Tailoring the topological surface state in ultrathin $\alpha$-Sn(111) films

We report on the electronic structure of $\alpha$-Sn films in the very low thickness regime grown on InSb(111)A. High-resolution low photon energy angle-resolved photoemission spectroscopy allows for the direct observation of the linearly dispersing two-dimensional (2D) topological surface state (TSS) that exists between the second valence band and the conduction band. The Dirac point of this TSS was found to be 200 meV below the Fermi level in 10-nm-thick films, which enables the observation of the hybridization gap opening at the Dirac point of the TSS for thinner films. The crossover to a quasi-2D electronic structure is accompanied by a full gap opening at the Brillouin-zone center, in agreement with our density functional theory calculations. We further identify the thickness regime of $\alpha$-Sn films where the hybridization gap in the TSS coexists with the topologically nontrivial electronic structure and one can expect the presence of a one-dimensional helical edge state.

Figure 1

(a) LEED taken at $E=45\mathrm{eV}$ on a clean InSb(111)A substrate exhibits $2\times 2$ surface reconstruction [orange circles denote $1\times 1$ spots]. (b) LEED taken at $E=45\mathrm{eV}$ on 10 nm-thick $\alpha$-Sn(111) film. Apart from the expected $1\times 1$ structure (orange circles), additional spots of high-order surface reconstruction are observed. (c) Spot-profile analysis LEED data taken at $E=87\mathrm{eV}$ and corresponding line profile (data plotted in red, four-peaks fit plotted in blue) through (00) and (10) spots allow us to assign the new surface reconstruction to be $8\times 8$. (d) STM data measured with $U=2\mathrm{V}, I=50\mathrm{pA}$ at $T=4\mathrm{K}$. (e) STM data on a smaller scale showing domains. (f) The height profile along the path labeled “1” in (d) reveals a step height of 3.6 Å.

Figure 2

Experimental electronic structure of a 10-nm-thick $\alpha$-Sn film on InSb(111)A. (a) Band map measured at a photon energy of $h\nu$ = 18 eV and at $T$ = 8 K along the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{K}}$ direction. (b) Photon energy scan between $h\nu$ = 33 and 120 eV (k${}_{\perp }\approx$ 3–5.5 Å${}^{-1}$), taken with the entrance slit oriented along the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{K}}$ direction ($E_{\mathrm{B}}$ = 100 meV). The spectra have been normalized to have equal intensity for each k${}_{\perp }$. (c–e) Stacks of experimental constant energy contours at different $E_{\mathrm{B}}$. Red dotted lines are guides for the eye indicating the TSS.

Figure 3

ARPES band maps as a function of $\alpha$-Sn film thickness. The photon energy was 18 eV and the temperature was 8 K. EDCs at normal emission are overlayed on the left of each panel. (a) 10-, (b) 3-, and (c) 1-nm-thick $\alpha$-Sn films. (d) Clean InSb(111)A substrate.

Figure 4

ARPES data measured on a 1-nm-thick $\alpha$-Sn film at different photon energies $h\nu$ of 18 eV (left), 39 eV (center), and 98 eV (right). EDCs at normal emission are overlayed in each panel.

Figure 5

DFT calculations of a 7.1-nm-thick (a), (c), (e) and 0.7-nm-thick (b), (d), (f) $\alpha$-Sn film on InSb(111)A. (a)–(d) The blue and red colors denote the spin polarization, while the size of the circles is a measure of the surface density of states of the $\alpha$-Sn film. (e) The size of the circles is proportional to the $\alpha$-Sn density of states in the middle of the $\alpha$-Sn film, i.e., bulk states. (f) Same as (d), however here the color indicates the respective contributions from the Sn and InSb states.