A topologically non-trivial band structure and reports of superconductivity have motivated significant investigation into the transport properties of the antiperovskite oxide Sr3SnO. Phase-pure films of Sr3SnO can be grown by molecular beam epitaxy, but they do not have the required extremely high hole-doping densities (>1 × 1021 cm−3) for which superconductivity has been observed in bulk materials. To date, high hole-doping densities have been achieved via inducing strontium deficiency, which inevitably results in impurity phases. Here, we show that indium acts as an effective hole dopant in Sr3SnO and can be used to achieve high hole doping densities in stoichiometric films. Films with carrier densities as high as 1.5 × 1021 cm−3 remain non-superconducting. We, therefore, suggest that Sr3SnO is probably not an intrinsic superconductor. A second question addressed in this work is the measurement of the intrinsic electrical transport properties of Sr3SnO, given its rapid degradation in air. We show that even in inert atmospheres, reducing the time needed for establishing electrical contacts and protecting the Sr3SnO film result in improved electrical properties. We demonstrate low carrier density films (4 × 1018 cm−3) with carrier mobilities of 400 cm2 V−1 s−1 at 10 K.

Antiperovskite oxides, where the positions of the A2+ and O2− ions are exchanged relative to their positions in the perovskite structure, are described by the chemical formula A3BO (A = alkaline earth ion and B = Pb or Sn) and feature a B4− ion that is in an unusual −4 valence state.1,21. A. Widera and H. Schafer, “ Transitional forms between Zintl phases and real salts—Compounds A3BO (A = Ca, Sr, Ba and B-Sn, Pb),” Mater. Res. Bull. 15, 1805–1809 (1980). https://doi.org/10.1016/0025-5408(80)90200-72. J. Nuss, C. Muhle, K. Hayama, V. Abdolazimi, and H. Takagi, “ Tilting structures in inverse perovskites, M3TtO (M = Ca, Sr, Ba, Eu; Tt = Si, Ge, Sn, Pb),” Acta Crystallogr., Sect. B 71, 300–312 (2015). https://doi.org/10.1107/S2052520615006150 Many A3BO compounds are topologically non-trivial and can host band inversions, Dirac nodes, non-trivial Chern numbers, and unique topological surface states.3–113. T. Kariyado and M. Ogata, “ Three-dimensional Dirac electrons at the Fermi energy in cubic inverse perovskites: Ca3PbO and its family,” J. Phys. Soc. Jpn. 80, 083704 (2011). https://doi.org/10.1143/JPSJ.80.0837044. T. H. Hsieh, J. W. Liu, and L. Fu, “ Topological crystalline insulators and Dirac octets in antiperovskites,” Phys. Rev. B 90, 081112 (2014). https://doi.org/10.1103/PhysRevB.90.0811125. Y. Obata, R. Yukawa, K. Horiba, H. Kumigashira, Y. Toda, S. Matsuishi, and H. Hosono, “ ARPES studies of the inverse perovskite Ca3PbO: Experimental confirmation of a candidate 3D Dirac fermion system,” Phys. Rev. B 96, 155109 (2017). https://doi.org/10.1103/PhysRevB.96.1551096. A. Ikeda, T. Fukumoto, M. Oudah, J. N. Hausmann, S. Yonezawa, S. Kobayashi, M. Sato, C. Tassel, F. Takeiri, H. Takatsu, H. Kageyama, and Y. Maeno, “ Theoretical band structure of the superconducting antiperovskite Sr3−xSnO,” Physica B 536, 752–756 (2018). https://doi.org/10.1016/j.physb.2017.10.0897. T. Kawakami, T. Okamura, S. Kobayashi, and M. Sato, “ Topological crystalline materials of J = 3/2 electrons: Antiperovskites, Dirac points, and high winding topological superconductivity,” Phys. Rev. X 8, 041026 (2018). https://doi.org/10.1103/PhysRevX.8.0410268. Y. Fang and J. Cano, “ Higher-order topological insulators in antiperovskites,” Phys. Rev. B 101, 245110 (2020). https://doi.org/10.1103/PhysRevB.101.2451109. T. Kariyado and M. Ogata, “ Low-energy effective Hamiltonian and the surface states of Ca3PbO,” J. Phys. Soc. Jpn. 81, 064701 (2012). https://doi.org/10.1143/JPSJ.81.06470110. C. K. Chiu, Y. H. Chan, X. Li, Y. Nohara, and A. P. Schnyder, “ Type-II Dirac surface states in topological crystalline insulators,” Phys. Rev. B 95, 035151 (2017). https://doi.org/10.1103/PhysRevB.95.03515111. R. Arras, J. Gosteau, D. Huang, H. Nakamura, H. J. Zhao, C. Paillard, and L. Bellaiche, “ Spin-polarized electronic states and atomic reconstructions at antiperovskite Sr3SnO(001) polar surfaces,” Phys. Rev. B 104, 045411 (2021). https://doi.org/10.1103/PhysRevB.104.045411 For example, Sr3SnO is a three-dimensional topological crystalline insulator with cubic symmetry that features six Dirac nodes along the six equivalent Γ–X directions, which are gapped by spin–orbit coupling.44. T. H. Hsieh, J. W. Liu, and L. Fu, “ Topological crystalline insulators and Dirac octets in antiperovskites,” Phys. Rev. B 90, 081112 (2014). https://doi.org/10.1103/PhysRevB.90.081112 Highly Sr-deficient Sr3−xSnO has been reported to be superconducting,1212. M. Oudah, A. Ikeda, J. N. Hausmann, S. Yonezawa, T. Fukumoto, S. Kobayashi, M. Sato, and Y. Maeno, “ Superconductivity in the antiperovskite Dirac-metal oxide Sr3−xSnO,” Nat. Commun. 7, 13617 (2016). https://doi.org/10.1038/ncomms13617 leading to suggestions that it may be an intrinsic topological superconducting candidate.77. T. Kawakami, T. Okamura, S. Kobayashi, and M. Sato, “ Topological crystalline materials of J = 3/2 electrons: Antiperovskites, Dirac points, and high winding topological superconductivity,” Phys. Rev. X 8, 041026 (2018). https://doi.org/10.1103/PhysRevX.8.041026 To date, superconductivity has only been observed in polycrystalline Sr3−xSnO samples, which also contain secondary phases,12–1412. M. Oudah, A. Ikeda, J. N. Hausmann, S. Yonezawa, T. Fukumoto, S. Kobayashi, M. Sato, and Y. Maeno, “ Superconductivity in the antiperovskite Dirac-metal oxide Sr3−xSnO,” Nat. Commun. 7, 13617 (2016). https://doi.org/10.1038/ncomms1361713. M. Oudah, J. N. Hausmann, S. Kitao, A. Ikeda, S. Yonezawa, M. Seto, and Y. Maeno, “ Evolution of Superconductivity with Sr-deficiency in antiperovskite oxide Sr3−xSnO,” Sci. Rep. 9, 1831 (2019). https://doi.org/10.1038/s41598-018-38403-814. J. N. Hausmann, M. Oudah, A. Ikeda, S. Yonezawa, and Y. Maeno, “ Controlled synthesis of the antiperovskite oxide superconductor Sr3−xSnO,” Supercond. Sci. Technol. 31, 055012 (2018). https://doi.org/10.1088/1361-6668/aab6c2 some of which may also be superconducting.Phase-pure, epitaxial Sr3SnO thin films have been grown by molecular beam epitaxy (MBE)1515. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.0068187 and, thus far, superconductivity has not been observed.15–1715. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.006818716. Y. J. Ma, A. Edgeton, H. Paik, B. D. Faeth, C. T. Parzyck, B. Pamuk, S. L. Shang, Z. K. Liu, K. M. Shen, D. G. Schlom, and C. B. Eom, “ Realization of epitaxial thin films of the topological crystalline insulator Sr3SnO,” Adv. Mater. 32, 2000809 (2020). https://doi.org/10.1002/adma.20200080917. H. Nakamura, D. Huang, J. Merz, E. Khalaf, P. Ostrovsky, A. Yaresko, D. Samal, and H. Takagi, “ Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO,” Nat. Commun. 11, 1161 (2020). https://doi.org/10.1038/s41467-020-14900-1 One possible reason for the absence of superconductivity is that the doping densities in the films were too low for superconductivity, which requires hole densities >1 × 1021 cm−3. Hole doping can be achieved by making the films ever more Sr-deficient, but, as shown in Ref. 1515. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.0068187, this inevitably results in the formation of impurity phases. To clarify whether hole-doped Sr3SnO is an intrinsic superconductor, it would, thus, be desirable to use a chemical dopant, rather than relying on non-stoichiometry. A second, related issue is the extreme air-sensitivity of Sr3SnO, which makes even simple ex situ processing steps, such as the application of electrical contacts, challenging, especially for thin films. If the films degrade, the measured transport properties may not reflect the intrinsic properties of Sr3SnO at any carrier density.

This Letter addresses both of these issues. We show that indium (In) can be used as a hole dopant by substituting Sn on the B-site of Sr3SnO, allowing for hole densities of up to 1.5 × 1021 cm−3. Even at these high doping levels, however, the films remain non-superconducting, pointing to impurity phases as the origin of the superconductivity reported in polycrystalline bulk samples. We also discuss a method to reduce the time needed for establishing electrical contacts inside a N2 glovebox and show that the reduced film degradation improves the measured electrical transport properties.

Sr3SnO films were grown by oxide MBE (GEN 930, Vecco Instruments) on (001) LaAlO3 substrates. High purity Sr (4N, Sigma Aldrich) and SnO2 (4N, Kurt J. Lesker) were co-evaporated from separate effusion cells. For details of the growth method and the characterization methods used to establish phase-pure Sr3SnO films, see Ref. 1515. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.0068187. The shaded area in Fig. 1, which shows the films’ properties as a function of Sr/SnOx beam equivalent pressure (BEP) ratio used during growth, indicates the growth window for 600 (±40 nm) thick, stoichiometric films. Previously, we made electrical contacts in van der Pauw geometry by soldering In-contacts inside a N2 glove bag into which the sample was transferred directly from the MBE exit chamber.1515. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.0068187 Here, instead, we used pre-soldered sample carriers (see supplementary material) that can be attached to the physical property measurement system (PPMS) sample puck. Contacts to the films’ corners were made mechanically by tightening the attachment onto the sample, with indium placed under the soldering holes. This greatly shortened the time for the contact formation compared to individually soldering the contacts. To protect the film, Apiezon-N grease diluted with a few drops of toluene was applied, which has a sufficiently low viscosity to allow for the grease to cover the entire sample, including the sides. Electrical measurements (longitudinal and Hall resistances) as a function of temperature and magnetic field were carried out using a PPMS (Quantum Design) system. Two-dimensional carrier densities and sign were determined from the Hall effect. All films showed metallic behavior with onset of localization at low temperatures and p-type conductivity, similar to Sr3SnO films reported in the literature.15,16,1815. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.006818716. Y. J. Ma, A. Edgeton, H. Paik, B. D. Faeth, C. T. Parzyck, B. Pamuk, S. L. Shang, Z. K. Liu, K. M. Shen, D. G. Schlom, and C. B. Eom, “ Realization of epitaxial thin films of the topological crystalline insulator Sr3SnO,” Adv. Mater. 32, 2000809 (2020). https://doi.org/10.1002/adma.20200080918. D. Huang, H. Nakamura, and H. Takagi, “ Planar Hall effect with sixfold oscillations in a Dirac antiperovskite,” Phys. Rev. Res. 3, 013268 (2021). https://doi.org/10.1103/PhysRevResearch.3.013268 The p-type conductivity indicates that the Fermi level is below the Dirac node even in nominally undoped films, which is likely caused by Sr-vacancies as an intrinsic defect.For indium doping, high purity In (7N, United Mineral Corp) was co-supplied from an effusion cell during the film growth. Indium was chosen because it is a group V element. Replacing some of the Sn4− on the B-site with In5− may then result in hole-doping of the films. Although it is known that In can adopt a −5 valence state,19,2019. J.-T. Zhao and J. D. Corbett, “ Square pyramidal clusters in La3In5 and Y3In5. La3In5 as a metallic Zintl phase,” Inorg. Chem. 34, 378–383 (1995). https://doi.org/10.1021/ic00105a05720. A. M. Guloy and J. D. Corbett, “ Synthesis, structure, and bonding of two lanthanum indium germanides with novel structures and properties,” Inorg. Chem. 35, 2616–2622 (1996). https://doi.org/10.1021/ic951378e its suitability as a p-type dopant in Sr3SnO is hardly a forgone conclusion. The ability of an impurity atom to act as a dopant depends on many factors, including the position of the dopant’s energy level within the manifold of bands of the host material. All In-doped films had thicknesses of 400 nm.Figure 1 shows that carrier mobility of films grown within the growth window is significantly improved when the degradation of the films is minimized by reducing the time required to make the contacts, i.e., with the mechanical contacting method. The highest Hall carrier mobility at 10 K is 400 cm2 V−1 s−1, which is achieved within the growth window and is the highest mobility reported to date for Sr3SnO and a related material, Sr3PbO.12–18,2112. M. Oudah, A. Ikeda, J. N. Hausmann, S. Yonezawa, T. Fukumoto, S. Kobayashi, M. Sato, and Y. Maeno, “ Superconductivity in the antiperovskite Dirac-metal oxide Sr3−xSnO,” Nat. Commun. 7, 13617 (2016). https://doi.org/10.1038/ncomms1361713. M. Oudah, J. N. Hausmann, S. Kitao, A. Ikeda, S. Yonezawa, M. Seto, and Y. Maeno, “ Evolution of Superconductivity with Sr-deficiency in antiperovskite oxide Sr3−xSnO,” Sci. Rep. 9, 1831 (2019). https://doi.org/10.1038/s41598-018-38403-814. J. N. Hausmann, M. Oudah, A. Ikeda, S. Yonezawa, and Y. Maeno, “ Controlled synthesis of the antiperovskite oxide superconductor Sr3−xSnO,” Supercond. Sci. Technol. 31, 055012 (2018). https://doi.org/10.1088/1361-6668/aab6c215. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.006818716. Y. J. Ma, A. Edgeton, H. Paik, B. D. Faeth, C. T. Parzyck, B. Pamuk, S. L. Shang, Z. K. Liu, K. M. Shen, D. G. Schlom, and C. B. Eom, “ Realization of epitaxial thin films of the topological crystalline insulator Sr3SnO,” Adv. Mater. 32, 2000809 (2020). https://doi.org/10.1002/adma.20200080917. H. Nakamura, D. Huang, J. Merz, E. Khalaf, P. Ostrovsky, A. Yaresko, D. Samal, and H. Takagi, “ Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO,” Nat. Commun. 11, 1161 (2020). https://doi.org/10.1038/s41467-020-14900-118. D. Huang, H. Nakamura, and H. Takagi, “ Planar Hall effect with sixfold oscillations in a Dirac antiperovskite,” Phys. Rev. Res. 3, 013268 (2021). https://doi.org/10.1103/PhysRevResearch.3.01326821. A. Ikeda, Z. Guguchia, M. Oudah, S. Koibuchi, S. Yonezawa, D. Das, T. Shiroka, H. Luetkens, and Y. Maeno, “ Penetration depth and gap structure in the antiperovskite oxide superconductor Sr3−xSnO revealed by μ SR,” Phys. Rev. B 101, 174503 (2020). https://doi.org/10.1103/PhysRevB.101.174503 This mobility is achieved at a carrier density of 4 × 1018 cm−3, which is the lowest density reported so far for Sr3SnO in any study. Both mobility and carrier density are very sensitive to the Sr/SnOx BEP ratio even within the growth window, indicating the formation of point defects at the edges of the relatively narrow window. This is also confirmed by x-ray diffraction rocking curves, which are narrowest for the highest mobility film (see the supplementary material). Together, these results show that revealing the intrinsic transport properties of Sr3SnO films requires both careful optimization of the growth conditions and minimizing the very rapid degradation of the films once they are removed from the MBE system. With regard to the latter, we briefly mention here that we have also used various capping layers (see also Ref. 1515. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.0068187). These proved successful for allowing structural characterization of areas in the middle of a sample; we believe, however, that they did not prevent degradation proceeding from the exposed sides.To achieve higher carrier densities while maintaining phase-purity, a method to chemically dope the films is required. We, therefore, next turn to the indium-doping experiments. Figure 2(a) shows the carrier density as a function of the indium effusion cell temperature during the growth. All films were p-type, implying a formal −5 valence state of In substituting for Sn. The carrier density increases exponentially with the increase in the In cell temperature, i.e., it linearly increases with In vapor pressure or In beam flux supplied. This implies that all In that is evaporated is incorporated in the films and that all dopants are activated, at least within the carrier density range studied here. Thus, fine control of doping using the In cell temperature can be achieved. Figure 2(b) presents the carrier mobility at 10 K as a function of the carrier density. The decrease in the low temperature mobility, which is dominated by defect scattering, with increasing carrier density reflects the ionized impurity scattering from the acceptor dopant (In), similar to what is found in semiconductors. Thus, at these carrier densities, the ionized dopant atoms, rather than other types of defects, are the main source of carrier scattering. The highest carrier density in the In-doped films in this study is 1.5 × 1021 cm−3. This is on the same order of the magnitude as the polycrystalline samples that were reported to be superconducting.12–14,2112. M. Oudah, A. Ikeda, J. N. Hausmann, S. Yonezawa, T. Fukumoto, S. Kobayashi, M. Sato, and Y. Maeno, “ Superconductivity in the antiperovskite Dirac-metal oxide Sr3−xSnO,” Nat. Commun. 7, 13617 (2016). https://doi.org/10.1038/ncomms1361713. M. Oudah, J. N. Hausmann, S. Kitao, A. Ikeda, S. Yonezawa, M. Seto, and Y. Maeno, “ Evolution of Superconductivity with Sr-deficiency in antiperovskite oxide Sr3−xSnO,” Sci. Rep. 9, 1831 (2019). https://doi.org/10.1038/s41598-018-38403-814. J. N. Hausmann, M. Oudah, A. Ikeda, S. Yonezawa, and Y. Maeno, “ Controlled synthesis of the antiperovskite oxide superconductor Sr3−xSnO,” Supercond. Sci. Technol. 31, 055012 (2018). https://doi.org/10.1088/1361-6668/aab6c221. A. Ikeda, Z. Guguchia, M. Oudah, S. Koibuchi, S. Yonezawa, D. Das, T. Shiroka, H. Luetkens, and Y. Maeno, “ Penetration depth and gap structure in the antiperovskite oxide superconductor Sr3−xSnO revealed by μ SR,” Phys. Rev. B 101, 174503 (2020). https://doi.org/10.1103/PhysRevB.101.174503 No superconductivity was found in the films studied here.Figure 3 shows the temperature dependence of the sheet resistance of four Sr3SnO films grown with the same Sr/SnOx BEP ratio (8.2) and different carrier densities (In doping concentrations). With the increase in the carrier density, the localization at low temperature is less pronounced and the temperature dependence at intermediate temperatures becomes weaker (for a quantitative analysis of the power laws describing the temperature dependence in the range of 80–200 K, see the supplementary material). The decrease in the localization correction to the resistance for films having a lower resistance (higher carrier densities) is expected.2222. G. Bergmann, “ Weak localization in thin-films: A time-of-flight experiment with conduction electrons,” Phys. Rep. 107, 1–58 (1984). https://doi.org/10.1016/0370-1573(84)90103-0 Notably, though, the temperature dependence of the resistance changes across this series and in the film with the highest carrier density, it is almost linear. One possible explanation is that at high hole densities, the semimetal Sr3SnO behaves like a Bloch–Grüneisen metal, whose temperature dependence is linear at temperatures greater than the Debye temperature (θD), when the number of phonons scales linearly with the increase in the temperature.2323. J. M. Ziman, Electrons and Phonons: The Theory of Transport Phenomena in Solids ( Oxford University Press, Oxford, 2001). The calculated value of θD for Sr3SnO is 276 K,2424. E. Haque and M. A. Hossain, “ First-principles study of mechanical, thermodynamic, transport and superconducting properties of Sr3SnO,” J. Alloys Compd. 730, 279–283 (2018). https://doi.org/10.1016/j.jallcom.2017.09.299 which is above the temperature range where the linearity is observed. It is possible that θD is substantially reduced in Sr3SnO thin films. Alternatively, more exotic explanations have been proposed in other correlated oxides that exhibit linear-in-temperature resistances, such as van Hove singularities and quantum critical points.

To summarize, we have shown that phase-pure Sr3SnO thin films exhibit mobilities up to 400 cm2 V−1 s−1 at carrier densities as low as 4 × 1018 cm−3. Even at these low carrier densities, the films exhibit only p-type (not mixed) conductivity, suggesting that the Fermi level is not yet in the small gap between the (massive) Dirac nodes. Higher hole densities (up to 1.5 × 1021 cm−3) while maintaining phase purity can successfully be achieved by using indium as a dopant. At these carrier densities, a linear-in-temperature resistivity is observed over a wide temperature range, reminiscent of more exotic materials, but no superconductivity. We speculate that the superconductivity observed in polycrystalline materials at similar carrier densities is probably not intrinsic. To further clarify this question, it would be interesting to use indium doping also in bulk samples.

See the supplementary material for photos and a schematic of the mechanical contacting method, x-ray diffraction rocking curves of stoichiometric films grown with different BEP ratios, sheet and Hall resistance data, and plots of the temperature-derivative of the resistances of the In-doped films as a function of temperature.

The authors thank Robert Kealhofer for discussions. This work was supported by the U.S. Department of Energy (Award No. DE-SC0020305). N.G.C. acknowledges the support through the UCSB Quantum Foundry, which is supported by the National Science Foundation (Award No. DMR-1906325). This work made use of the MRL Shared Experimental Facilities, which are supported by the MRSEC Program of the U.S. National Science Foundation under Award No. DMR 1720256.

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Wangzhou Wu: Conceptualization (equal); Data curation (equal); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Visualization (lead); Writing – original draft (lead). Nicholas G Combs: Investigation (supporting); Methodology (supporting); Validation (supporting); Writing – review & editing (supporting). Susanne Stemmer: Conceptualization (equal); Funding acquisition (lead); Investigation (supporting); Project administration (lead); Resources (lead); Supervision (lead); Validation (supporting); Visualization (supporting); Writing – review & editing (lead).

The data that support the findings of this study are available within the article and its supplementary material.

REFERENCES

1. A. Widera and H. Schafer, “ Transitional forms between Zintl phases and real salts—Compounds A3BO (A = Ca, Sr, Ba and B-Sn, Pb),” Mater. Res. Bull. 15, 1805–1809 (1980). https://doi.org/10.1016/0025-5408(80)90200-7, Google ScholarCrossref2. J. Nuss, C. Muhle, K. Hayama, V. Abdolazimi, and H. Takagi, “ Tilting structures in inverse perovskites, M3TtO (M = Ca, Sr, Ba, Eu; Tt = Si, Ge, Sn, Pb),” Acta Crystallogr., Sect. B 71, 300–312 (2015). https://doi.org/10.1107/S2052520615006150, Google ScholarCrossref3. T. Kariyado and M. Ogata, “ Three-dimensional Dirac electrons at the Fermi energy in cubic inverse perovskites: Ca3PbO and its family,” J. Phys. Soc. Jpn. 80, 083704 (2011). https://doi.org/10.1143/JPSJ.80.083704, Google ScholarCrossref4. T. H. Hsieh, J. W. Liu, and L. Fu, “ Topological crystalline insulators and Dirac octets in antiperovskites,” Phys. Rev. B 90, 081112 (2014). https://doi.org/10.1103/PhysRevB.90.081112, Google ScholarCrossref5. Y. Obata, R. Yukawa, K. Horiba, H. Kumigashira, Y. Toda, S. Matsuishi, and H. Hosono, “ ARPES studies of the inverse perovskite Ca3PbO: Experimental confirmation of a candidate 3D Dirac fermion system,” Phys. Rev. B 96, 155109 (2017). https://doi.org/10.1103/PhysRevB.96.155109, Google ScholarCrossref6. A. Ikeda, T. Fukumoto, M. Oudah, J. N. Hausmann, S. Yonezawa, S. Kobayashi, M. Sato, C. Tassel, F. Takeiri, H. Takatsu, H. Kageyama, and Y. Maeno, “ Theoretical band structure of the superconducting antiperovskite Sr3−xSnO,” Physica B 536, 752–756 (2018). https://doi.org/10.1016/j.physb.2017.10.089, Google ScholarCrossref7. T. Kawakami, T. Okamura, S. Kobayashi, and M. Sato, “ Topological crystalline materials of J = 3/2 electrons: Antiperovskites, Dirac points, and high winding topological superconductivity,” Phys. Rev. X 8, 041026 (2018). https://doi.org/10.1103/PhysRevX.8.041026, Google ScholarCrossref8. Y. Fang and J. Cano, “ Higher-order topological insulators in antiperovskites,” Phys. Rev. B 101, 245110 (2020). https://doi.org/10.1103/PhysRevB.101.245110, Google ScholarCrossref9. T. Kariyado and M. Ogata, “ Low-energy effective Hamiltonian and the surface states of Ca3PbO,” J. Phys. Soc. Jpn. 81, 064701 (2012). https://doi.org/10.1143/JPSJ.81.064701, Google ScholarCrossref10. C. K. Chiu, Y. H. Chan, X. Li, Y. Nohara, and A. P. Schnyder, “ Type-II Dirac surface states in topological crystalline insulators,” Phys. Rev. B 95, 035151 (2017). https://doi.org/10.1103/PhysRevB.95.035151, Google ScholarCrossref11. R. Arras, J. Gosteau, D. Huang, H. Nakamura, H. J. Zhao, C. Paillard, and L. Bellaiche, “ Spin-polarized electronic states and atomic reconstructions at antiperovskite Sr3SnO(001) polar surfaces,” Phys. Rev. B 104, 045411 (2021). https://doi.org/10.1103/PhysRevB.104.045411, Google ScholarCrossref12. M. Oudah, A. Ikeda, J. N. Hausmann, S. Yonezawa, T. Fukumoto, S. Kobayashi, M. Sato, and Y. Maeno, “ Superconductivity in the antiperovskite Dirac-metal oxide Sr3−xSnO,” Nat. Commun. 7, 13617 (2016). https://doi.org/10.1038/ncomms13617, Google ScholarCrossref13. M. Oudah, J. N. Hausmann, S. Kitao, A. Ikeda, S. Yonezawa, M. Seto, and Y. Maeno, “ Evolution of Superconductivity with Sr-deficiency in antiperovskite oxide Sr3−xSnO,” Sci. Rep. 9, 1831 (2019). https://doi.org/10.1038/s41598-018-38403-8, Google ScholarCrossref14. J. N. Hausmann, M. Oudah, A. Ikeda, S. Yonezawa, and Y. Maeno, “ Controlled synthesis of the antiperovskite oxide superconductor Sr3−xSnO,” Supercond. Sci. Technol. 31, 055012 (2018). https://doi.org/10.1088/1361-6668/aab6c2, Google ScholarCrossref15. W. Wu, N. G. Combs, and S. Stemmer, “ Molecular beam epitaxy of phase-pure antiperovskite Sr3SnO thin films,” Appl. Phys. Lett. 119, 161903 (2021). https://doi.org/10.1063/5.0068187, Google ScholarScitation, ISI16. Y. J. Ma, A. Edgeton, H. Paik, B. D. Faeth, C. T. Parzyck, B. Pamuk, S. L. Shang, Z. K. Liu, K. M. Shen, D. G. Schlom, and C. B. Eom, “ Realization of epitaxial thin films of the topological crystalline insulator Sr3SnO,” Adv. Mater. 32, 2000809 (2020). https://doi.org/10.1002/adma.202000809, Google ScholarCrossref17. H. Nakamura, D. Huang, J. Merz, E. Khalaf, P. Ostrovsky, A. Yaresko, D. Samal, and H. Takagi, “ Robust weak antilocalization due to spin-orbital entanglement in Dirac material Sr3SnO,” Nat. Commun. 11, 1161 (2020). https://doi.org/10.1038/s41467-020-14900-1, Google ScholarCrossref18. D. Huang, H. Nakamura, and H. Takagi, “ Planar Hall effect with sixfold oscillations in a Dirac antiperovskite,” Phys. Rev. Res. 3, 013268 (2021). https://doi.org/10.1103/PhysRevResearch.3.013268, Google ScholarCrossref19. J.-T. Zhao and J. D. Corbett, “ Square pyramidal clusters in La3In5 and Y3In5. La3In5 as a metallic Zintl phase,” Inorg. Chem. 34, 378–383 (1995). https://doi.org/10.1021/ic00105a057, Google ScholarCrossref20. A. M. Guloy and J. D. Corbett, “ Synthesis, structure, and bonding of two lanthanum indium germanides with novel structures and properties,” Inorg. Chem. 35, 2616–2622 (1996). https://doi.org/10.1021/ic951378e, Google ScholarCrossref21. A. Ikeda, Z. Guguchia, M. Oudah, S. Koibuchi, S. Yonezawa, D. Das, T. Shiroka, H. Luetkens, and Y. Maeno, “ Penetration depth and gap structure in the antiperovskite oxide superconductor Sr3−xSnO revealed by μ SR,” Phys. Rev. B 101, 174503 (2020). https://doi.org/10.1103/PhysRevB.101.174503, Google ScholarCrossref22. G. Bergmann, “ Weak localization in thin-films: A time-of-flight experiment with conduction electrons,” Phys. Rep. 107, 1–58 (1984). https://doi.org/10.1016/0370-1573(84)90103-0, Google ScholarCrossref,