Structural and electronic properties of the pure and stable elemental 3D topological Dirac semimetal α-Sn

α-Sn is a low-temperature phase of tin, which in the bulk state becomes stable below 13.2 °C. In contrast to its much more commonly known metallic allotrope β-Sn, bulk α-Sn is a semi-metal (zero bandgap) with a pronounced covalent character. This material has attracted the researchers’ attention since it has been theoretically predicted that α-Sn is the only elemental strong 3D topological insulator (TI) if subjected to uniaxial strain, which would open a bulk bandgap.¹ Strain in α-Sn has been, to a certain extent, achieved in α-Sn films epitaxially grown on a substrate with appropriate lattice mismatch (InSb, CdTe).^2–4 Although the 2D electron gas behavior of the surface states of α-Sn films was detected more than 30 years ago,⁵ the topological character was confirmed only recently in Te and/or Bi doped thin films by angle-resolved photoemission spectroscopy (ARPES) measurements, depicting the surface electronic properties below the Fermi level.^6–10 ARPES revealed a topological Dirac cone in the electronic band structure of doped α-Sn, locating the Dirac point near the Fermi level. Interestingly, the most recent studies emphasized that the type of strain in the case of α-Sn is important: in-plane compressive strain turns it into a topological Dirac semimetal (TDS), while in-plane tensile strain transforms α-Sn into a TI.^8–13 Very recently, the signature of the topological charge carriers has also been demonstrated in electronic magneto-transport experiments through the analysis of Shubnikov–de Haas oscillations.¹⁴ These interesting findings make α-Sn films useful for spintronics and put this TDS in the group of materials, which could become a building unit (qubit) of future quantum computers.

The growth of α-Sn thin films is associated with difficulties since this allotrope of Sn is not stable in bulk at room temperature. To stabilize it by inducing the epitaxial growth of α-Sn, a suitable substrate with a matching lattice constant is needed (acting as a crystallization seed). InSb(100) provides that matching and, in addition, introduces strain in the grown α-Sn film. However, the use of InSb substrates brings along challenges such as surface degradation (InSb is very volatile to surface oxidation) and thermal instability (InSb decomposes far below its melting point), complicating the preparation of the substrate surface by annealing. These challenges can be, to a certain extent, overcome by employing a procedure that includes combined ion-beam sputtering and thermal annealing in ultra-high vacuum (UHV).^2,15 This procedure can lead to the formation of In islands on the substrate surface, enhancing the already known issue of In interdiffusion during the deposition of Sn on InSb(100) substrates that are only slightly heated.¹⁶ As a consequence, the surface analysis of α-Sn films shows a substantial amount of In.^3,7,10 At this point, there is a gap in knowledge about the scale on which this affects the phase purity and consequentially, indirectly, the topological electronic transport properties of the α-Sn films. Having this in mind, the most favorable scenario is to avoid In and Sb interdiffusion while still achieving a good surface quality and with that maintaining the topological properties of α-Sn.

As α-Sn crystallizes in the diamond structure, the dangling sp³-bonds of the topmost surface atomic layer of the (100) planes are unsaturated and they are pointing diagonally [lying in the (110) plane]. Such a bond orientation leads to the formation of asymmetric dimers on the film surface, similar to the cases of Si(100) and Ge(100).^17–20 In previous works, in order to avoid Sn dimer formation and thus enhance the surface quality of the grown films, elevated substrate temperature and/or doping with substantial amounts of Bi^7,14 and Te^6,10 were employed. The use of Bi and Te results in a disturbed chemical purity of the Sn film surface and a modified surface reconstruction. The influence that these impurities, combined with In interdiffusion, have on the stability and the topological electronic transport properties of α-Sn is, for now, difficult to predict. Particularly intriguing can be the use of Te as a surfactant for the α-Sn film growth since the possible formation of Sn_1−xTe_x would make the surface very susceptible to degradation^21,22 and would result in a slight distortion of the cubic crystal structure.^23,24 If 3D TDSs are to be used as a robust unit for quantum computing related applications (“chiral qubits”),^25,26 growing a pure, continuous, and homogeneous α-Sn film surface is a priority.

Here, we present the possibility of growing high-quality films of the 3D TDS α-Sn in its full elemental form, showing a great stability. A combined study of growth and structural and electronic properties of α-Sn is presented. We demonstrate the existence of strain with conversion electron Mössbauer spectroscopy (CEMS) and take a special closer look at the local surface morphology of the α-Sn films with scanning tunneling microscopy (STM). We report topological surface electronic states in this type of samples using ARPES and also provide a unique insight into the surface electronic properties above the Fermi level using scanning tunneling spectroscopy (STS).

Before the film growth, the high-quality single-crystal undoped (n-type) InSb(100) substrates (Wafer Technology, Ltd.) were cleaned and polished in an UHV environment using a multi-step process (see the supplementary material). This included several cycles of Ar⁺ ion-beam sputtering using two energy modes in order to clean and achieve a gentle polishing of the InSb(100) substrate surface. Every cycle of the ion-beam sputtering is followed by a short multi-step thermal annealing cycle. The preparation process was monitored by Auger electron spectroscopy (AES), low-energy electron diffraction (LEED), and reflection high-energy electron diffraction (RHEED). This multi-step preparation procedure resulted in atomically flat and contamination free InSb(100) surfaces, with maintained stoichiometry and the characteristic c(8 × 2) surface reconstruction (see the supplementary material). This achievement was crucial for the subsequent successful α-Sn film growth.

The α-Sn films were grown using molecular beam epitaxy (MBE) by evaporating Sn from a Knudsen cell onto a InSb(100) substrate held at 5 °C. Some of the samples were also grown on slightly heated substrates (30 °C, 50 °C, and 80 °C) for the sake of comparison (see the supplementary material). Rutherford backscattering spectrometry (RBS) was used on calibration samples in order to precisely determine the Sn deposition rate. In this way, a film thickness accuracy in the range of ±1 nm was achieved. Sn films of 10 nm, 20 nm, and 30 nm thickness were successfully grown while being monitored using RHEED. During the Sn deposition, RHEED oscillations were recorded [Fig. 1(a)] and it was confirmed that the growth rate (10 Å/min) matches the targeted deposition rate.

The chemical purity of the surface in the case of 20 nm and 30 nm thick Sn films grown at a substrate temperature of 5 °C is confirmed by AES [Fig. 1(d)]. The films are uniformly covered with Sn with no traces of other chemical elements, indicating an excellent elemental purity of the Sn film surface. The AES spectra of the thinner films (10 nm) show minor traces of In, while in the cases where the InSb(100) substrate was heated, In and Sb were also detected by AES, regardless of the thickness (see the supplementary material). This implies that a slight increase in the substrate temperature (around room temperature) deteriorates the chemical homogeneity of the surface. The x-ray photoelectron spectroscopy (XPS) spectra of the grown films do show (see the supplementary material) a very small presence of In (<2% and <1% for 20 nm and 30 nm thick Sn films, respectively), originating from the deeper layers of the sample since the AES spectra show no traces of In in these cases. This is only partially in agreement with previous reports about the α-Sn/InSb pseudomorphic growth.^3,16 Indium interdiffusion is indeed enhanced if the temperature of the substrate is elevated. However, contrary to these reports, we were able to observe the “layer by layer” growth [Fig. 1(a)] without raising the temperature of the InSb(100) substrate and maintain the full elemental purity of the Sn film surface. RHEED and LEED images [Figs. 1(b) and 1(c)] exhibit sharp features of the two-domain (2 × 1) surface reconstruction of α-Sn.

The STM topography images (Fig. 2) acquired in situ at room temperature show the same features for all α-Sn samples grown at a substrate temperature of 5 °C. Uniform surfaces with sub-nanometer roughness were observed (RMS₅₀₀ ∼ 0.4 nm—root mean square roughness for a 500 × 500 nm² surface). The terraces of the substrate are covered with evenly spread grains, still leaving the substrate steps visible in the overlay [Fig. 2(a)]. The average lateral size of the grains is 10 − 20 nm. Linking this finding to the electron diffraction data, we confirm a high degree of crystallinity of these grains which, combined with the low film roughness, accounts for the acquired sharp RHEED and LEED patterns.

In contrast to the shown LEED, RHEED, and STM data (for non-heated substrates), the films grown on slightly heated InSb(100) exhibited disturbed epitaxial growth (see the supplementary material).

Figure 3 presents the analysis of the CEMS data of a 20 nm thick α-Sn film. The acquired spectra are almost completely dominated by the α-Sn peak at 2.13(1) mm/s, considering that the CEMS sensitivity for SnO₂ (small peak observed at 0 mm/s) is approximately 10 times larger compared to α-Sn and β-Sn.²⁷ Importantly, the peak from β-Sn is completely absent [appearing at 2.64(1) mm/s for our Sn/SiO₂/Si reference samples (see the supplementary material)]. The Mössbauer isomer shift (δ) is defined in the hyperfine interaction theory²⁷ as a difference between the electron density values near the nucleus of the absorber (sample), ∼|Ψ_A(0)|², and the source of the probing γ-photon, ∼|Ψ_S(0)|², with

The significantly higher δ value for α-Sn in our samples, compared to bulk samples^27–31 and films,^32,33 implies an elevated 5s electron density value^34,35 as this shift cannot be an intrinsic effect of the Sn nucleus but results from a difference in the electron density around it. Since we observed only one crystallographic site of Sn, without any quadruple splitting, and since the crystal structure of the grown α-Sn films remains unchanged compared to bulk α-Sn, the existence of the compressive strain is confirmed.³⁶ This strain indirectly diminishes the screening effect of the 5p electrons toward the 5s electrons by enhancing the covalent nature of the bonding in strained α-Sn.

Unfortunately, by using the CEMS technique alone, it is not possible to estimate the magnitude of strain in this particular case. The energy resolution of Mössbauer spectroscopy is, without doubt, astonishing (in the range of neV), but being a relative technique to estimate the magnitude of strain, a comparative study involving x-ray diffraction spectroscopy (XRD) and/or first-principles calculations is needed. The conclusion drawn from the CEMS data is in accordance with the experimentally determined room temperature bulk lattice parameter values for α-Sn and InSb reported in the literature (a ⩾ 6.489 Å for α-Sn^37–39 and a ⩽ 6.479 Å in the case of InSb^40–43). Moreover, authors who have grown thicker films were able to directly measure this difference in lattice parameters^2,44 again showing that the lattice parameter of the room temperature α-Sn is indeed slightly bigger than in the case of InSb. In order to estimate the magnitude of strain in our samples, we have also performed XRD (θ-2θ) measurements. We have detected no lattice relaxation in the grown α-Sn films (20 nm and 30 nm) and estimated the lattice parameter of the prepared InSb substrate (after sputtering and annealing) to be 6.475 Å. Comparing this value with the value for α-Sn, 6.489 Å, we can conclude that the compressive strain of ∼0.22% corresponds to the detected increase in the IS value of 0.13 mm/s measured by CEMS.

Excellent crystallinity and phase purity of the α-Sn samples in this study are crucial for the success of the further ex-situ measurements (ARPES and STS). The robustness of the samples allowed us to use Ar⁺ sputtering to clean the surface before these measurements. Even if the samples were kept under normal ambient conditions for several weeks, it was still possible to remove contamination by low-energy Ar⁺ sputtering, observing only Sn in the AES spectrum and fully recovering the two-domain (2 × 1) reconstruction of α-Sn, as reflected by LEED and RHEED (see the supplementary material). This implies prominent stability and robustness of the sample surface, which seemingly becomes passivated in air, not leading to further degradation of the grown film. Combined with the previous reports on the enhanced temperature stability of strained α-Sn films (up to 170 °C),^2,45,46 our findings give this material an additional application value. Having the reports on the fragile air-stability of the more widely investigated 3D topological materials, Bi₂Te₃^47–49 and Bi₂Se₃^50,51 (caused by adsorption of molecular species from ambient), this finding could make α-Sn more favorable for applications.

After growth, α-Sn film samples were exposed to ambient conditions and transferred to the ARPES setup of the BaDElPh beamline⁵² at the Elettra synchrotron. Before the measurement, the surface of the films was cleaned by Ar⁺ sputtering (500 eV). The conducted ARPES measurements on 20 nm thick α-Sn, grown at a substrate temperature of 5 °C, depict the topologically protected surface electronic states, forming a Dirac cone at the $Γ¯$ point [Fig. 4(a)] as a consequence of the lack of back-scattering of the topological electronic charge carriers. This proves that topological surface states are indeed an intrinsic property of pure elemental α-Sn¹ and can also be detected in samples grown without the use of any Bi or Te dopants. The intensity of the background overlay around the zero energy value [Fig. 4(a)] shows, as previously reported,^6,10 that the $Γ8+$ bulk energy band crosses the Fermi level (E_F). By fitting the line profiles of the acquired spectrum [Fig. 4(b)], we were able to estimate the position of the Dirac point (E_D) at ∼60 meV above E_F (slight p-type behavior). From the fit of the slopes of the Dirac cone branches, we extracted Fermi velocity values (v_F) of 0.48(1) × 10⁶ m/s (left) and 0.52(1) × 10⁶ m/s (right). These v_F values are close to the theoretically predicted value for thick films of elemental α-Sn (0.58 × 10⁶ m/s)⁵³ but are clearly reduced compared to the previously reported values for Bi/Te doped α-Sn (∼0.7 × 10⁶ m/s).^7,10 This suggests that the effect of shifting E_F upward in the case of Bi/Te doped α-Sn is actually accompanied by a contraction of the $Γ7−$ energy band (which hosts the Dirac cone), spanning, in that case, a smaller k-space in the surface Brillouin zone. To precisely determine if this is a direct effect of doping or rather an indirect effect induced by the change in strain in the grown films, additional and more detailed studies are needed.

As in the case of the ARPES experiments, the same type of samples was, after growth, transferred in nitrogen atmosphere to the low-temperature STM/STS setup (4.5 K). The samples were carefully cleaned by Ar⁺ sputtering, and a stable tunneling current was achieved. The acquired STM topography images [Fig. 4(d)] showed the same features as in the case of our in situ STM measurements performed at room temperature (Fig. 2). The measured differential tunneling conductance dI/dV (area averaged) on top of the α-Sn grains shows a p-type behavior (E_F shifted toward the valence band) of the grown film [Fig. 4(c)], while deviations from this trend are noticed along the edges.

The STS technique, in contrast to ARPES, can also probe the electronic states above the Fermi level. Hence, it was possible to observe the existence of the surface state at the positive bias voltages in the acquired STS characteristics of our α-Sn samples [Fig. 4(c)]. Additionally, comparing the differential tunneling conductance (dI/dV) spectrum with that of the ARPES allows us to extract the topological surface state Dirac point of the α-Sn film. The dI/dV spectrum, which has been averaged over several α-Sn grains, reveals two minima positions at the positive voltages located at ∼70 meV and ∼280 meV. Moreover, the dI/dV spectrum also reveals that the Fermi level lies within the valence band, indicating the p-type behavior of our α-Sn film akin to the ARPES observations. Comparing this to our ARPES data and having the previous ARPES reports on α-Sn/InSb in mind,^{6,7,9,10,14,54} we anticipate the first dI/dV minimum (∼70 meV) to be the Dirac point of the topological Dirac cone of α-Sn/InSb that exists above E_F in our films and the second minimum (∼280 meV) to be the bulk band edge contribution. On the other hand, if we analyze the spectra as in the case of Bi₂Se₃ (a 3D TI with similar electronic properties around E_F),^55,56 we are able to estimate E_D using the global minimum of the STS averaged spectrum [Fig. 4(c)] around 70 meV above E_F, where the bulk valence bands start to dominate. Such an electronic behavior is consistent with our ARPES measurements (the acquired E_D values and the observations of the $Γ8+$ bulk energy band crossing E_F). It is also noteworthy that if single-point STS spectra are taken, the E_D value fluctuates depending on the acquisition position (within the range 50 − 100 meV above E_F). This is, in general, an expected nature of the STS spectra taken near the grain boundaries. Nevertheless, future grain sizes and grain shape dependent studies may clarify this electronic behavior.

Finally, we further comment on the observed p-type electrical behavior in our ARPES and STS data (Fig. 4), which confirm the previous transport measurement reports.^2,14 Three possible causes for this electrical behavior of α-Sn films have been suggested:² thermal decomposition of the boron-nitride in the walls of the Sn-source Knudsen cell, autodoping through interdiffusion of the substrate elements, and a possible localized β-Sn nucleation. At this point, we cannot exclude the boron impurities scenario (small amounts of boron are very difficult to detect by AES and XPS). It is also not possible to fully exclude the influence of In, whose signal was detected by XPS (absent in the AES spectrum). On the other hand, since no presence of the β-Sn nucleation was detected on the surface of our samples grown at a substrate temperature of 5 °C, the third scenario for explaining the origin of the p-type behavior is unlikely.

We successfully grew pure, strained 3D TDS α-Sn films on InSb(100). To achieve this, two crucial steps were required: modifying the substrate preparation procedure and lowering the temperature of the substrate during the film growth. The quality of the samples was examined using multiple complementary techniques, including STM, providing new insights into the α-Sn surface morphology. For the first time, we report experimental evidence for the presence of compressive strain in α-Sn films by Mössbauer spectroscopy. We observed an excellent robustness of the film surface against ambient conditions, which could be crucial for possible future applications. We verified the existence of the topological electronic states in α-Sn using ARPES, and we characterized its electronic properties both below and above the Fermi level, using the STS technique.

The MBE growth of the samples was performed by evaporating Sn (deposition/growth rate ≈10 Å/min) from a Knudsen cell (1170 °C) in UHV (<5 × 10⁻¹⁰ mbar).

AES was conducted using an 8 kV electron beam, while XPS was realized with the use of the Mg Kα x rays (E = 1.254 keV).

RHEED and LEED images were recorded using an electron beam energy of 10 keV and 48 eV, respectively. The screen voltage used for LEED measurements was 1 keV.

In situ room temperature STM was performed using an Omicron Nanotechnology LS-STM setup (base pressure of 10⁻¹⁰ mbar).

The CEMS experiments were carried out at room temperature in a low-pressure acetone gas atmosphere using a parallel plate detector and a ^119mSn/CaSnO₃ source. The spectra were analyzed relative to SnO₂ using the “VindaD” package.⁵⁷ 

XRD measurements were performed using an X’Pert “PANalytical” x-ray diffractometer with Cu K_α1 radiation.

The ARPES experiments (21 eV, 77 K) were performed at the BaDElPh beamline⁵² at the Elettra synchrotron radiation facility in Trieste (Italy).

Ex-situ STM and STS were performed using an Omicron Nanotechnology LT setup operated at 4.5 K (base pressure of 10⁻¹¹ mbar). All of the STS dI/dV spectra were acquired using a sample bias voltage U = 0.5 V and a tunneling current I = 300 pA. The spectrum was averaged over 5 nm × 5 nm areas on top of the α-Sn grains and averaged over 6 grains.

See the supplementary material for the detailed information about the following: the InSb(100) substrate preparation process, XPS, LEED, RHEED, and STM investigations of the α-Sn films grown on slightly heated InSb(100) substrates, the CEMS data of β-Sn grown on the SiO₂/Si substrate, and the Ar⁺ cleaning procedure for the α-Sn films grown at a substrate temperature of 5 °C.

The authors thank B. Opperdoes, L. Sancin, and V. Joly for technical support. This work was supported by the Research Foundation – Flanders (FWO) and by the KU Leuven C1 program (Grants Nos. C14/18/074 and C12/18/006). G. L. acknowledges the support from the FWO (File No. 27531 and 52751). M. N. N. acknowledges funding from Horizon 2020-MSCA-IF-GA No. 796940. The authors would like to thank Elettra Sincrotrone Trieste for providing access to its synchrotron radiation facilities.