Topological surface state of $\alpha -\mathrm{Sn}$ on InSb(001) as studied by photoemission

We report on the electronic structure of the elemental topological semimetal $\alpha -\mathrm{Sn}$ on InSb(001). High-resolution angle-resolved photoemission data allow us to observe the topological surface state (TSS) that is degenerate with the bulk band structure and show that the former is unaffected by different surface reconstructions. An unintentional $p$-type doping of the as-grown films was compensated by deposition of potassium or tellurium after the growth, thereby shifting the Dirac point of the surface state below the Fermi level. We show that, while having the potential to break time-reversal symmetry, iron impurities with a coverage of up to 0.25 monolayers do not have any further impact on the surface state beyond that of K or Te. Furthermore, we have measured the spin-momentum locking of electrons from the TSS by means of spin-resolved photoemission. Our results show that the spin vector lies fully in-plane, but it also has a finite radial component. Finally, we analyze the decay of photoholes introduced in the photoemission process, and by this gain insight into the many-body interactions in the system. Surprisingly, we extract quasiparticle lifetimes comparable to other topological materials where the TSS is located within a bulk band gap. We argue that the main decay of photoholes is caused by intraband scattering, while scattering into bulk states is suppressed due to different orbital symmetries of bulk and surface states.

Figure 1

(a) Illustration of the surface-truncated diamond crystal structure (top) and the reconstructed surface (bottom). Smaller size of atoms denotes atoms situated farther from the (110) plane along the $\left[1\overline{1}0\right]$ direction. (b) Evolution of the LEED pattern from a $c\left(8\times 2\right)$ surface reconstruction for in situ prepared InSb (top), to a nearly $\left(1\times 1\right)$ for the Te buffer on InSb (center), to a $\left(2\times 1\right)$ double-domain pattern for Sn grown on top of the buffer layer (bottom). (c) Angle-dependent XPS (Al $\mathrm{K}\alpha )$ data.

Figure 2

(a) Sketch of the bulk band structure of $\alpha -\mathrm{Sn}$ on InSb(001) along the in-plane $\mathrm{\Gamma }$-K direction and the $\mathrm{\Gamma }$-Z direction perpendicular to the (001) surface. (b) Bulk and surface Brillouin zone of strained $\alpha -\mathrm{Sn}$ with symmetry points labeled.

Figure 3

Experimental electronic structure data. (a) Band maps of an as-grown $\alpha -\mathrm{Sn}$ film measured with $h\nu =18$ eV at $T=8$ K along the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{X}}$ direction (left) and $\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ direction (right). (b) Photon energy scan between $h\nu =18$ eV and $h\nu =32$ eV taken along the the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ direction at normal emission at $E_{\mathrm{F}}$ (left) and $E_{\mathrm{B}}=250$ meV (right). Spectra have been normalized to have equal intensity for each $k_{\mathrm{z}}$. The features that show up between $k_{\mathrm{z}}=2.5{\AA }^{-1}$ and $k_{\mathrm{z}}=2.7{\AA }^{-1}$ correspond to core levels that appear due to higher order excitations and can thus be ignored. (c) Stack of experimental CECs with black dotted lines following the TSS dispersion. (d) MDCs extracted at $E_{\mathrm{F}}$ for the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{X}}$ and $\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ directions. (e), (f) Experimental CECs for different binding energies overlaid with sketches that show the overlap of circular TSS (red) and elliptic bulk bands (white), as well as surface state SS (green).

Figure 4

Study of K and Te adatom deposition. (a) ARPES band maps for the pristine sample (left), an intermediate K coverage (center; 3 min K deposition), and the final K coverage (right; 15 min K deposition) along the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{X}}$ direction with $h\nu =18$ eV at 8 K. (b) ARPES band maps for the pristine sample (left), an intermediate Te coverage (center), and high Te coverage (right) along the $\overline{\mathrm{\Gamma }}-\overline{\mathrm{M}}$ direction at room temperature. Plots have been normalized to equal MDC intensity. (c) While the as-grown sample shows a $\left(2\times 1\right)$ double-domain diffraction pattern in LEED (left), we observe a $\left(1\times 1\right)$ pattern at the end of K deposition study (right). (d) By comparing the CECs at the same energy relative to $E_{\mathrm{D}}$ for the pristine and highly Te-doped sample, we find no obvious difference (left-hand panel). The right-hand panel compares MDCs for the two orthogonal directions $k_x$ and $k_y$ for pristine $(E_{\mathrm{B}}=200$ meV; black) and highly Te-doped $(E_{\mathrm{B}}=250$ meV; red) samples.

Figure 5

Study of Fe deposition. Pristine sample (left) and after deposition of $\sim 0.25$ ML Fe (right).

Figure 6

Spin-resolved MDCs for varying azimuthal angles $\alpha$. (a) Spin-integrated ARPES map of an $\alpha -\mathrm{Sn}$ sample. The yellow dashed line shows the $E_{\mathrm{B}}$ of spin-resolved MDCs in panels (b)–(d). (b)–(d) All three components $(S_x,S_y,S_z)$ of the spin vector measured for three azimuthal rotations $\alpha =0^{\circ },{23}^{\circ }$, and ${45}^{\circ }$, respectively. The circles represent CECs of TSS, while the red (blue) color corresponds to a positive (negative) sign of the $S_x$ component of the spin vector.

Figure 7

Analysis of the circular dichroism in $\alpha -\mathrm{Sn}$ at $h\nu =18$ eV. Panels (a) and (b) show the intensity distribution measured with circular right- and left-polarized light, respectively. Panel (c) shows the normalized difference between (a) and (b). (d) Direct comparison of MDCs extracted at 30 meV binding energy from (a) (red curve) and (b) (blue curve).

Figure 8

Analysis of MDCs of an $\alpha -\mathrm{Sn}$ sample. The straight white line is a linear fit to the peak positions (gray diamonds) of the TSS. The bottom-left inset shows an MDC at $E_{\mathrm{B}}=0.31$ eV fitted with 2 pairs of background peaks (green) and 1 pair of TSS peaks (red). The bottom-right inset shows a comparison of the linear fit to the experimental peak position (black line) with our $GW$ calculations. The size of the symbol is a measure of the surface localization, while the color represents the spin polarization (adapted from Ref. [2]). The imaginary part of the electron self-energy $\left(\mathrm{Im}\mathrm{\Sigma }\right)$ (white circles), extracted from the data, is shown in the top panel.