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Strain- and confinement-induced topological phases in noncentrosymmetric wurtzite HgTe

Antoine Hage1, Jing Li2,*, and Christophe Delerue1,†

  • *Contact author: jing.li@cea.fr
  • †Contact author: christophe.delerue@iemn.fr
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Phys. Rev. Research 8, 033323 – Published 16 September, 2026

DOI: https://doi.org/10.1103/5pj7-34v4

Abstract

While three-dimensional Dirac semimetals have been extensively studied in centrosymmetric materials such as Cd3As2 and Na3Bi, the recent colloidal synthesis of wurtzite HgTe (wz-HgTe) opens new opportunities for exploring topological quantum phases in noncentrosymmetric systems. Building on recent evidence that bulk wz-HgTe is a noncentrosymmetric Dirac semimetal, we investigate how strain and quantum confinement reshape its topology. To this end, we combine ab initio density-functional theory, semiempirical tight-binding, and k·p approaches. Bulk wz-HgTe hosts two Dirac points along the Γ–A line, i.e., along the c axis, located only 37 meV above the Fermi level, indicating that the Dirac regime should be experimentally accessible by doping or electrostatic gating. We show that biaxial strain drives a sequence of topological phase transitions from a Dirac semimetal to a three-dimensional topological insulator and eventually to a multiband metal. In (0001) thin films, quantum confinement induces oscillatory transitions between trivial and topological insulating phases. We demonstrate that this behavior is governed not only by the underlying s–p band inversion, but also by the crystal-field splitting specific to the wurtzite structure and by the presence of bulk Dirac points. In contrast, (11¯00) films exhibit a single topological transition and, above a critical thickness, develop surface states forming Fermi-arc-like contours that connect the projections of the Dirac points in the two-dimensional Brillouin zone. In the same weak-confinement regime, semimetallic nanowires oriented along the c axis are predicted to host localized edge states that should be accessible to transport measurements or scanning tunneling spectroscopy. These results establish the topological phase diagram of wz-HgTe beyond the strong-confinement regime explored so far and reveal how crystal symmetry, inversion breaking, strain, and confinement combine to reshape the topology of a Dirac material. More broadly, they identify wurtzite HgTe as a promising platform for engineering topological phases in experimentally relevant nanostructures.

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References (61)

  1. S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimensions, Phys. Rev. Lett. 108, 140405 (2012).
  2. Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Dirac semimetal and topological phase transitions in A3Bi (a=Na, K, Rb), Phys. Rev. B 85, 195320 (2012).
  3. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  4. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  5. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  6. Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Three-dimensional Dirac semimetal and quantum transport in Cd3As2, Phys. Rev. B 88, 125427 (2013).
  7. Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Discovery of a three-dimensional topological Dirac semimetal, Na3Bi, Science 343, 864 (2014).
  8. S.-Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Alidoust, T.-R. Chang, H.-T. Jeng, C.-Y. Huang, W.-F. Tsai, H. Lin, P. P. Shibayev, F.-C. Chou, R. J. Cava, and M. Z. Hasan, Observation of Fermi arc surface states in a topological metal, Science 347, 294 (2015).
  9. Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, A stable three-dimensional topological Dirac semimetal Cd3As2, Nat. Mater. 13, 677 (2014).
  10. S. Jeon, B. B. Zhou, A. Gyenis, B. E. Feldman, I. Kimchi, A. C. Potter, Q. D. Gibson, R. J. Cava, A. Vishwanath, and A. Yazdani, Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2, Nat. Mater. 13, 851 (2014).
  11. M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2, Nat. Commun. 5, 3786 (2014).
  12. H. Zheng, S.-Y. Xu, G. Bian, C. Guo, G. Chang, D. S. Sanchez, I. Belopolski, C.-C. Lee, S.-M. Huang, X. Zhang, et al., Atomic-scale visualization of quantum interference on a Weyl semimetal surface by scanning tunneling microscopy, ACS Nano 10, 1378 (2016).
  13. J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, and N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi, Science 350, 413 (2015).
  14. B.-J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5, 4898 (2014).
  15. N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
  16. C.-X. Liu, H. Zhang, B. Yan, X.-L. Qi, T. Frauenheim, X. Dai, Z. Fang, and S.-C. Zhang, Oscillatory crossover from two-dimensional to three-dimensional topological insulators, Phys. Rev. B 81, 041307 (2010).
  17. C. Lyi and Y. Kim, Strain-driven higher-order topological Dirac semimetal in noncentrosymmetric γ-GeSe, Nano Lett. 25, 6592 (2025).
  18. H. Pan, M. Wu, Y. Liu, and S. A. Yang, Electric control of topological phase transitions in Dirac semimetal thin films, Sci. Rep. 5, 14639 (2015).
  19. J. L. Collins, A. Tadich, W. Wu, L. C. Gomes, J. N. B. Rodrigues, C. Liu, J. Hellerstedt, H. Ryu, S. Tang, S.-K. Mo, S. Adam, S. A. Yang, M. S. Fuhrer, and M. T. Edmonds, Electric-field-tuned topological phase transition in ultrathin Na3Bi, Nature (London) 564, 390 (2018).
  20. H. Xia, Y. Li, M. Cai, L. Qin, N. Zou, L. Peng, W. Duan, Y. Xu, W. Zhang, and Y.-S. Fu, Dimensional crossover and topological phase transition in Dirac semimetal Na3Bi films, ACS Nano 13, 9647 (2019).
  21. M. Uchida, Y. Nakazawa, S. Nishihaya, K. Akiba, M. Kriener, Y. Kozuka, A. Miyake, Y. Taguchi, M. Tokunaga, N. Nagaosa, Y. Tokura, and M. Kawasaki, Quantum Hall states observed in thin films of Dirac semimetal Cd3As2, Nat. Commun. 8, 2274 (2017).
  22. T. Schumann, L. Galletti, D. A. Kealhofer, H. Kim, M. Goyal, and S. Stemmer, Observation of the quantum Hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2, Phys. Rev. Lett. 120, 016801 (2018).
  23. C. Zhang, Y. Zhang, X. Yuan, S. Lu, J. Zhang, A. Narayan, Y. Liu, H. Zhang, Z. Ni, R. Liu, E. S. Choi, A. Suslov, S. Sanvito, L. Pi, H.-Z. Lu, A. C. Potter, and F. Xiu, Quantum Hall effect based on Weyl orbits in Cd3As2, Nature (London) 565, 331 (2019).
  24. C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, Multi-Weyl topological semimetals stabilized by point group symmetry, Phys. Rev. Lett. 108, 266802 (2012).
  25. H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X 5, 011029 (2015).
  26. S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, et al., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015).
  27. B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5, 031013 (2015).
  28. N. Xu, H. M. Weng, B. Q. Lv, C. E. Matt, J. Park, F. Bisti, V. N. Strocov, D. Gawryluk, E. Pomjakushina, K. Conder, N. C. Plumb, M. Radovic, G. Autes, O. V. Yazyev, Z. Fang, X. Dai, T. Qian, J. Mesot, H. Ding, and M. Shi, Observation of Weyl nodes and Fermi arcs in tantalum phosphide, Nat. Commun. 7, 11006 (2016).
  29. S.-Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T.-R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang, et al., Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nat. Phys. 11, 748 (2015).
  30. D.-F. Xu, Y.-P. Du, Z. Wang, Y.-P. Li, X.-H. Niu, Q. Yao, D. Pavel, Z.-A. Xu, X.-G. Wan, and D.-L. Feng, Observation of Fermi arcs in non-centrosymmetric Weyl semi-metal candidate NbP, Chin. Phys. Lett. 32, 107101 (2015).
  31. M. Kargarian, M. Randeria, and Y.-M. Lu, Are the surface Fermi arcs in Dirac semimetals topologically protected? Proc. Natl. Acad. Sci. USA 113, 8648 (2016).
  32. H. Gao, J. Strockoz, M. Frakulla, J. W. F. Venderbos, and H. Weng, Noncentrosymmetric topological Dirac semimetals in three dimensions, Phys. Rev. B 103, 205151 (2021).
  33. M. Sato, J. Bouaziz, S. Sumita, S. Kobayashi, I. Tateishi, S. Bluegel, A. Furusaki, and M. Hirayama, Ideal spin-orbit-free Dirac semimetal and diverse topological transitions in Y8CoIn3 family, Commun. Mater. 5, 253 (2024).
  34. K. A. Sergeeva, H. Zhang, A. S. Portniagin, E. Bossavit, G. Mu, S. V. Kershaw, S. Ithurria, P. Guyot-Sionnest, S. Keuleyan, C. Delerue, X. Tang, A. L. Rogach, and E. Lhuillier, The rise of HgTe colloidal quantum dots for infrared optoelectronics, Adv. Funct. Mater. 34, 2405307 (2024).
  35. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007).
  36. C. Brüne, C. X. Liu, E. G. Novik, E. M. Hankiewicz, H. Buhmann, Y. L. Chen, X. L. Qi, Z. X. Shen, S. C. Zhang, and L. W. Molenkamp, Quantum Hall effect from the topological surface states of strained bulk HgTe, Phys. Rev. Lett. 106, 126803 (2011).
  37. A. S. Portniagin, K. A. Sergeeva, S. V. Kershaw, and A. L. Rogach, Cation-exchange-derived wurtzite HgTe nanorods for sensitive photodetection in the short-wavelength infrared range, Chem. Mater. 35, 5631 (2023).
  38. K. A. Sergeeva, A. S. Portniagin, D. Mastrippolito, C. Gureghian, A. Hage, D. De Pesseroey, M. Paye, E. Bossavit, A. A. Sergeev, Z. Li, et al., Confining metastable wurtzite HgTe for infrared optoelectronics, ACS Nano 20, 10686 (2026).
  39. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  40. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  41. A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, Influence of the exchange screening parameter on the performance of screened hybrid functionals, J. Chem. Phys. 125, 224106 (2006).
  42. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  43. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  44. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  45. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  46. J. Gao, Q. Wu, C. Persson, and Z. Wang, Irvsp: To obtain irreducible representations of electronic states in the VASP, Comput. Phys. Commun. 261, 107760 (2021).
  47. A. P. Cracknell, B. L. Davies, S. C. Miller, and W. F. Love, General Introduction and Tables of Irreducible Representations of Space Groups (IFI/Plenum, New York, 1979).
  48. L. Elcoro, B. Bradlyn, Z. Wang, M. G. Vergniory, J. Cano, C. Felser, B. A. Bernevig, D. Orobengoa, G. d. l. Flor, and M. I. Aroyo, Double crystallographic groups and their representations on the Bilbao crystallographic server, J. Appl. Cryst. 50, 1457 (2017).
  49. G. H. Wannier, The structure of electronic excitation levels in insulating crystals, Phys. Rev. 52, 191 (1937).
  50. G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
  51. C. Delerue and M. Lannoo, Nanostructures: Theory and modeling (Springer, Berlin, 2004).
  52. Y. M. Niquet, C. Delerue, G. Allan, and M. Lannoo, Method for tight-binding parametrization: Application to silicon nanostructures, Phys. Rev. B 62, 5109 (2000).
  53. J.-M. Jancu, R. Scholz, F. Beltram, and F. Bassani, Empirical spds* tight-binding calculation for cubic semiconductors: General method and material parameters, Phys. Rev. B 57, 6493 (1998).
  54. G. Allan, Y. M. Niquet, and C. Delerue, Quantum confinement energies in zinc-blende III–V and group IV semiconductors, Appl. Phys. Lett. 77, 639 (2000).
  55. A. Hage and C. Delerue, Unusual optoelectronic and topological properties of HgTe nanocrystals, Phys. Rev. B 113, 205430 (2026).
  56. G. Bastard and J. Brum, Electronic states in semiconductor heterostructures, IEEE J. Quantum Electron. 22, 1625 (1986).
  57. Y. Wu, N. H. Jo, L.-L. Wang, C. A. Schmidt, K. M. Neilson, B. Schrunk, P. Swatek, A. Eaton, S. L. Bud’ko, P. C. Canfield, and A. Kaminski, Fragility of Fermi arcs in Dirac semimetals, Phys. Rev. B 99, 161113 (2019).
  58. A.-Q. Wang, T.-Y. Zhao, C. Li, A. Brinkman, C.-G. Chu, and Z.-M. Liao, From surface Fermi arcs to Fermi loops in the Dirac semimetal Cd3As2, arXiv:2502.07499.
  59. J. C. Slater and G. F. Koster, Simplified LCAO method for the periodic potential problem, Phys. Rev. 94, 1498 (1954).
  60. Y. M. Niquet, D. Rideau, C. Tavernier, H. Jaouen, and X. Blase, Onsite matrix elements of the tight-binding Hamiltonian of a strained crystal: Application to silicon, germanium, and their alloys, Phys. Rev. B 79, 245201 (2009).
  61. G. Fishman, Semi-Conducteurs: Les Bases de la Théorie K.P (Editions de l’Ecole Polytechnique, Palaiseau, 2010).

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Phys. Rev. Research 8, 033323– Published 16 September, 2026
  • Received 12 April 2026
  • Accepted 20 July 2026
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