Abstract
Topological superconductors are fascinating platforms for realizing Majorana zero modes, which are crucial for the advancement of topological quantum computing. Ta3Sb is one of the A15 superconductors that possesses topologically nontrivial electronic structures, along with associated topological surface states. Here, we theoretically investigate the topological surface states of Ta3Sb using first-principles calculations based on density functional theory. We examine how the configurations of surface states change depending on surface termination and atomic relaxation. Our findings reveal that different surface terminations and atomic relaxation effects lead to significantly varied topological surface band structures with distinct Dirac point energies, while still preserving the topologically nontrivial characteristics. Additionally, chemical passivation of the surface atoms can be employed to simplify the configurations of the surface states. Our results provide critical insights into the tunability and stability of surface states in Ta3Sb, which are essential for future experimental studies and the practical realization of topological quantum computing.
Similar content being viewed by others
Data availability
The data that support the findings of this study are available from the corresponding author upon request.
References
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).
Sarma, S. D., Freedman, M. & Nayak, C. Majorana zero modes and topological quantum computation. npj Quantum Inf. 1, 15001 (2015).
Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Rep. Prog. Phys. 75, 076501 (2012).
Beenakker, C. W. J. Search for Majorana fermions in superconductors. Annu. Rev. Condens. Matter Phys. 4, 113–136 (2013).
Read, N. & Green, D. Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum hall effect. Phys. Rev. B 61, 10267–10297 (2000).
Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Uspekhi 44, 131 (2001).
Ivanov, D. A. Non-abelian statistics of half-quantum vortices in p-wave superconductors. Phys. Rev. Lett. 86, 268–271 (2001).
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).
Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).
Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).
Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).
Alicea, J. et al. Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nat. Phys. 7, 412–417 (2011).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Qi, X. L & Zhang, S. C Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).
Sato, M. & Ando, Y. Topological superconductors: a review. Rep. Prog. Phys. 80, 076501 (2017).
Kim, M., Wang, C. Z & Ho, K. M Topological states in a15 superconductors. Phys. Rev. B 99, 224506 (2019).
Zhang, P. et al. Observation of topological superconductivity on the surface of an iron-based superconductor. Science 360, 182–186 (2018).
Wang, Z. et al. Topological nature of the fese0.5te0.5 superconductor. Phys. Rev. B 92, 115119 (2015).
Sakano, M. et al. Topologically protected surface states in a centrosymmetric superconductor β-PdBi2. Nat. Commun. 6, 8595 (2015).
Bian, G. et al. Topological nodal-line fermions in spin-orbit metal PbTaSe2. Nat. Commun. 7, 10556 (2016).
Guan, S. Y. et al. Superconducting topological surface states in the noncentrosymmetric bulk superconductor pbtase2. Sci. Adv. 2, e1600894 (2016).
Sattigeri, R. M. et al. Dirac surface states, multiorbital dimerization, and superconductivity in NB- and ta-based A15 compounds. Phys. Rev. B 109, 075119 (2024).
Derunova, E. et al. Giant intrinsic spin hall effect in w3ta and other a15 superconductors. Sci. Adv. 5, eaav8575 (2019).
Chapai, R. et al. Superconducting properties of the spin Hall candidate Ta3Sb with eightfold degeneracy. Phys. Rev. B 105, 184510 (2022).
Fu, L. & Kane, C. L. Topological insulators with inversion symmetry. Phys. Rev. B 76, 045302 (2007).
Bradlyn, B. et al. Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).
Sun, S. P. et al. First-principles investigations on the electronic properties and stabilities of low-index surfaces of L12-Al3Sc intermetallic. Appl. Surf. Sci. 288, 609–618 (2014).
Penev, E. S., On the theory of surface diffusion in InAs/GaAs(001) heteroepitaxy, https://doi.org/10.14279/depositonce-577 Ph.D. thesis, Technische Universität Berlin (2002).
Dannenberg, A., Gruner, M. E., Hucht, A. & Entel, P. Surface energies of stoichiometric FePt and CoPt alloys and their implications for nanoparticle morphologies. Phys. Rev. B 80, 245438 (2009).
Katoch, J. et al. Transport spectroscopy of sublattice-resolved resonant scattering in hydrogen-doped bilayer graphene. Phys. Rev. Lett. 121, 136801 (2018).
Singh-Miller, N. E. & Marzari, N. Surface energies, work functions, and surface relaxations of low-index metallic surfaces from first principles. Phys. Rev. B 80, 235407 (2009).
Leung, T. C., Kao, C. L., Su, W. S., Feng, Y. J. & Chan, C. T. Relationship between surface dipole, work function and charge transfer: Some exceptions to an established rule. Phys. Rev. B 68, 195408 (2003).
Pielmeier, F. et al. Response of the topological surface state to surface disorder in tlbise2. N. J. Phys. 17, 023067 (2015).
Benia, H. M., Lin, C., Kern, K. & Ast, C. R. Reactive chemical doping of the bi2se3 topological insulator. Phys. Rev. Lett. 107, 177602 (2011).
Roy, S. et al. Tuning the Dirac point position in bi2se3(0001) via surface carbon doping. Phys. Rev. Lett. 113, 116802 (2014).
Bianchi, M. et al. Simultaneous quantization of bulk conduction and valence states through adsorption of nonmagnetic impurities on bi2se3. Phys. Rev. Lett. 107, 086802 (2011).
Yue, Z. et al. Topological surface state evolution in bi2se3 via surface etching. Nano Lett. 24, 12413–12419 (2024).
Giannozzi, P. et al. Quantum espresso toward the exascale. J. Chem. Phys. 152, 154105 (2020).
Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum Espresso. J. Phys.: Condens. Matter 29, 465901 (2017).
Giannozzi, P. et al. Quantum espresso: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).
Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008).
Momma, K. & Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).
Acknowledgements
This research was supported by Seoul National University of Science and Technology. Computations were performed with the support of the Center for Advanced Computation at the Korea Institute for Advanced Study.
Author information
Authors and Affiliations
Contributions
M.K. conceived the study, carried out the calculations, performed the analysis, interpreted the results, and wrote the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Communications Physics thanks Carmine Autieri, Mario Cuoco and Amar Fakhredine for their contribution to the peer review of this work.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Kim, M. Topological surface states in Ta3Sb. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02575-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s42005-026-02575-x


