Formation of surface states on Pb(111) by Au adsorption

Using low-energy electron diffraction and angle-resolved photoemission spectroscopy, we investigated the lattice and electronic structures of the Pb(111) surface upon the adsorption of Au atoms at the low temperature T = 40 K. Unlike earlier results showing the formation of PbAu-alloy layers at room temperature, we found that Au atoms form a ultra-thin superstructure, Au/Pb(111)-3 × 3, on top of the Pb(111) surface. Moreover, three surface-state bands, S1, S2, and S3, are induced within and immediately adjacent to the Pb bulk projected band gap centered at the surface zone boundary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{\text{M}}}_{Pb(111)}$$\end{document}M¯Pb(111) at the energies of − 0.02, − 1.05, and − 2.56 eV, respectively. First-principles calculation based on Au/Pb(111)-3 × 3 confirms the measured surface-state bands among which the most interesting are the S1 and S3 surface states. They are derived from surface resonances in Pb(111). Moreover, S1, which disperses across Fermi level, exhibits a large anisotropic Rashba splitting with α of 1.0 and 3.54 eVÅ in the two symmetry directions centered at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{\text{M}}}_{Pb(111)}$$\end{document}M¯Pb(111). The corresponding Rashba splitting of S1 bands in Cu/Pb(111)-3 × 3 and Ag/Pb(111)-3 × 3 was calculated for comparison.

www.nature.com/scientificreports/ superstructure phase of Au/Pb(111)-3 × 3 formed. Moreover, three new SS bands were observed to exist within and around the Pb bulk projected band gap centered at the surface zone boundary M Pb (111) . Their characteristics as well as their contributions towards the interesting properties at the surfaces are discussed. Figure 1a shows the calculated energy band structures of a 24-layer Pb(111) slab. The purple color indicates the weight of the surface component. As reported previously 5 , there is a non-inverted 6sp bulk band gap ranging from − 8.3 to − 3.7 eV projected to the surface zone center Ŵ . With the top band edge p-type and bottom band edge s-type, the SS is unlikely to exist within the band gap according to Shockley's model 9 . Our focus is rather at the surface zone boundary M , where a projected bulk band gap ranges between − 2.14 eV at the bottom bulk band edge (BBBE) and 0.42 eV at the top bulk band edge (TBBE). This gap originates from the strong SOC of 6p bands 5 ; the main orbital components of TBBE and BBBE are both p-type, which doesn't fit Shockley's model, either 9 . Figure 1b shows the measured energy band dispersions of Pb(111) at RT in the symmetry direction ŴM Pb(111) (M Pb(111) at 1.03 Å −1 ). This band gap spans in k space as a rhombus centered at M Pb(111) due to the mirror-image symmetry with respect to it. The calculated subbands in Fig. 1a are superimposed onto the measured one as shown in Fig. 1c Figure 2a,b exhibit LEED patterns of Pb(111) before and after Au deposition at an electron energy of 40 eV. The red circles enclose the Pb(111)-1 × 1 spots and other spots emerging between them after Au deposition are 3 × 3 spots. Note that the 2/3 order spots of 3 × 3 are coincident with √ 3 × √ 3R30 • spots; however, the intensities of 1/3 and 2/3 order spots, as seen in Fig. 2b, are about even, making the possibility of the existence of √ 3 × √ 3R30 • phase unlikely. Figure 2c also shows the LEED pattern after Au deposition at 70 eV, where the Pb(111)-1 × 1 spots are brighter than those in Fig. 2b due to the change in diffraction conditions. The measured energy band structures of Pb(111) and Au/Pb(111)-3 × 3 are displayed in Fig. 2d,e, respectively for comparison. As observed, the rhombus bulk band gap centered at M Pb(111) is occupied by two SS bands, S 1 and S 2 . A third band, S 3 , disperses beneath the BBBE of the rhombus bulk band gap. Photon-energy dependent measurement, as shown in the Fig. S1 of supplementary material, confirms their 2-dimensional (2D) nature. The faint trace of the measured intense Pb bulk band in Fig. 2d can be still detected, as indicated by an arrow, in the measured spectrum of Au/Pb(111)-3 × 3 in Fig. 2e. When the superstructure Au/Pb(111)-3 × 3 forms, the 3 × 3 lattice can inflict an extra reciprocal vector � G 3×3 to the momentum of photoelectrons. This means that the final-state band is altered and the observed bulk band observed in Pb(111) due to the direct transition can diminish 24 . The energy distribution curves (EDCs) of    www.nature.com/scientificreports/ material, the corresponding EDCs and the further 2nd derivative image processing of the measured energy band structures in Fig. 3d, f are displayed to help clarify S 1 , S 2 , and S 3 bands. As one can see, the measured S 1, S 2 and S 3 bands correspond to the calculated counterparts with dominant red and deep blue colors. S 1 band disperses across the Fermi level within the bulk band gap. S 2 band disperses through the bulk band edge to fall partially into the gap while S 3 band completely falls below BBBE and concentrates at M 1 3×3 (M Pb(111) ). In the symmetry direction Ŵ

Results and discussion
, there is an extra upward band outside the gap, as indicated by the dark dashed lines, connecting from S 3 to S 2 and then extending toward Fermi level. It appears that this extra band corresponds to higher aggregation density of calculated QWS subbands of the slab model. The calculation (Fig. S5 of supplementary material) shows that those subbands have more or less Au components and hence can be considered as SRs. However, their surface weights are not as large as those of S 2 and S 3 so the intensity of the extra band is substantially lower than them in Fig. 3d. In the symmetry direction , such an extra band is not observed. Because the entire S 3 band dispersion is merely below the BBBE, much more extended dispersion of S 3 band is observed in this direction. Although the calculated SS bands still extend out of the rhombus Pb bulk projected band gap, only those within and just outside the gap are observed in the measurement. Calculation also shows the measured S 3 band is actually composed of aggregated SR subbands and S 2 covers two bands, the lower one of which has more surface weight in the symmetry direction 3×3 so it can be identified in the measured counterpart (Fig. 3f). Charge of the S 2 state at M 1 3×3 (M Pb(111) ) distributes as 43.14, 25.49, 5.88, and 9.8% in the Au and first three Pb layers (Fig. S6 of supplementary material). Its large surface weight is in line with its energy position located in the middle of bulk projected band gap 9 . The main contributing Au and Pb orbitals are Au-6s and Pb-6p x -6p y . S 1 state is pertinent to the conducting property of Au/Pb(111)-3 × 3 phase since it is near to and crosses the Fermi level.  (Fig. S6 of supplementary  material). The main contributing Au and Pb orbitals are Au-5d xz -5d yz and Pb-6p x -6p y . Compared to S 1 and S 2 , S 3 state has quite less charge in the top three Pb layers, indicating its longer decay length into the bulk.
The similarity of S 1 and S 3 bands of Au/Pb(111)-3 × 3 to the two SR bands at TBBE and BBBE, respectively, centered at M of Pb(111) points out that a SR state existing at the edge of a bulk band gap in the substrate that may at first seem irrelevant can turn much more pronounced after being covered with a superstructure or thin layer made of foreign atoms. Au atoms have a higher electronegativity than Pb (2.4 vs 1.9) so Au atoms attracts electron charges of SR in Pb(111) to cause more distribution of its wave function at the interface. Intriguingly, this begs the question "Does such SR wavefunction distribution enhance the Rashba effect that requires the breaking of inversion-symmetry through the interface?" Fig. 4a . The Rashba constants α of the SS of Au(111) and the QWS of Pb(111) thin films were measured to be 0.33 25,26 and 0.044 eVÅ 8 , respectively. Therefore the absorbed Au 3 × 3 layer on Pb(111) not only promotes the original SR state but also significantly enhance Rashba effect of it. According to the chargedistribution percentage of S 1 , S 2 , and S 3 over the top four layers, as described above, S 1 has more charge than S 2 at the top Au layer and the second Pb layer, hence triggering Rashba effect more effectively via considering the first Pb layer as the interface.
One remaining ambiguity for the Rashba effect is the role of Au that is also a heavy element like Pb (Z Au = 79, Z Pb = 82). Figure 5a . Cu and Ag are lighter elements (Z Cu = 29, Z Ag = 47). As indicated by green rectangles, one can spot the corresponding S 1 , S 2 and S 3 bands with energies lower than the counterparts of Au/Pb(111)-3 × 3 by ~ 0.3 eV. The S 1 band is specially magnified to examine the Rashba splitting. Unlike Au/Pb(111)-3 × 3, the S 1 bands for Cu/Pb(111)-3 × 3 and Ag/Pb(111)-3 × 3 turn to disperse downward with splitting being small for the former and negligible for the latter. It appears that the high Z value of Au is important for the observed large Rashba splitting of the S 1 band in Au/Pb(111)-3 × 3. Nevertheless, it is intriguing that the S 1 band in Cu/Pb(111)-3 × 3 exhibits a bit more Rashba effect than Ag/Pb(111)-3 × 3 while Cu atom have a much lower Z value than Ag. Figure 6 shows the calculated charge distribution of S 1 state at M 1 3×3 (M Pb(111) ) in the Au, Cu, Ag and six Pb layers below, for the three cases. The charge distribution for Cu/ Pb(111)-3 × 3 is clearly different, in that the charge percentages at the top Au layer and the first Pb layer are even and hence may assist Rashba effect at the interface. Above all, the actual factors involved in Rashba effect at the interface can be more. For example, pervious investigation of of Au, Cu, and Ag monolayers on W(110) 27,28 showed the SS of Au monolayer on W(110) had the least Rashba splitting. SOC contribution in opposite directions from Au and W, and the degree of overlayer-substrate hybridization were considered.

Conclusion
We deposited Au atoms onto Pb(111) surface at 40 K to form a Au/Pb(111)-3 × 3 superstructure. ARPES measurement reveals three distinct SS energy bands (S 1 , S 2 , and S 3 ) disperse within and around the rhomboidal bulk energy band gap centered at the surface zone boundary M 1 3×3 (M Pb(111) ). The calculated SS bands based on Au/ Pb(111)-3 × 3 on a 6-layer Pb slab match the measured bands well. These three SS bands are composed of mainly Pb p orbitals and a few Au s and d orbitals. S 1 and S 3 states of Au/Pb(111)-3 × 3 originate from SRs at the TBBE and BBBE of Pb(111). As revealed from S 1 , the Rashba effect is greatly enhanced (α = 1.0 and 3.54 eVÅ) with respect to that of Au(111) surface and the Pb(111) thin film. Calculation of Rashba splitting for corresponding S 1 bands in Cu/Pb(111)-3 × 3 and Ag/Pb(111) indicates the important role of Au atoms. Our results show an interesting idea that an irrelevant SR state in a substrate can be promoted by a suitable superstructure or a 2D material on the top, which can further help induce its novel property.

Experimental procedures and calculation methods
The Pb(111) single crystal substrate was cleaned by repeated cycles of sputtering with a 1.0 keV Ar + ion for an hour followed by annealing at 473 K for 30 min and the surface quality was confirmed by the observations of sharp spots in LEED. During the Au deposition for the formation of Au/Pb(111)-3 × 3 and the subsequent measurements, the temperature of Pb(111) was kept at 40 K using liquid He. When the temperature increases above 40 K, the PbAu alloy starts forming. A water-cooled Knudsen cell was operated at 1523 ± 10 K to deposit Au with a rate of 0.25 Å/min as calibrated from a quartz-crystal thickness monitor. ARPES measurements on Au/Pb(111)-3 × 3 were carried out with a Scienta R4000 energy analyzer using a p-polarized light source at 22 eV at the undulator beamline BL21B1 at the National Synchrotron Radiation Research Center (NSRRC) in Taiwan

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.