Correlation between morphology, electron band structure, and resistivity of Pb atomic chains

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1 Home Search Collections Journals About Contact us My IOPscience Correlation between morphology, electron band structure, and resistivity of Pb atomic chains on the Si(5 5 3)-Au surface This content has been downloaded from IOPscience. Please scroll down to see the full text J. Phys.: Condens. Matter ( View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: This content was downloaded on 08/06/2016 at 12:02 Please note that terms and conditions apply.

2 (9pp) Journal of Physics: Condensed Matter doi: / /28/28/ Correlation between morphology, electron band structure, and resistivity of Pb atomic chains on the Si(5 5 3)-Au surface M Jałochowski, T Kwapiński, P Łukasik, P Nita and M Kopciuszyński Institute of Physics, M. Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, PL Lublin, Poland mieczyslaw.jalochowski@umcs.lublin.pl Received 7 March 2016, revised 11 April 2016 Accepted for publication 18 April 2016 Published 26 May 2016 Abstract Structural and electron transport properties of multiple Pb atomic chains fabricated on the Si(5 5 3)-Au surface are investigated using scanning tunneling spectroscopy, reflection high electron energy diffraction, angular resolved photoemission electron spectroscopy and in situ electrical resistance. The study shows that Pb atomic chains growth modulates the electron band structure of pristine Si(5 5 3)-Au surface and hence changes its sheet resistivity. Strong correlation between chains morphology, electron band structure and electron transport properties is found. To explain experimental findings a theoretical tight-binding model of multiple atomic chains interacting on effective substrate is proposed. Keywords: vicinal surfaces, atomic chains, surface resistivity, RHEED, STM, ARPES (Some figures may appear in colour only in the online journal) 1. Introduction The influence of surface roughness on electric conductance was tackled very early by Thomson [1] and Fuchs [2] who elaborated the first classical theory of the size effect. A quantum-mechanical description of electron scattering on a metal surface was elaborated by Tesanowic et al [3] and by Trivedi and Ashcroft [4]. Soon it was evident that surface roughness correlations may play a significant role in electrical conductivity of thin films [5 7]. Theoretical predictions were confirmed in a series of electrical resistivity experiments on spatially isotropic two-dimensional (2D) phases, namely ultrathin metallic films [8 10]. For studying anisotropic 2D phases vicinal Si surfaces are particularly well suited. Since the discovery that submono layer coverage of gold stabilizes the stepped surfaces of Si(1 1 1) vicinals [11] the finding was successfully used to study the coherently ordered atomic chains on Si(5 5 7)-Au [12 15], Si(3 3 5)-Au [12, 13, 15 18], and Si(5 5 3)-Au [19 23]. In most studies the emphasis was put on studying the atomic and electronic structures of chains of metallic atoms adhered to a semiconducting surface. In contrast, only recently have the studies on electrical transport of /16/ $33.00 metallic nanostructures on Si(5 5 3), Si(5 5 7) and Si(3 3 5) [24 26], on a bare vicinal Si(1 1 1) [27, 28], on domains of In wires on Si(1 1 1) [29] been carried out, but no combined surface topography, band structure, electron diffraction and electron transport in situ were made during the formation of atomic chains. The description of the electron transport through a vicinal Si surface with foreign atomic chains is much more complicated than on ultrathin metallic film, where electron scattering plays the crucial role. On Si vicinal surfaces the atoms of chains are coupled to the quasi-one-dimensional terrace atoms and the resulting bonds introduce new, or modify existing, one-dimensional electron bands. Also possible charge transfer to or from the atoms of chain to the substrate is localized to the terrace. It is clear that upon the formation of new atomic chains the system composed of the vicinal substrate and the chains changes its one-dimensional properties, including surface electron transport. The measurement method we apply in this work possesses the unique property it allows to trace the sheet resistivity during the growth of different atomic chains, thus it detects the variation of combined effects of electron scattering and electron bonding between deposited atoms and the substrate IOP Publishing Ltd Printed in the UK

3 In this paper we present the in situ electric resistivity variation study of Si(5 5 3)-Au surface during the growth of Pb atomic chains. The system is fully characterized by scanning tunneling microscopy (STM), reflection high energy electron diffraction (RHEED) and angular resolved photoemission electron spectroscopy (ARPES) methods. The study is supplemented by the effective substrate tight-binding model of electron transport through the unified atomic chains-substrate system. To model the atomic chains growth mode, and its influence on electron transport, the theory considers an ensemble of various Pb atom configurations on a Si(5 5 3)-Au terrace as is known from the experimental data. We show that this model is capable of mimicking observed coverage dependent sheet resistivity variation of Pb atomic chains on the Si(5 5 3)-Au surface, simultaneously giving insight into the interaction character of Pb atoms with the substrate. The paper is organized as follows. In section 2 we briefly present experimental details of the sample, atomic chains preparation and the electrical resistance measurements method. In section 3 we outline a sequential growth mode of the atomic chains, their structural properties, and surface electron band structure changes. We also present and discuss surface resistance variations for the current flowing parallel and perpendicular to atomic chains. In section 4 we describe theoretically our experimental results of the resistance variations and we propose the effective substrate model with conducting atomic chains. We conclude with a summary. 2. Experimental The electrical resistance and RHEED measurements were performed in a UHV chamber with a base pressure of around mbar. The n-type Si(5 5 3) samples, with dimensions of mm 3 and specific resistivity of Ω cm, were used in experiments. The sample cutoff angle was 12,27 from the [ 111 ] direction toward [ 112 ] with an accuracy After ultrasonically cleaning in acetone and methanol and degassing in UHV chamber, the sample was cleaned by flashing several times up to 1500 K. Perfectly ordered Si(5 5 3) surface on the macroscopic scale was fabricated after the deposition at room temperature (RT) of 0.48 ML Au (with 1 ML corresponding to the atomic density of a half of the bulk terminated Si(1 1 1) bilayer) at rate of 0.1 ML min 1, annealing at 950 K, and gradual lowering the temperature to the RT within 5 min. A well-ordered surface with two Au chains per terrace running along the atomic steps was obtained. The electrical resistance was determined in situ by measuring the voltage drop V between two tungsten electrochemically etched tips placed on two thick Pb pads. Two Mo clamps at the sample edges served as contacts for the current. The Au atomic chains and Pb contact pads were newly prepared before each resistance measurement. The method was successfully used previously in the electrical conductivity studies of metallic quantum wells on Si(1 1 1) [8]. This method, in comparison to other techniques thoroughly discussed in the review paper by Miccoli and others [30], is relatively easy to apply and more direct to interpret results. Next, atomic chains were fabricated by deposition of Pb on the Si(5 5 3)-Au sample at a rate of about 0.1 ML min 1. measured with a quartz crystal microbalance with accuracy better than ±15%. During Pb deposition an AC (alternating current) voltage signal from the pair of tips was detected by the lock-in whereas 2 μa 70 Hz amplitude stabilized current was applied to the sample clamps. Measurements for the current directed parallel and perpendicular to the atomic chains were performed on separate samples cut from the same Si(5 5 3) wafer. Before resistance measurements the I(V) linearity of all sample-tip contacts was carefully verified. STM and ARPES measurements were performed in a separate UHV chamber equipped with precise quartz crystal thickness monitors, where the crystal structure of a substrate and the growing Pb chains were also monitored by means of RHEED. 3. Results and discussion 3.1. Pb atomic chain ordering, crystal structure and electron band structure Formation of perfectly ordered Pb chains on a Si(5 5 3)-Au surface is governed by the diffusion and occurs only within a narrow temperature window around 280 K [31]. At lower temperatures the Pb atoms are not mobile enough and form small, separate clusters. At liquid nitrogen temperatures the mobility of Pb is strongly reduced and atoms form a continuous, smooth layer, as was confirmed by observation of the RHEED intensity oscillations with 1 ML(1 1 1) Pb periodicity. Pb atoms deposited above room temperature tend to coalesce into large crystalline islands surrounded by a 1 ML thick wetting layer [32]. Within the most interesting temperature range Pb atoms self-assemble into chains growing in a sequential way. The first chain, C1, with the periodicity 2 a[ 110 ] grows at the step edge of each Si(5 5 3)-Au terrace, figure 1(a). The chain is completed at the coverage equal to 0.11 ML corresponding to one half of the density of step-edge Si atoms. Next, for larger coverages, the second chain C2 with atomic site occupation twice as much as in the chain C1 is formed in the middle of each terrace, figure 1(b). These two chains are well resolved and separated by 0.62 nm. In the STM images the chain C2 shows also 2 a[ 110 ] topographic modulation caused by periodic variation of its internal structural and electronic nature [33]. STM studies reveal also that this chain grows as small patches randomly distributed over the uniform surface covered with C1 chains. Thus, after deposition of 0.35 ML Pb two complete chains, albeit with different structural and electronic properties are formed, figure 1(b). Further deposition results in formation of the chain C3 with a single lattice constant periodicity, figure 1(c). Figure 2 displays the in situ electron diffraction patterns recorded during Pb deposition. Figure 2(a) shows the pattern for pristine Si(5 5 3)-Au, figure 2(b) for Si(5 5 3)-Au with chain C1 after deposition of 0.11 ML Pb, figure 2(c) for chains C1 and C2, after deposition of 0.35 ML Pb, and figure 2(d) for chains C1, C2 and C3, after deposition of 0.69 ML Pb. All patterns show similarities. The most streaking feature is 2

4 C1 (a) C2 (b) C3 (c) Figure 1. Schematic representation of Pb atomic chains on Si(5 5 3)-Au terrace. (a) Chain C1 with periodicity of 2 a[ 110 ] at the terrace edge for coverage of 0.11 ML. (b) Chains C1 and C2 for coverage of 0.35 ML. (c) Chains C1, C2 and C3 with periodicity of 1 a[ 110 ] for coverage of 0.69 ML. Ball colors differentiate sequential growth of the Pb chains. the presence of the main diffraction spot distribution in all RHEED patterns. Without a doubt, the fact that there are no other main diffraction spots suggests that the coherence between crystal structure of Si(5 5 3)-Au and crystal structure of Pb atomic chains is strong. The double periodicity along the [ 110 ] direction in Si(5 5 3)-Au seen in figure 2(a) and confirmed by DFT calculations [23] appears even more intense for samples with single and two atomic chains on terrace, figures 2(b) and (c). A more complicated structure appears in figure 2(d), where diffraction streaks characteristic of 8 a[ 110 ] periodicity are present. Although, due to metallicity of the surface, this superstructure is not recognized in our STM images it was recently observed in STM images of Pb nanoribbons on Si(5 5 3) surface [34], where nanoribbons were composed of five Pb atomic chains on each terrace with the lattice unit cell along the [ 110 ] direction corresponding to eight Pb interatomic distances (26.96 Å). It is worth noticing that the nanoribbons were produced on a bare Si(5 5 3) surface covered with 1.3 ML Pb and were fabricated after annealing at 250 C whereas the presently investigated nanostructures consist of three chains growing on Si(5 5 3)-Au at RT and with Pb coverage of 0.69 ML only. The STM topographic images recorded for samples with different Pb coverages deliver the more detailed description of atomic chains. Figure 3 presents typical images of Si(5 5 3)-Au substrate with (a) 0.08 ML Pb, (b) 0.22 ML Pb, (c) 0.35 ML Pb, and (d) 0.69 ML Pb deposited at RT. In figure 3(a) only single atomic chains C1 are seen, whereas in figure 3(b) two chains C1 and C2 form relatively compact patches merging together at the coverage of 0.35 ML, figure 3(c). Due to the enhanced diffusion of Pb atoms along the atomic steps the C1 chain in figure 3(a) looks fuzzy. Completion of the chain C1 reduces the diffusion of Pb at the step edge, and the next chains, depending on the Pb coverage, Figure 2. RHEED diffraction patterns of Si(5 5 3)-Au recorded at RT and after deposition of Pb. (a) Bare Si(5 5 3)-Au substrate with outlined 1 1 surface reciprocal lattice unit cell of Si(5 5 3)-Au, (b) after deposition of 0.11 ML Pb corresponding to a single atomic chain C1 on each terrace, (c) after deposition of 0.35 ML Pb with two Pb atomic chains, C1 and C2, and (d) with 3 Pb atomic chains, C1, C2, and C3, after deposition of 0.69 ML Pb. appear as well resolved patches in figure 3(b) or long chains with some defects, figure 3(c). Formation of the third atomic chain, C3, on a terrace dramatically changes the STM image, figure 3(d). Now chains show very weak modulation along the [ 110 ] direction. Another sign of their transition into metallic state is the presence of end states observed previously in atomic chains of Au on Si(5 5 7)-Au [35] and Si(5 5 3)-Au [36, 37]. The above findings were confirmed in the photoemission experiments. Figure 4 presents a set of second derivative of the photoemission intensity maps for Si(5 5 3)-Au samples with characteristic coverages of 0, 0.11, 0.35 and 0.69 ML Pb. The bare surface shows two parabolic bands, figure 4(a), centered at the Brillouine zone (BZ) border with k = Å 1. This 3

5 J. Phys.: Condens. Matter 28 (2016) Figure 3. STM images of Pb atomic chains on Si(5 5 3)-Au. (a) 50 nm 50 nm image of the sample with the Pb coverage of 0.08 ML, Ubias = 2.10 V. (b) 50 nm 50 nm with 0.22 ML Pb, Ubias = 1.90 V. (c) 30 nm 30 nm with 0.33 ML Pb, Ubias = 1.96 V. and (d) 30 nm 30 nm with 0.66 ML Pb, Ubias = 2.0 V. Insets in (a) and (c) show corresponding 5 nm 5 nm images with outlined 1 2 Si(5 5 3)-Au surface unit cell. surface is metallic, as it was confirmed in several experiments [15, 20, 24, 25]. The bands originate from two Au chains located in the middle of the (1 1 1) terrace [23]. Formation of a single Pb chain with double periodicity, figure 4(b), slightly shifts the upper band to lower binding energy. Although a clear energy gap is not seen yet, the photoemission intensity at the Fermi level vanishes, indicating the energy gap opening. This situation becomes more clear for the sample with two Pb atomic chains, figure 4(c). Now the energy gap is about 0.3 ev and the observed shift of the bands is caused by adsorbed Pb atoms acting as donors, as was observed in [33]. Note that electron energy gaps and possible surface states (which appear in the gap region) can be observed for different wire geometries and for various atom species e.g. [38, 39]. In the sample with three atomic chains, figure 4(d), the energy gap vanishes, the metallicity is recovered and new bands emerge. The most characteristic is a flat band at k = 0 and about 0.15 ev below the Fermi level. This band can be identified with a quantum well state in two-dimensional Pb(1 1 1) single layer [40, 41]. when atomic chains self-assemble due to the enhanced onedimensional diffusion. Figure 5 shows the sheet resitivity variations measured during the Pb deposition onto the sample held at 300 K. Sheet resitivities ρ and ρ correspond to the geometry with current flowing parallel to the step edges and perpendicular to them, accordingly, as is shown schematically in the insets. The resistivity ρ shows characteristic features that can be linked to the results obtained from STM and ARPES photoemission experiments. For very low coverages, when only the C1 chain is formed, the resistivity increases rapidly and saturates when the first chain is completed at about 0.11 ML. At coverage of about 0.2 ML the resistivity again begins to increase, and reaches the maximum at the coverage of about 0.35 ML which corresponds to the formation of two atomic chains, C1 and C2. The sheet resistivity changes are in accordance with the band structure variations determined from the photoemission intensity measurements. As is shown in figure 4, during the growth of Pb atomic chains the energy gap opens and reaches the maximal value at the coverage of 0.35 ML corresponding to the formation of two atomic chains shown in figure 3(c). It is expected that in such chains an inelastic electron scattering due to the structure imperfection should be small and one expects a minimum of the resistivity. However, in contrast to this expectation, the sample shows the maximal resistivity. Since the electrical transport is mediated by electron scattering and electron density, it is apparent that the main reason 3.2. Surface electron transport mediated by Pb atomic chains In order to determine the Si(5 5 3)-Au surface resistivity upon formation of Pb atomic chains C1, C2, and C3, we measured in situ the resistance during the Pb deposition at the temper ature 4

6 for the resistivity increase is the electron density decrease at the Fermi level. The photoemission experiments show that the formation of third atomic chain, accompanied by completion of chain C1, transforms surface into a metallic state. This is confirmed by the electron transport measurements. In figure 5, for coverages larger than 0.35 ML, the resistivity ρ rapidly decreases below the initial resistivity of the pristine Si(5 5 3)-Au. Interestingly, the sheet resitivity ρ variation within the coverage range from 0 to 0.35 ML is 8 times smaller than ρ. The weak coverage-dependent variation of ρ further indicates that the electron transport mostly occurs along the chains and is rather weak across the terraces. It is worth noting there that for coverages larger than 0.35 ML Pb the ρ varies much faster than ρ. 4. Model and theoretical description To describe our experimental results shown in figure 5 we propose the effective substrate model which corresponds to a single vicinal terrace of the bare Si(5 5 3)-Au substrate and consists of a two-dimensional rectangular lattice of atomic sites (array of m n) between two metallic electrodes, figure 6. The central region of this system (unfilled circles in figure 6(a)) is composed of three rows of coupled atoms and stands for the effective substrate used in the experiment. To model effectively the growth of Pb chains on the substrate, we analyze the experimental results described in the previous section which provide essential information about the Pb distribution at the Si(5 5 3)-Au surface. Pb atoms are deposited onto the substrate (filled circles) and form one-dimensional structures chains C1, C2 and C3, see also figure 1. In our calculations we assume that these chains grow in the following sequential processes. Chain C1, coverage ML. At the first stage of the deposition process (Pb coverage below 0.11 ML) lead atoms are placed randomly near the step edge of the terrace and they are separated by 2 lattice constant along the steps. For the coverage 0.11 ML every second site in row I is occupied, which is shown in figure 6(b), filled circles, see also figure 1(a). Note that each Pb atom is coupled with only one substrate site which is under it. Chain C2, coverage ML. Next, for the coverage greater than 0.11 ML (but below 0.35 ML) Pb atoms occupy the substrate sites on the row III (chains C1 and C2 are separated by 0.62 nm), panel (c). However, due to the atomic diffusion along terraces (see [31, 42]) we observe specific 1D growth of the C2 chain i.e. randomly deposited Pb atoms move along the terrace and join together to form small paths (short wires) which grow and grow with the Pb coverage. Finally, for the coverage 0.35 ML, they form a single perfect Pb chain on the row III with a single lattice constant. To model this stage of epitaxy we choose up to three initial sites from the row III, and Pb atoms are deposited randomly at the nearest-neighbor unoccupied sites starting from the initial atoms. This procedure is continued until the C2 chain EB (ev) Γ Figure 4. Photoemission intensity second derivative maps for (a) bare Si(5 5 3)-Au sample, (b) with 0.11 ML Pb, (c) with 0.35 ML Pb, and (d) with 0.69 ML Pb. Origin of horizontal axis along step edges direction denotes the middle of the surface Brillouin zone (Γ). The border of the Brillouin zone (K ) is at k 0.82 ( 1Å 1 ). is completed. Note that this chain shows two-atom internal periodicity, see figures 1(b) and 3. Chain C3, coverage ML. For a higher coverage, above 0.35 ML (and below 0.69 ML), the remaining sites are randomly occupied by Pb atoms, figure 6(d). Thus, finally, for the coverage about 0.69 ML, the model substrate is covered by three perfect Pb chains C1, C2 and C3. Note, that the Pb coverage used in the experiment is expressed in the units of Si(1 1 1) surface density and the value of 0.69 ML does not ensure the full coverage (100%) of the Si(1 1 1) surface. Due to the effective one-terrace model considered here, in this section we express the model substrate coverage in percents of the terrace coverage, i.e. the experimental coverages 0 ML, 0.11 ML, 0.35 ML, and 0.69 ML correspond to 0%, 16.6%, 50%, and 100%, respectively. The model Hamiltonian H of the system can be written in the following form (in the standard second-quantized notation): K k (1/Å) = (a) (b) (c) (d)

7 ρ (kω/ ) Pb coverage (ML) Figure 5. Si(5 5 3)-Au surface resistivity dependence on the amount of Pb deposited at 300 K. ρ and ρ correspond to geometry with current flowing parallel to the step edges and perpendicular to the step edges. Characteristic coverages corresponding to formation of complete chains C1, C2 and C3 are marked with arrows. Electric contacts arrangements are shown as insets. + H = Vαβ, aαaβ (1) αβ, where α and β represent single-particle electron states in the substrate and in both electrodes, and a + (a) is the electron creation (annihilation) operator at the appropriate state. The parameter V αβ, for α = β describes the on-site electron energies, V αβ, = εα, and for α β it corresponds to hopping integrals between α and β states. We use the following notation of the parameters: εα = εs for electrons in the substrate atoms, ε d for electrons of deposited Pb atoms, ε kl / kr for electron states in the left or right electrode. The tunnel matrix elements Vαβ, = V n or V m denote the hopping int egrals between the nearest-neighboring atoms in the substrate along the n or m direction. Here we will always assume that all onsite energies of the substrate and intra-substrate tunnel matrix elements are position independent. Similarly, V nd and V md relate to Pb atoms on the substrate and V 1, V 2, V 3 describe the couplings between the C1, C2 and C3 chains and the substrate, respectively (due to the internal two-atom periodicity of the C2 chain we introduce different couplings V 2 for every other atom i.e. V 2a, and V 2b ). The couplings V kl, V kr are the hopping integrals between the states in the left/right electrode and the first/last column of atoms. The matrix elements V kl and V kr enter the expressions for the LR / spectral densities Γ = 2π k VkLR / 2 δ( ε εklr / ) which we model within the wide-band approximation as energy independent. With the above single-particle Hamiltonian it is assumed that electron electron interactions do not play any significant role in the system and can be captured by an effective shift of the onsite energies. In that case the spin index can be omitted in the Hamiltonian as both spin directions are independent of each other. Such a model allows ρ J ρ J us to describe qualitative the experimental results shown in previous sections. In our calculations we use the coupling L R strength Γ =Γ as energy unit and we measure energies with respect to the Fermi energy, which implies EF = 0. The values of the on-site electron energies in the substrate and in the Pb chains as well as all coupling strengths were chosen in order to satisfy the realistic situation in our experiments. Typical values of hopping integrals are in the range of a few ev for strongly coupled atoms and smaller for weak couplings, see also other theoretical calculations, e.g. [43]. Moreover, the parameters were fitted to obtain satisfactory qualitative agreement with the experimental results. Note that small modifications of the system parameters, in the range of about 15%, do not significantly change the obtained results. It is worth noting that we use here the effective substrate model thus it is natural that the coupling strengths and level energies can somewhat differ from the real parameters of the Si(5 5 3)-Au surface. In order to obtain the conductance of the central region (during Pb deposition) one needs to compute the Green function for the total tight-binding Hamiltonian. The linear conductance at zero temperature for the Fermi energy is given by the Landauer formula: 2e L GE = Tr Γ G r R r ( F) { ˆ Γ ˆ ( G ) } (2) h where G r stands for the square matrix of the retarded Green functions which can be found from the equation of motion technique (see [43, 44] for details). The dimension of G r (and ˆΓ) matrix depends on the number of atoms in the central system. Note, that non-zero elements of Γˆ LR / are the spectral / density functions, Γ LR, and are related to sites coupled to the L or R lead. In our calculations we obtain the relative conductance changes G/ G S, where G S corresponds to the conductance of the bare substrate (without deposited atoms). The relative resistance of the system, R/R s, is inversely proportional to the obtained conductance. In figure 7 we show the relative resistivity of the system schematically shown in figure 6 as a function of the Pb coverage. Due to randomly placed atoms on the substrate along the steps (on rows I, II and III) all resistivity curves were averaged over 300 different distributions of Pb atoms. In the upper panel we show the resistivity for the perfect sequential growth of Pb chains on the terrace and study the coupling asymmetry in the C2 chain on the electron transport. The bottom curve corresponds to the same couplings of all C2 atoms with the surface, V2a = V2 b, and three upper curves are obtained for V2b = 2V2 a, 4V 2a and 5V 2a, respectively. As one can see in the first stage of epitaxy (0 16.6%) the resistivity increases due to single Pb atoms on the substrate (on row I), see also [43]. For the coverage of 16.6% we observe an ideal Pb chain with 2 periodicity (figure 6(b)) on the considered terrace, chain C1. Such a chain-substrate system is characterized by the energy gap at the Fermi level in the density of states. It is known that for regularly placed impurities along a wire, depending on the periodicity of impurities, energy gaps in the structure of the density of states appear [45]. 6

8 (a) (b) (c) (d) Figure 6. (a) Top view of the effective rectangular substrate of atomic sites ( m n array of empty circles for m = 3 and n = 20 which stand for three rows of atoms: row I, row II and row III) between two, left and right, electrodes. Lead atoms (filled circles) are deposited on the substrate sites and, depending on the Pb coverage, they form one, two or three atomic chains on the substrate: (b) chain C1, (c) chains C1 and C2, (d) chains C1, C2 and C3, for the coverage 16%, 40% and 88%, respectively. The parameters ε s, V n, V m (ε d, V nd, V md ) describe the substrate atoms (Pb atoms on the substrate) and the couplings between them. For details see the text. In the next step, for the coverage between 16.6% 50% the second atomic chain (C2) with a single lattice constant is fabricated on the terrace (figure 6(c)). During this process two opposite effects take place: single Pb atoms at the substrate increase resistivity but they join together and form short wires which decrease the resistivity. Thus, at the beginning of this process, a local plateau in the resistivity is observed. As one can see, for the same coupling strengths of all atoms in this chain with the substrate, V2a = V2 b, the resistivity of the system drastically decreases for the coverage about 50%. In this case the C2 chain is complete and it stands for an additional perfect path for electrons to flow between electrodes, thus the resistivity decreases. However, the C2 chain reveals the two-atom internal periodicity and thus we modify everysecond atom-substrate couplings in C2, V 2a and V 2b. In the presence of the coupling asymmetry between V 2a and V 2b the local minimum in the resistivity vanishes (upper curves) and we observe a local maximum for this coverage, like in the experiment, figure 5. For the coverage above 50% the remaining sites on the substrate are occupied randomly by Pb atoms the third atomic chain in the row II, C3, is fabricated and empty sites in the row I are occupied. In this case, as before, two opposite effects occur but we do not observe any resistivity plateau due to the fully randomly process of the chain growth. Note that similarly to the experimental results from figure 5 for the maximal coverage, 100%, all sites of the substrate are occupied by Pb atoms and the relative resistance is lower than for the bare substrate. As one can see for the almost ideal substrate (very low or full coverage) the resistance is lower than for the disordered substrate. For intermediate coverages electron waves are reflected by disorder centres (Pb atoms) and the resistance increases. However, for periodic ordered disorders, like for R/R s R/R s perfect growth V 2a = % mobile atoms V 2b = V 2b =0.07 V 2a =0.07 V 2b = Pb coverage [%] Figure 7. The relative resistance of the system shown in figure 6 as a function of the Pb coverage for the perfect growth of atoms (upper panel) and for 2 8% of the total number of atoms moved from their original sites (mobile atoms, bottom panel). The curves were averaged over 300 different distributions of atoms along the substrate. The system parameters are: Γ = 1 (energy unit), ε s = 0, V n = 1.5, V m = 0.35 for the substrate atoms, ε d = 0.4, m = 3, n = 50, V nd = 2, V md = 0.4 for Pb atoms, V 1 = 0.35, V2a = V3 = 0.07 and V 2b = 0.07, 0.14, 0.28, 0.35 (upper panel) and V 2b = 0.07, 0.14 (bottom panel). R s stands for the resistivity of a bare substrate. the coverage 16.6% or 50%, electron waves are mostly propagated through the system which leads to local minima in the resistance. 7

9 Note that the theoretical curves from the upper panel were obtained for the perfect growth of chains on the substrate. In real experiments all stages of epitaxy are not exactly separated i.e. before one atomic chain is completed the next one begins to grow, which is visible in the STM images, figure 3(c). Taking this into account in our calculations we assume that during the deposition process a small number of Pb atoms (mobile atoms) can occupy arbitrary free sites. These mobile atoms stand for 2% 8% of the total number of deposited atoms which corresponds to 2 12 atoms for the lattice composed of 150 substrate sites. As a consequence for the coverage 50% there are some free sites in the C2 chain and some occupied sites in the C3 chain (row II). Such process is analyzed in the bottom panel of figure 7. We have found that the local minimum in the resistivity for the coverage 50% vanishes even for the same couplings of all atoms in the C2 chain to the substrate, V2a = V2 b(broken curve). However, for asymmetrical couplings V 2a and V 2b (solid curve, bottom panel) we have obtained a better qualitative agreement between the theoretical and experimental data. 5. Summary In conclusion, the structural and electron transport properties of multiple Pb atomic chains growing on a Si(5 5 3)-Au surface are investigated by scanning tunneling spectroscopy, reflection high electron energy diffraction, angular resolved photoemission electron spectroscopy and in situ electrical resistance. Three well ordered atomic chains on each terrace were grown in a sequential mode. First two chains reduced the sheet conductivity, whereas formation of the third chain enhanced it. These studies find that the chains substantially change the electronic band structure of the surface. As was originally confirmed by electrical resistivity and photoemission measurements, the metallic surface of Si(5 5 3)-Au transforms into the insulating after the formation of two Pb atomic chains, and becomes metallic after the growth of the third atomic chain. The resistivity changes during the Pb deposition on Si(5 5 3)-Au surface were analyzed within the tight-binding Hamiltonian for the effective substrate. We have found that both structure imperfection of Pb chains during the epitaxy (related to mobile atoms) and the band structure modifications due to periodically placed atoms (in C1 and C2 chains) should be considered to obtain satisfactory qualitative agreement with the experimental data. Acknowledgments This work was supported by National Science Centre, Poland, under Grant No. 2014/13/B/ST5/ We are grateful to M Stróżak for his participation in the measurements and for technical assistance. References [1] Thomson J J 1901 Proc. Camb. Phil. Soc [2] Fuchs K 1938 Proc. Camb. 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