Elemental Topological Dirac Semimetal: $\alpha$-Sn on InSb(111)

Three-dimensional (3D) topological Dirac semimetals (TDSs) are rare but important as a versatile platform for exploring exotic electronic properties and topological phase transitions. A quintessential feature of TDSs is 3D Dirac fermions associated with bulk electronic states near the Fermi level. Using angle-resolved photoemission spectroscopy, we have observed such bulk Dirac cones in epitaxially grown $\alpha$-Sn films on InSb(111), the first such TDS system realized in an elemental form. First-principles calculations confirm that epitaxial strain is key to the formation of the TDS phase. A phase diagram is established that connects the 3D TDS phase through a singular point of a zero-gap semimetal phase to a topological insulator phase. The nature of the Dirac cone crosses over from 3D to 2D as the film thickness is reduced.

Figure 1

Crystal structure, RHEED pattern, and strain analysis of $\alpha$-Sn films on InSb(111). (a) Top and side views of the crystal structures of $\alpha$-Sn films. The red dashed rectangle in the side view shows the BL unit of $\alpha$-Sn. (b) Bulk Brillouin zone and (111)-projected surface Brillouin zone of $\alpha$-Sn. (c) A RHEED pattern of a 30-BL $\alpha$-Sn film. The orange (green) arrows mark main (fractional) streaks. (d) RHEED intensity as a function of growth time. The blue arrows mark when each BL is formed. (e) A core-level photoemission spectrum for a 30-BL $\alpha$-Sn film shows the characteristic Sn $4d$ doublet. (f) Strain analysis of a 30-BL $\alpha$-Sn film based on ${\sin }^2\psi$ technique. $d_{hkl}^{\prime }$ ($d_{hkl}^0$) is the interplanar spacing for the ($hkl$) plane of the measured $\alpha$-Sn film (unstrained $\alpha$-Sn). $\psi$ is the angle of each ($hkl$) plane with respect to the film surface plane.

Figure 2

Calculated electronic structure of $\alpha$-Sn and its dependence on strain. (a) Bulk band structure of $\alpha$-Sn without strain. (b) Bulk band structure of $\alpha$-Sn with the same strain $({ϵ}_{\parallel }=-0.14\%)$ as that observed experimentally. (c) Close-up view of (b) along the $\mathrm{\Gamma }A$ direction ($k_z$ direction). The wave number of the band crossing point is $k_D=0.017(2\pi /c)$. (d) Bulk band structure of strained $\alpha$-Sn along the $k_x$ and $k_y$ directions near the bulk Dirac point. [(e) and (f)] Same as (b), but with in-plane strain ${ϵ}_{\parallel }$ different in signs and magnitude as indicated. (g) Schematic illustration of the 3D TDS electronic structure of strained $\alpha$-Sn. BDP1 and BDP2 mark the positions of two bulk Dirac points. (h) Phase diagram and band gap of $\alpha$-Sn as a function of in-plane strain ${ϵ}_{\parallel }$. The band gap is defined as $E_c-E_v$, where $E_c(E_v)$ is the band edge of the conduction (valence) band.

Figure 3

Electronic structure of a 6-BL $\alpha$-Sn film. (a) Experimental Fermi surface. (b) Experimental band dispersion along $\overline{\mathrm{K}}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{K}}$. (c) Calculated ARPES spectral function of a semi-infinite $\alpha$-Sn slab in the same scale as that in (b). [(d) and (e)] Band dispersion before and after in situ electron doping using a potassium metal dispenser, respectively. (f) Close-up view of band dispersion in $e$ around the zone center near the Fermi level. (g) Calculated bulk bands projected onto (111) for comparison with (f). (h) Stacking plots of constant-energy contours at different binding energies to show a Dirac cone. (i) Second-derivative plot of experimental data shown in (f). (j) Momentum distribution curves obtained from experimental data in (f) (black curves) and peak fitting results (blue curves); these curves are essentially indistinguishable. Red triangles mark the peak positions for each blue curve. (k) Peak positions from fitting results show a Dirac cone.

Figure 4

Evolution of band dispersion of $\alpha$-Sn films with film thickness and incident photon energy. (a) ARPES maps from 6-, 10-, and 30-BL $\alpha$-Sn films under selected incident photon energies. (b) Calculated band dispersions of bulk $\alpha$-Sn along the $k_x$ axis at various out-of-plane wave vector $k_z$. (c) Evolution of the energy positon of the valence band top with incident photon energy for 6-, 10-, and 30-BL $\alpha$-Sn films. (d) Band dispersions of a 30-BL $\alpha$-Sn film along the out-of-plane direction ($k_z$) from experiment.