PHYSICAL REVIEW B 99, 155408 (2019) Substrate-mediated umklapp scattering at the incommensurate interface of a monatomic alloy layer Santosh Chiniwar, 1 Angus Huang, 1 Ting-Yu Chen, 1 Chung-Huang Lin, 1 Cheng-Rong Hsing, 2 Wei-Chuan Chen, 1 Cheng-Maw Cheng, 3 H.-T. Jeng, 1, 4 , * C. M. Wei, 2 Woei Wu Pai, 5, 6, † and S.-J. Tang 1, 3, 4 , ‡ 1 Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan 2 Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan 3 National Synchrotron Radiation Research Center (NSRRC), Hsinchu 30076, Taiwan 4 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan 5 Center for Condensed Matter Sciences, National Taiwan University, Taipei 106, Taiwan 6 Department of Physics, National Taiwan University, Taipei 106, Taiwan (Received 26 October 2018; revised manuscript received 18 February 2019; published 8 April 2019) Ultrathin Pb and Ge films deposited on Ag(111) surfaces have been investigated and compared. We found that at 1/3 ML, both films formed surface alloys, Ag 2 Pb and Ag 2 Ge, with √ 3 × √ 3R30 ◦ and 19 20 √ 3 × 19 20 √ 3R30 ◦ structures on Ag(111) but the surface electronic structures exhibit a most evident difference at the Ag(111) surface zone boundary ¯ M Ag(111) , where the single band and the splitting ones were observed, respectively. Up to 1 ML, Ag 2 Ge subsequently develops into germanene with a striped phase and then a quasifreestanding phase, as previously reported [Lin et al., Phys. Rev. Mater. 2, 024003 (2018)], while Ag 2 Pb evolves to a dense Pb(111) phase that also reveals splitting bands at ¯ M Ag(111) . We discover that the larger (smaller) atomic size of a Pb (Ge) atom with respect to an Ag atom causes the commensurate (incommensurate) interfaces and further demonstrate that the splitting bands of Ag 2 Ge surface alloy and 1-ML Pb film originated from the commonly incommensurate interface with Ag(111), which mediates umklapp scattering by inducing the mirror image of the pristine Ag 2 Ge and Pb(111) bands relative to ¯ M Ag(111) . DOI: 10.1103/PhysRevB.99.155408 I. INTRODUCTION Two-dimenstional (2D) materials have been a research focus in recent years. 2D-xenes such as silicene [1,2], ger- manene [3,4], stanene [5,6], borophene [7,8], bismuthine [9], and transition metal dichalcogenices monolayers (TMD), such as MoS 2 [10], WS 2 [11], MoSe 2 [12], WSe 2 [13,14], MoTe 2 [15], are considered as 2D topological insulators and 2D semiconductors with major potential for industrial applications. For TMD, the bonding is a mainly weak van der Waals type so the epitaxial layer grows with the lattice constants of their bulk structure in spite of large lattice mis- match at the interface. The condition for epitaxial growth of xenes on substrates is stricter than the commensurate interface suggested to be necessary [16], and the growth configurations are more varied. For example, germanene was found to have dual phases grown on Ag(111), that is, a striped phase (SP) and a quasifreestanding phase (QP) [3]. The former is uniax- ially commensurate with the Ag(111)- √ 3 × √ 3R30 0 lattice (hereafter denoted as Ag3-R30) and exhibits a well-ordered but tensile-strained honeycomb lattice; the latter is incommen- surate with Ag(111) and reveals a twisted or imperfect honey- comb lattice. However, the intrinsic σ band of germanene was only observed in the latter [3]. Therefore, commensurability is not a necessary condition for growing a monoatomic layer on a substrate, and incommensurability can even preserve * jeng@phys.nthu.edu.tw † wpai@ntu.edu.tw ‡ sjtang@phys.nthu.edu.tw better the intrinsic electronic structures, such as σ bands, of a monolayer [3] due to a less effective interaction with the substrate. However, the π bands appear more vulnerable to the interaction with the substrate regardless of the commensurate or incommensurate interface [3,17,18]. The stability of a film was mainly investigated in terms of surface energies with a model of a freestanding slab, while the interfacial effect from the substrate was considered as a secondary factor [19]. However, when the film thickness reduces to one monolayer, the interfacial effect should become more relevant. Tang et al. [20] found that Pb films grown on Ge(111) are dominated by the configuration with 13% lattice mismatch at a thickness less than 2 ML. This was attributed to the stronger electron hybridization at the interface between the Pb film and Ge(111) substrate. In this paper, we focus on surface alloys of Ag 2 Ge [21,22] and Ag 2 Pb [21,23] first, which are actually single alloy lay- ers forming on the bulk Ag(111) surface. From the distinct features of electronic structures between the two surface al- loys, mainly the splitting and nonsplitting surface state bands centered at ¯ M Ag(111) , we correlate this presence or absence of the band splitting to the corresponding incommensurate and commensurate interfaces of these two systems. Upon further deposition of Pb on Ag 2 Pb/Ag(111), a dealloying process occurs; the commensurate Ag 2 Pb/Ag(111) evolves into an in- commensurate 1-ML dense Pb(111) layer on Ag(111) with its Pb band splitting at ¯ M Ag(111) , as well. The substrate-mediated umklapp scattering of the monolayer electrons at the interface is proposed to explain the observed band split and help the layer stability despite incommensurability. 2469-9950/2019/99(15)/155408(7) 155408-1 ©2019 American Physical Society