BIBECHANA Vol. 20, No. 3, December 2023, 309-315 ISSN 2091-0762 (Print), 2382-5340 (Online) Journal homepage: http://nepjol.info/index.php/BIBECHANA Publisher: Dept. of Phys., Mahendra Morang A. M. Campus (Tribhuvan University) Biratnagar Exploring topological phase transition in Pt2Hg1−xTlxSe3 Deergh Bahadur Shahi, Dipak Bhattarai, Madhav Prasad Ghimire∗ 1Central Department of Physics, Tribhuvan University, Kirtipur, 44613,Kathmandu, Nepal ∗Corresponding author. Email: madhav.ghimire@cdp.tu.edu.np Abstract The transition from trivial to non-trivial phase in two-dimensional materials are called a topological phase transition (TPT). The Berry phase, non-local string order parameter, and edge states define the topological nature of the system. A newly discovered jacutingaite ma- terial Pt2HgSe3 is a layered material which occurs naturally in the form of minerals. The material can be exfoliated and was predicted as a quantum spin Hall insulator. Here, on the basis of density functional theory and tight-binding calculations, we explore Pt2Hg1−xTlxSe3 (x = 0.25, 0.50, 0.75, 1) to understand the electronic and topological properties. We start with the parent material Pt2HgSe3 wherein Hg is replaced partially with x amount of Tl, to tune the topological phases. From the electronic structure calculations, Pt2HgSe3 is found to be a non-trivial semimetal in it’s bulk. Upon electron doping, the material transforms to strong topological metallic phase. The topological Z2 invariant calculation shows TPT in Pt2Hg1−xTlxSe3 with weak topological insulating state (0;001) for x=0, to strong topological metal (1;000) for x=1, respectively. Keywords Density functional theory, Jacutingaite materials, Spin-orbit coupling, Topological invariants, Topo- logical phase transition. Article information Manuscript received: September 16, 2023; Accepted: November 1, 2023 DOI https://doi.org/10.3126/bibechana.v20i3.58632 This work is licensed under the Creative Commons CC BY-NC License. https://creativecommons. org/licenses/by-nc/4.0/ 1 Introduction Topological concept in material science has a crucial role in condensed matter and materials sci- ence. Topological notion not only enhances the understanding of various physical phenomena, but also play an important role in the development and innovation in materials science [1]. The study of topological properties is thriving research area due to its promising applications in electronics and quantum computing. Topology and topological in- variants plays a significant role in understanding and classification of new states of matter in mate- rial science. By using the concepts of mirror Chern number, chern number and topological invariant (Z2) we can explain the properties and different be- haviors exhibited by various quantum Hall systems, topological insulators (TIs), topological semimetals 309 http://nepjol.info/index.php/BIBECHANA madhav.ghimire@cdp.tu.edu.np https://doi.org/10.3126/bibechana.v20i3.58632 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ Deergh Bahadur Shahi et al./ BIBECHANA 20 (2023) 309-315 310 such as Dirac, Weyl and nodal line. The surface or edge effects in topological materi- als are found to change in several properties such as in electronic, optical, transport, magnetic, etc. [2,3] and can be detected using transmission electron mi- croscopy. Two-dimensional (2D) quantum spin Hall insulator (QSHI) are characterized by a gapless heli- cal edge states with small electronic band gap in it’s bulk. Though they resists interaction and disorder extending up to room temperature, the study re- lated to QSHI are limited [4,5]. Topological features of the materials can be identified by calculating the Z2 invariant. Z2 consists of four components: ν0; ν1, ν2, ν3 based on which the material can be distin- guished whether they are strong or weak topological materials. For instance, when ν0 = 1; and any of its ν1, ν2, ν3 are either 0 or 1, the material are called strong topological insulator/metal, but, if ν0 = 0 and any other invariants ( ν1, ν2, ν3) are non-zero, they are called weak topological material. Among several group of materials, Pt2HgSe3 is one of the natural mineral of platinum group be- longing to jacutingaite family discovered in 2008 [6] and successfully synthesized in 2012 [7–10]. This material has been cleaved to its monolayer and from the density functional theory (many-body G0W0 calculations, it was reported to be a QSHI with a band gap of ∼0.15 eV (0.5 eV) at the Dirac point [11]. QSHI to quantum anamolous Hall (QAH) phase was also observed in monolayer of Pt2HgSe3 by chemical functionalization [12]. In materials belonging to topological materials, topological phase transition (TPT) can be achieved by chemical functionalization, applying magnetic and electric field, pressure and doping, etc. TPT has been observed in bilayer of jacutingaite when perpendicular electric field was applied wherein the bilayer changes from a normal insulator to QSHI [13]. Likewise, unconventional superconductivity was observed in monolayer of Pt2HgSe3 by electron and hole doping along with other exotic property such as QSHI [14]. Monolayer of Pt2HgSe3 has also been studied recently in which the material losses its symmetric behavior due to presence of ferromag- netic substrate (NiBr2). Charge transfer takes place at the interface resulting in spin degeneracy band gap of ∼134.2 meV and valley dependent global gap of 58.8 meV, respectively [15]. Further, it was no- ticed that lattice defect can shift the Fermi level (EF ) above the van Hove singularity in Pt2HgSe3 , and thus can potentially serve as an effective means to regulate doping effect [16]. Band inversion is one of the key parameter that dictates the nontrivial property and is associated with a bulk topological invariant. Further, calcula- tion of parities in the Brillouin zone (BZ) of occu- pied bands at the time reversal invariant momen- tum (TRIM) are used in determining the topologi- cal invariant of the system following inversion sym- metry [17]. Thus, in inversion symmetric system, a material with strong spin-orbit coupling (SOC) strength is required to flip the maximum of the va- lence band to the minimum of conduction band with opposite parities at the TRIM point. This allows to change the phase from normal insulator (NI) to topological insulator (TI). In topological band in- version, band gap is denoted by a negative sign to distinguish it from a trivial band gap in an even topological invariant scenario. TI to NI phase tran- sition was observed also by nonmagnetic substitu- tion [18–20]. While the overall idea of such a tran- sition seems intuitive, specifics are yet unknown. Therefore we can expect that the band gap of a TI would decrease linearly on substitution of a lighter element with weaker SOC strength. The traditional interpretation of nonmagnetic doping phase transi- tion behavior in TIs has been challenged by the low concentration (x ), say about 5% in (Bi1−xInx)2Se3 system. The low concentration of x in a linear band-closure system, has been carried out by sev- eral experimental groups [20,21]. Essentially, a good dopant should have a shal- low defect level and reach optimal solubility in its host material, however, performance of the device is significantly impacted by a few basic doping con- straints. For instance, it was discovered that n- type and p- type doping in ZnO were challenging [22]. Consequently, bipolar doping issues arise in numerous large band gap semiconductors, wherein dopants of either the n-type or p-type semicon- ductor can be introduced, rather than both [23]. Therefore, materials’ qualities such as carrier den- sity, mechanical strength, and magnetism are found to change through doping or alloying method [24]. Here, by means of electron doping to Hg site in Pt2HgSe3 we report that with increase in doping concentration the material undergoes topological phase transition. 2 Crystal Structure and Computational Details The crystal structure of Pt2HgSe3 is shown in Fig- ure 1 and belongs to space group P-3m1 (space group number 164). The crystal consist of 12 atoms in a unit cell with two structural formula unit (Z = 2). Unit cell of Pt2HgSe3 jacutingaite has two dis- tinct position of platinum denoted as Pt1 and Pt2. Six selenium atoms encircle Pt1, while the Pt2 are connected to Hg atoms positioned at the middle of a planar square of selenium atoms (see Fig. 1). The lattice parameters of Pt2HgSe3 used for our calculations are a = 7.3477 Å and c = 5.2955 Å with lattice angles α = 900 , β = 900 and γ = 1200. The corresponding atomic positions are [0, 0, 0] for Pt1, [-1/2, 0, 0] for Pt2, [1/3, -1/3, 0.3507] for Hg and Deergh Bahadur Shahi et al./ BIBECHANA 20 (2023) 309-315 311 [-0.1804, 0.1804, 0.2492] for Se, respectively. We perform the density functional theory (DFT) calculations both in the scalar and full- relativistic mode using the full-potential local or- bital code (FPLO) version 22.00-62 [25]. Dop- ing effects has been considered in Pt2Hg1−xTlxSe3 (x = 0.25, 0.50,0.75 and 1) by means of virtual crystal approximation (VCA) method implemented in the FPLO code. The standard generalized- gradient approximation (GGA) in the parametriza- tion of Perdew, Burke, and Ernzerhof (PBE) [26] has been used for the exchange-correlation poten- tial. A 16×16×16 k-mesh grid was used in the irre- ducible BZ for the self-consistent calculations. The energy and charge convergence criteria are set to 10−8 Hartree and 10−6 C, respectively. Figure 1: Crystal structure of jacutingaite Pt2HgSe3 having hexagonal crystal system. 3 Results and Discussion Electronic Structure: Here we show the results for the parent material Pt2HgSe3 and the end ma- terial Pt2TlSe3. From the total and partial density of states (DOS) shown in Figure 2a for Pt2HgSe3, it can be observed that the major contribution are from Se-4p orbitals hybridizing with the inequiva- lent Pt-5d, and Hg-6s orbitals extending in the va- lence region from -1 eV upto the conduction region, with a crossover at EF . Band structure for the par- ent material Pt2HgSe3 is shown in Fig. 2b within scalar and full-relativistic (with SOC) mode. With- out SOC, the two Dirac crossing were observed at K and H close to EF . With the application of SOC, Dirac points at high symmetry points are gapped with a band gap of ∼30.3 meV at point H as shown in Fig. 2b (inset) followed by band inversion reveal- ing the topological semimetallic behavior. Moving on to the electronic structure of the end material Pt2TlSe3 which results from an electron doping via VCA, the total and partial DOS in the valence and conduction region are found to change abruptly. As seen in Fig. 2c, total DOS at EF is found to in- crease significantly giving rise to metallic state. The main reason for accumulation of large DOS at EF is due to the electron occupancy. The total DOS in Pt2TlSe3 is mainly contributed by Se-4p with sub- stantial contribution from Pt-5d and Tl-6s orbitals. The orbital-resolved electronic band structure of Pt2TlSe3 shows that the major contribution at and around EF are from Se- 4px,y,z, Pt-5dyz and Tl-6s states. Furthermore, it is interesting to note that electron and hole pocket increases along the Γ - A - L – H path in the BZ with increase in Tl doping (see Fig. 2 (b,d)). Topological Properties: We extend our study to understand the topological properties in jacutin- gaite materials. As is well-known, four independent topological invariants, (i.e., Z2 =ν0 ; ν1 ν2 ν3) pro- posed by Fu and Kane [27] is given by (−1)ν0 = ∏ ni=0,1 δn1δn2δn3 (1) (−1)ν0 = ∏ nj ̸=i=0,1;ni=1 δn1δn2δn3 (2) Connecting it with the bulk band structures of Pt2HgSe3 and Pt2TlSe3 (see Fig. 2 (b, d), it reveals that at each k-point the conduction band and the valence band are gapped. This allows us to define Z2 index [28]. Basing on this, we perfrom Z2 invari- ant calculations. Note that, for 3D systems, odd Z2 (ν0 = 1) index signify strong TI, whereas for even Z2 (0 = 0) index with odd indices for the other three (ν1 ν2 ν3) characterizes the signature of weak TIs. Thus Z2 index indicates the distribution of gapless surface states at TRIM in the BZ of 2D surface. Two fold degenerate four occupied bands between energy range -1 to 0.8 eV are used to calculate the Deergh Bahadur Shahi et al./ BIBECHANA 20 (2023) 309-315 312 Z2 invariants by using FPLO code [25]. Our calcu- lation shows that Z2 index is [0;001] for Pt2HgSe3 and [1;000] for Pt2TlSe3. This clearly suggest that the parent material Pt2TlSe3 is a weak TI while the end material Pt2TlSe3 is a strong TI. Z2 in- variants for different values of x concentration in Pt2Hg1−xTlxSe3 are also summarized in Table 1. In a crystal lattice with inversion symmetric sys- tem, Wannier charge center (WCC) are used to cal- culate Z2 index. Yu and co-workers recently pre- dicted the topological transition in Sb2Mg3 by cal- culating the Z2 invariant which was based on U(2N) non-Abelian Berry connection [29,30]. For this, the number of crossing to any horizontal reference line and evolution of WCC in k-space in a random direc- tion are used to calculate the topological invariant. With odd number of crossings to a reference gives rise to Z2 = 1, confirming the topological phase of system. Likewise, an even number of crossing to the reference line will characterize Z2 = 0, indicating a trivial phase of system. Following this we computed the WCC. From our calculations of Z2 for the highest occu- pied molecular orbital, represented by band number 88 for Pt2HgSe3, and band number 82 for Pt2TlSe3, we observed a horizontal reference line (blue line) that intersects the WCC (see Fig. 3). It is interest- ing to note that the intersection are odd numbers (say one crossing for Pt2Hge3 and three crossings for Pt2HgSe3 which confirms that the two jacutin- gaite are topological materials. Figure 2: Density of states (a,c) and band structures (b,d) of Pt2HgSe3 (left) and Pt2TlSe3 (right). Blue and red colors in Fig. b represents scalar-relativistic and full-relativistic for Pt2HgSe3. Table 1: Calculation of Z2 invariants. Z2 invariants of different material Material ν0; ν1ν2ν3 Pt2HgSe3 0;001 Pt2Hg0.25Tl0.75Se3 0;001 Pt2Hg0.5Tl0.5Se3 0;001 Pt2Hg0.75Tl0.25Se3 0;001 Pt2TlSe3 1;000 Deergh Bahadur Shahi et al./ BIBECHANA 20 (2023) 309-315 313 Figure 3: Wannier centers and reference line for band 88 of Pt2HgSe3 (top) and band 82 of Pt2TlSe3 (bottom). 4 Conclusion We studied the electronic and topological proper- ties of Pt2Hg1−xTlxSe3 by means of density func- tional theory and tight-binding calculations using FPLO code [25]. Topological invariants Z2 are com- puted by taking Wannier function as a Bloch func- tion. Pt2HgSe3 is found to be a weak topological semimetal while Pt2TlSe3 is predicted as a strong topological metal. This is confirmed by the odd number of intersection from the Wannier charge center. Thus a topological phase transitions are noted in Pt2Hg1−xTlxSe3 with weak topological in- sulating state (0;001) for x=0, to strong topological metal (1;000) for x=1, respectively. Acknowledgments This work was supported by a grant from UNESCO-TWAS and the Swedish International Development Cooperation Agency (SIDA) with TWAS Research Grant Award No. 21-377 RG/PHYS/ASG-FR3240319525. The views ex- pressed herein do not necessarily represent those of UNESCO-TWAS, SIDA or its Board of Gover- nors. D.B. thanks Nepal Academy of Science and Technology for the PhD fellowship. We are thank- ful to IFW Dresden, Germany for providing large scale computation facility. Conflict of Interest The authors claims that there is no conflict of in- terest. References [1] S. Gupta and A. Saxena. The role of topol- ogy in materials. Materials, 189, 2018. https: //doi.org/10.1007/978-3-319-76596-9 [2] B. Yan and S.C. Zhang. Topological materials: Reports on Progress in Physics. 75(9):096501, 2012. https://doi:10.1088/0034-4885/75/ 9/096501 [3] L. Nguyen, H.-P. Komsa, E. Khestanova, R. J. Kashtiban, J. J. Peters, S. Lawlor, A. M. Sanchez, J. Sloan, R. V. Gor- bachev, and I. V. Grigorieva. Atomic de- fects and doping of monolayer NbSe2. ACS Nano, 11(3):2894, 2017. https://doi.org/ 10.1021/acsnano.6b08036 [4] J. Wang and S. C. Zhang. Topological states of condensed matter. Nature Mate- rials, 16(11):1062–1067, 2017. https://doi. org/10.1038/nmat5012 [5] F. Reis, G. Li, L. Dudy, M. Bauern- feind, S. Glass, W. Hanke, R. Thomale, J. Schäfer, and R. Claessen. Bismuthene on a sic substrate: A candidate for a high- temperature quantum spin hall material. Sci- https://doi.org/10.1007/978-3-319-76596-9 https://doi.org/10.1007/978-3-319-76596-9 https://doi:10.1088/0034-4885/75/9/096501 https://doi:10.1088/0034-4885/75/9/096501 https://doi.org/10.1021/acsnano.6b08036 https://doi.org/10.1021/acsnano.6b08036 https://doi.org/10.1038/nmat5012 https://doi.org/10.1038/nmat5012 Deergh Bahadur Shahi et al./ BIBECHANA 20 (2023) 309-315 314 ence, 357(6348):287–290, 2017. https://doi. org/10.1126/science.aai8142 [6] A. Cabral, H. Galbiatti, R. Kwitko-Ribeiro, and B. Lehmann. Terra nova. 20(1):32– 37, 2008. https://doi.org/10.1111/j. 1365-3121.2007.00783.x [7] K. Kandrai, P. Vancsó, G. Kukucska, J. Koltai, G. Baranka, Á. Hoffmann, Á. Pekker, K. Ka- marás, Z. E. Horváth, and A. Vymazalová. Sig- nature of large-gap quantum spin hall state in the layered mineral jacutingaite. Nano Letters, 20(7):5207–5213, 2020. https://doi.org/10. 1021/acs.nanolett.0c01499 [8] I. Cucchi, A. Marrazzo, E. Cappelli, S. Riccò, F. Bruno, S. Lisi, M. Hoesch, T. Kim, C. Cacho, and C. Besnard. Bulk and sur- face electronic structure of the dual-topology semimetal Pt2HgSe3. Phys. Rev. Lett., 124(10):106402, 2020. https://doi.org/10. 1103/PhysRevLett.124.106402 [9] A. Vymazalová, F. Laufek, M. Drábek, A. R. Cabral, J. Haloda, T. Sidorinová, B. Lehmann, H. F. Galbiatti, and J. Dra- hokoupil. Jacutingaite, Pt2HgSe3, a new platinum-group mineral species from the cauê iron-ore deposit, itabira district, mi- nas gerais, brazil. The Canadian Mineralo- gist, 50(2):431–440, 2012. https://doi.org/ 10.3749/canmin.50.2.431 [10] R. Longuinhos, A. Vymazalová, A. R. Cabral, S. S. Alexandre, R. W. Nunes, and J. Ribeiro- Soares. Raman spectrum of layered jacutin- gaite (Pt2HgSe3) crystals-experimental and theoretical study. Journal of Raman Spec- troscopy, 51(2):357–365, 2020. https://doi. org/10.1002/jrs.5764 [11] A. Bafekry, M. Obeid, C. V. Nguyen, M. Ghergherehchi, and M. B. Tagani. Graphene hetero-multilayer on layered plat- inum mineral jacutingaite (Pt2HgSe3), van der waals heterostructures with novel optoelectronic and thermoelec- tric performances. Journal of Materials Chemistry A, 8(26):13248–13260, 2020. https://doi.org/10.1039/D0TA02847A [12] F. Luo, X. Hao, Y. Jia, J. Yao, Q. Meng, S. Zhai, J. Wu, W. Dou, and M. Zhou. Functionalization induced quantum spin hall to quantum anomalous hall phase transi- tion in monolayer jacutingaite. Nanoscale, 13(4):2527–2533, 2021. https://doi.org/10. 1039/D0NR06889F [13] L. Rademaker and M. Gibertini. Gate- tunable imbalanced kane-mele model in en- capsulated bilayer jacutingaite. Phys. Rev. M, 5(4):044201, 2021. https://doi.org/10. 1103/PhysRevMaterials.5.044201 [14] X. Wu, M. Fink, W. Hanke, R. Thomale, and D. Di Sante. Unconventional supercon- ductivity in a doped quantum spin hall in- sulator. Physical Review B, 100(4):041117, 2019. https://doi.org/10.1103/PhysRevB. 100.041117 [15] X. Zhu, Y. Chen, Z. Liu, Y. Han, and Z. Qiao. Valley-polarized quantum anomalous hall ef- fect in van der waals heterostructures based on monolayer jacutingaite family materials. Fron- tiers of Physics, 18(2):23302, 2023. https: //doi.org/10.48550/arXiv.2211.14109 [16] K. Kandrai, P. Vancsó, G. Kukucska, J. Koltai, G. Baranka, Á. Hoffmann, and P. Nemes- Incze. Signature of large-gap quantum spin hall state in the layered mineral jacutingaite. Nano Letters, 20(7):5207–5213, 2020. https: //doi.org/10.1021/acs.nanolett.0c01499 [17] L. Fu and C. L. Kane. Topological insula- tors in three dimensions. Phys. Rev. Lett., 98(10):106803, 2007. https://doi.org/10. 1103/PhysRevLett.98.106803 [18] T. Sato, K. Segawa, K. Kosaka, S. Souma, K. Nakayama, K. Eto, T. Minami, Y. Ando, and T. Takahashi. Unexpected mass acquisi- tion of dirac fermions at the quantum phase transition of a topological insulator. Nature Physics, 7(11):840–844, 2011. https://doi. org/10.1038/nphys2058 [19] S.-Y. Xu, Y. Xia, L. Wray, S. Jia, F. Meier, J. Dil, J. Osterwalder, B. Slom- ski, A. Bansil, and H. Lin. Topologi- cal phase transition and texture inversion in a tunable topological insulator. Science, 332(6029):560–564, 2011. https://doi.org/ 10.1126/science.1201607 [20] S. Chadov, J. Kiss, C. Felser, K. Chadova, D. Ködderitzsch, J. Minár, and H. Ebert. Topological phase transition induced by random substitution. arXiv preprint arXiv:1207, page 3463, 2012. https: //doi.org/10.48550/arXiv.1207.346 [21] M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh. Topological-metal to band-insulator transition in (Bi1−xInx)2Se3 thin films. Phys. Rev. Lett., 109(18):186403, 2012. https://doi.org/10. 1103/PhysRevLett.109.186403 https://doi.org/10.1126/science.aai8142 https://doi.org/10.1126/science.aai8142 https://doi.org/10.1111/j.1365-3121.2007.00783.x https://doi.org/10.1111/j.1365-3121.2007.00783.x https://doi.org/10.1021/acs.nanolett.0c01499 https://doi.org/10.1021/acs.nanolett.0c01499 https://doi.org/10.1103/PhysRevLett.124.106402 https://doi.org/10.1103/PhysRevLett.124.106402 https://doi.org/10.3749/canmin.50.2.431 https://doi.org/10.3749/canmin.50.2.431 https://doi.org/10.1002/jrs.5764 https://doi.org/10.1002/jrs.5764 https://doi.org/10.1039/D0TA02847A https://doi.org/10.1039/D0NR06889F https://doi.org/10.1039/D0NR06889F https://doi.org/10.1103/PhysRevMaterials.5.044201 https://doi.org/10.1103/PhysRevMaterials.5.044201 https://doi.org/10.1103/PhysRevB.100.041117 https://doi.org/10.1103/PhysRevB.100.041117 https://doi.org/10.48550/arXiv.2211.14109 https://doi.org/10.48550/arXiv.2211.14109 https://doi.org/10.1021/acs.nanolett.0c01499 https://doi.org/10.1021/acs.nanolett.0c01499 https://doi.org/10.1103/PhysRevLett.98.106803 https://doi.org/10.1103/PhysRevLett.98.106803 https://doi.org/10.1038/nphys2058 https://doi.org/10.1038/nphys2058 https://doi.org/10.1126/science.1201607 https://doi.org/10.1126/science.1201607 https://doi.org/10.48550/arXiv.1207.346 https://doi.org/10.48550/arXiv.1207.346 https://doi.org/10.1103/PhysRevLett.109.186403 https://doi.org/10.1103/PhysRevLett.109.186403 Deergh Bahadur Shahi et al./ BIBECHANA 20 (2023) 309-315 315 [22] C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle. First-principles calcu- lations for point defects in solids. Reviews of Modern Physics, 86(1):253, 2014. https: //doi.org/10.1103/RevModPhys.86.253 [23] S.-H. Wei. Overcoming the doping bottleneck in semiconductors. Computational Materials Science, 30(3-4):337–348, 2004. https://doi. org/10.1016/j.commatsci.2004.02.024 [24] S. Pearton, C. Abernathy, M. Overberg, G. Thaler, D. Norton, N. Theodoropoulou, A. Hebard, Y. Park, F. Ren, and J. Kim. Wide band gap ferromagnetic semiconductors and oxides. Journal of Applied Physics, 93(1):1–13, 2003. https://doi.org/10.1063/1.1517164 [25] K. Koepernik and H. Eschrig. Full- potential nonorthogonal local-orbital minimum-basis band-structure scheme. Phys. Rev. B, 59(3):1743, 1999. https: //doi.org/10.1103/PhysRevB.59.1743 [26] J. P. Perdew, K. Burke, and M. Ernzerhof. Generalized gradient approximation made simple. Phys. Rev. Lett., 77(18):3865, 1996. https://doi.org/10.1103/PhysRevLett. 77.3865 [27] J. I. Facio, S. K. Das, Y. Zhang, K. Koepernik, J. van den Brink, and I. C. Fulga. Dual topology in jacutingaite Pt2HgSe3. Phys. Rev. M, 3(7):074202, 2019. https://doi.org/10. 1103/PhysRevMaterials.3.074202 [28] U. Dey, M. Chakraborty, A. Taraphder, and S. Tewari. Bulk band inversion and surface dirac cones in LaSb and LaBi: Prediction of a new topological heterostructure. Scientific Reports, 8(1):14867, 2018. https://doi.org/ 10.1038/s41598-018-33273-6 [29] R. Yu, X. L. Qi, A. Bernevig, Z. Fang, and X. Dai. Equivalent expression of Z2 topo- logical invariant for band insulators using the non-abelian berry connection. Phys. Rev. B, 84(7):075119, 2011. https://doi.org/10. 1103/PhysRevB.84.075119 [30] Y. Sun, X.-Q. Chen, S. Yunoki, D. Li, and Y. Li. New family of three-dimensional topo- logical insulators with antiperovskite struc- ture. Phys. Rev. Lett., 105(21):216406, 2010. https://doi.org/10.1103/PhysRevLett. 105.216406 https://doi.org/10.1103/RevModPhys.86.253 https://doi.org/10.1103/RevModPhys.86.253 https://doi.org/10.1016/j.commatsci.2004.02.024 https://doi.org/10.1016/j.commatsci.2004.02.024 https://doi.org/10.1063/1.1517164 https://doi.org/10.1103/PhysRevB.59.1743 https://doi.org/10.1103/PhysRevB.59.1743 https://doi.org/10.1103/PhysRevLett.77.3865 https://doi.org/10.1103/PhysRevLett.77.3865 https://doi.org/10.1103/PhysRevMaterials.3.074202 https://doi.org/10.1103/PhysRevMaterials.3.074202 https://doi.org/10.1038/s41598-018-33273-6 https://doi.org/10.1038/s41598-018-33273-6 https://doi.org/10.1103/PhysRevB.84.075119 https://doi.org/10.1103/PhysRevB.84.075119 https://doi.org/10.1103/PhysRevLett.105.216406 https://doi.org/10.1103/PhysRevLett.105.216406 Introduction Crystal Structure and Computational Details Results and Discussion Conclusion