Structural and electronic properties of Tl films on Ag(111): From $(\sqrt{3}\times \sqrt{3})$ surface alloy to moiré superstructure

We present a detailed study of the growth behavior and the electronic properties of thin Tl films epitaxially grown on Ag(111). We combine experimental results obtained by Auger electron spectroscopy, low-energy electron diffraction, scanning tunneling microscopy, scanning tunneling spectroscopy (STS), and inverse photoemission (IPE). The electronic properties identified by STS and IPE are substantiated via density functional theory (DFT) calculations. For a Tl coverage of 0.33 atomic layers (AL), our experimental results show the formation of small patches with a $(\sqrt{3}\times \sqrt{3})$ reconstruction. With STS and IPE, we observe two dominant empty-state electronic features at $E-E_{\text{F}}\approx 1.6$ and 3.5 eV, which are attributed to downward dispersing $s,p_z$-derived states and to states with $p_z$ orbital symmetry, respectively. On the basis of band structure and charge distribution calculations, we discuss the variation of the binding energies of the respective electronic features observed by STS and IPE. Above 0.5 AL, a moiré superstructure evolves due to the rather large lattice mismatch between the Tl adlayer and Ag(111) which exhibits a sharp spectroscopic feature at around $E-E_{\text{F}}\approx 3.1$ eV in STS and IPE. The comparison with DFT calculations suggests that it originates from a predominantly $p_z$-like surface state. For even larger film thicknesses up to 4 AL, we find a rotation of the Tl layer with respect to the Ag(111) substrate of $\alpha =\pm {(2.50\pm 0.20)}^{\circ }$.

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Figure 1

Auger electron spectroscopy (AES) data of Tl/Ag(111) for Tl coverages of up to 4 AL. During Tl growth the substrate was held at a temperature $T_{\text{sample}}=478\text{K}$. The AES measurements were performed at room temperature at a primary electron beam energy $E_{\text{p}}=3\mathrm{k}\mathrm{e}\mathrm{V}$.

Figure 2

Thickness-dependent LEED study for Tl/Ag(111): (a) clean Ag(111) substrate and (b)–(i) Tl film thicknesses between 0.33 and 4.0 AL. Colored hexagons indicate the hexagonal reciprocal lattice of Ag(111) (blue), the $(\sqrt{3}\times \sqrt{3})$ surface alloy (orange), the moiré superstructure (green), and the rotated reciprocal lattice of a thick Tl(111) film (brown). The LEED data were acquired at room temperature at a primary electron energy $E_{\text{kin}}^{\text{LEED}}=60\mathrm{eV}$. During Tl growth the temperature of the Ag(111) substrate was $T_{\text{sample}}=478\mathrm{K}$.

Figure 3

STM data of a Tl film on Ag(111) with a coverage slightly above $0.33\text{AL}$. (a) STM topography overview showing overgrown step edges as well as islands with diameters between several tens of nanometers up to about 200 nm. (b) Height profile measured along the red line in panel (a). (c) Zoom-in from panel (a) showing the phase boundary between the moiré and the $(\sqrt{3}\times \sqrt{3})$ structure. (d) 2D-FFT from panel (c): cyan, moiré; orange, $(\sqrt{3}\times \sqrt{3})$; red, Tl. Scan parameters: (a) $U_{\text{bias}}=1.0\text{V}, I_{\text{set}}=100\text{pA}$ and (c) $U_{\text{bias}}=10\text{mV}, I_{\text{set}}=25\text{nA}$.

Figure 4

(a) STM topographic overview of a 4-AL-thick Tl film grown on Ag(111) at a substrate temperature $T_{\text{sample}}=478\text{K}$. (b) The height profile measured along the red line in panel (a) reveals that several step edges exhibit a height which is equivalent to several atomic layers of Ag(111), with $h_{\text{Ag(111)}}=(233\pm 4)\text{pm}$, with two exceptions marked $h_1=224\text{pm}$ and $h_2=240\text{pm}$. (c) High spatial resolution STM data of the same film showing two coexisting patterns with periodicities of $a_{\text{Tl}}=(348\pm 17)\text{pm}$ and $a_{\text{moiré}}=(1.67\pm 0.17)\text{nm}$, corresponding to the atomic lattice of the Tl surface and the moiré superstructure, respectively. (d) 2D-FFT of the data presented in panel (c). Bragg peaks originating from the Tl atomic lattice are marked by white circles. The spots of the moiré pattern are marked with green circles. (e) Structural model of a Tl layer (dark gray) on the Ag(111) substrate (bright gray) with a rotational angle of $\alpha =\pm 2.{50}^{\circ }$. Scan parameters: (a), (c) $U_{\text{bias}}=200\text{mV}, I_{\text{set}}=100\text{pA}$.

Figure 5

Coverage-dependent series of STM images of Tl on Ag(111): (a) 0.27 AL, (b) 0.30 AL, and (c) 0.33 AL. The size of $(\sqrt{3}\times \sqrt{3})$-ordered domains increases from panel (a) to panel (c). Scan parameters: $U_{\text{bias}}=10\text{mV}, I_{\text{set}}=100\text{pA}$. (d), (e) $dI/dU$ spectra taken with an active feedback loop at the position marked with a purple star in panel (c). STS parameters: (d) $U_{\text{mod}}=10\text{mV}, I_{\text{set}}=1\text{nA}, \nu =733$ Hz and (e) $U_{\text{mod}}=30\text{mV}, I_{\text{set}}=250\text{pA}, \nu =733$ Hz.

Figure 6

(a) IPE spectra of the $(\sqrt{3}\times \sqrt{3})$ surface alloy for three angles of electron incidence $\theta$ along $\overline{\mathrm{\Gamma }\text{K}}$. For normal electron incidence, a spectral feature appears at $1.7\mathrm{e}\mathrm{V}$ which disperses downward in energy with increasing $\theta$. (b) IPE spectra for a larger energy and angle range. At around $3\mathrm{e}\mathrm{V}$, a prominent feature is visible highlighted by the blue line. The red line in panel (b) represents the $0^{\circ }$ spectrum of panel (a) overlayed on the $-0.5^{\circ }$ spectrum.

Figure 7

Band structure of the $(\sqrt{3}\times \sqrt{3})$ surface alloy along $\overline{\mathrm{\Gamma }\text{M}}$ and $\overline{\mathrm{\Gamma }\text{K}}$. The surface-projected bulk band structure is indicated by the light blue shaded area. (a) Red (blue) dots indicate the Rashba component of the spin expectation value for spin-up (spin-down) electrons of surface states. (b) Calculations including matrix elements with free-electron-like initial states to model IPE results with $\hslash \omega =9.9\mathrm{e}\mathrm{V}$. The dot size is a measure of the expected spectral intensity.

Figure 8

Charge-distribution plots of surface states at $\overline{\mathrm{\Gamma }}$ for the $(\sqrt{3}\times \sqrt{3})$ surface alloy. The green (black) circles indicate the positions of the Tl (Ag) atoms in the drawing plane. The charge density is given in units of $a_B^{-1/3}$. The states $m_j=3/2$ and ${\tilde{p}}_z$ are energetically resonant with silver bulk states.

Figure 9

(a) Atomic resolution STM topography data of the moiré superstructure. (b), (c) $dI/dU$ spectra taken at the position marked with a red star in panel (a). Scan parameters: (a) $U_{\text{bias}}=10\text{mV}, I_{\text{set}}=25\text{nA}$. STS parameters: (b) $U_{\text{mod}}=10\text{mV}, I_{\text{set}}=1\text{nA}, \nu =733$ Hz, feedback loop active and (c) $U_{\text{mod}}=5\text{mV}, \nu =733$ Hz, feedback loop off.

Figure 10

(a) Spin-integrated IPE spectra for various angles of incidence showing two parabolic dispersing features. The parabolic dispersion is sketched via a guide to the eye (purple and orange lines). (b) Spin-resolved spectra for three exemplary angles.

Figure 11

Charge-distribution plot of the surface state at $\overline{\mathrm{\Gamma }}$ for the moiré superstructure. The green (black) circles indicate the positions of the Tl (Ag) atoms in the drawing plane. The drawing plane is rotated by ${90}^{\circ }$ with respect to the drawing plane used in Fig. 8. The charge density is given in units of $a_B^{-1/3}$.