 4651.

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(29) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169. (30) Kleinman, L.; Bylander, D. M. Phys. ReV. Lett. 1982, 48, 1425. (31) According to the experimental conditions,13 we have placed the STM tip at ztip ) 5.5 Å with respect to the center of the atomic wire. (32) Limot, L.; Maroutian, T.; Johansson, P.; Berndt, R. Phys. ReV. Lett. 2003, 91, 196801. (33) Wahl, P.; Schneider, M.A.; Diekh¨; oner, L.; Vogelgesang, R.; Kern, K. Phys. ReV. Lett. 2003, 91, 106802. (34) Whereas the ground state peak widths are directly deducible from the exemplary spectra in Figure 1, evaluation of the resonances associated with excited states involve the subtraction of a monotonous background and a peak fitting assuming Gaussian line shapes. (35) Corriol, C.; Silkin, V. M.; Sanchez-Portal, D.; Arnau, A.; Chulkov, E. V.; Echenique, P. M.; von Hofe, T.; Kliewer, J.; Kro¨ger, J.; Berndt, R. Phys. ReV. Lett. 2005, 95, 176802. (36) Nordlander, P.; Tully, J. C. Phys. ReV. B 1990, 42, 5564.

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