Topologically nontrivial phase in Na2CuX (X= As, Sb, Sn and Bi) full Heusler compounds: Insights from DFT-based computer simulation


  • Ahmed Youcef Université Djillali Liabès de Sidi Bel-Abbès
  • Noureddine Bettahar Université Djillali Liabès de Sidi Bel-Abbès
  • Oualid Cheref Université Djillali Liabès de Sidi Bel-Abbès
  • Salah Eddine‬ Benalia Université Djillali Liabès de Sidi Bel-Abbès
  • ‪Djamel Rached‬ Université Djillali Liabès de Sidi Bel-Abbès
  • Noureddine Benkhettou Université Djillali Liabès de Sidi Bel-Abbès
  • D. Bezzerga University of Relizane



FP-LMTO, Heusler, Spin orbital couplings, topological ordering


The inspection of materials supporting topological excitations is one of the prospective areas of condensed matter physics. This paper is devoted to studying the possibility of the existence of topological phases in Na2CuX (X= As, Sb, Sn and Bi) full Heusler compounds using the FP-LMTO (Full-Potential Linear Muffin-Tin Orbital) method with and without spin-orbit coupling (SOC). The study of structural properties has found that these materials are energetically stable in the Hg2CuTi type structure. Also, formation energy calculations have shown that these materials are convenient to manufacture. Otherwise, band structure calculations show that these materials exhibit the behavior of non-trivial topological materials with a semi-metallic nature. The obtained results in this study, generally, showed that SOC is not a primary cause of the band inversion mechanism.


H. Gao, J. W. F. Venderbos, Y. Kim, and A. M. Rappe, Topological Semimetals from First Principles, Annual Review of Materials Research, 49 (2019) 153,

A. K. Singh, S. D. Ramarao, S. C. Peter, Rare-earth based half-Heusler topological quantum materials: A perspective, APL Materials, 8 (2020) 060903. 1063/5.0006118.

M. G. Vergniory et al., A complete catalogue of high-quality topological materials, Nature. 566 (2019) 480-485.

B. Yan, S.-Cheng, Zhang, Topological materials, Reports on Progress in Physics, 75 (2012) 096501,

E. J. Bergholtz and Z. Liu, Topological Flat Band Models and Fractional Chern Insulators, International J. Mod. Phys. B, 27 (2013) 1330017, 27 1330017,

H. Polshyn et al., Electrical switching of magnetic order in an orbital Chern insulator, Nature, 588 (2020) 66,

P. Kotetes, Topological Insulator, Morgan and Claypool Publishers, Springer Berlin, Heidelberg, 75-84 (2019) 6,

Y. Ando, L. Fu, Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials, Annual Review of Condensed Matter Physics, 6 (2015) 361,

N. P. Armitage, E. J. Mele, A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys, 90 (2018), 015001. 90, 015001,

J. Benjamin Wieder et al., Strong and fragile topological Dirac semimetals with higher-order Fermi arcs, Nature communications, 11 (2020) 1-13.

K. Manna, Y. Sun, L. Muechler, J. Kubler and C. Felser, Heusler, Weyl and Berry. Nat Rev Mater 3 (2018) 244,

Y.-M. Dong et al., Stability of two-dimensional asymmetric materials with a quadratic band crossing point under fourfermion interaction and impurity scattering, Physical Review B. 102 (2020) 134204.

T. Klimczuk et al., Superconductivity in the Heusler family of intermetallics, Physical Review B 85 (2012) 174505,

X.-L. Qi, and S.-C. Zhang, Topological insulators and superconductors, Reviews of modern physics, 83 (2011) 1057,

F. Schindler et al., Higher-order topology in bismuth, Nature Phys 14 (2018) 918,

F. Munoz et al., Topological Crystalline Insulator in a New Bi Semiconducting Phase, Sci Rep 6 (2016) 21790.

Shi et al., Imaging quantum spin Hall edges in monolayer WTe2, Science Advances, 5 (2019) 8799,

F. Casper et al., Half-Heusler compounds: novel materials for energy and spintronic applications, Semiconductor Science and Technology, 27 (2012) 063001.

C. Felser, and A. Hirohata, Heusler alloys: Springer, 222 (2015) 8, 978-3-319-21449-8.

T. Graf, C. Felser, and S. S. Parkin, Handbook of spintronics, (2014) 1-24.

W. Al-Sawai et al., Topological electronic structure in halfHeusler topological insulators. Physical Review B. 82 (2010) 125208. 125208.

B. Yan and A. de Visser, Half-Heusler topological insulators. MRS Bulletin, 39 (2014) 859,

H. Lin et al., Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena, Nature Mater 9 (2010) 546,

M. Z. Hasan and C. L. Kane, Colloquium: topological insulators, Reviews of modern physics 82 (2010) 3045,

J. Ma et al., Computational investigation of half-Heusler compounds for spintronics applications, Physical Review B 95 (2017) 024411. PhysRevB.95.024411.

H. Mengyun, H.S. Qing Lin He, Topological insulator: Spintronics and quantum computations. Front. Phys, 14 (2019) 43401,

Y. Xu, D. Awschalom, and J. Nitta, Handbook of spintronics: Springer, 2016.

S. Y. Savrasov and D. Y. Savrasov, Full-potential linear-muffintin-orbital method for calculating total energies and forces. Physical Review B 46 (1992) 12181,

S. Y. Savrasov, Linear-response theory and lattice dynamics: A muffin-tin-orbital approach. Physical Review B 54 (1996) 16470,

P. Hohenberg, and W. Kohn, Inhomogeneous electron gas, Physical review B, 136.3 (1964) B864,

W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects. Physical review 140 (1965) A1133,

J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Physical review B 45 (1992) 13244,

J. P. Perdew and Y. Wang, Pair-distribution function and its coupling-constant average for the spin-polarized electron gas. Physical Review B, 46 (1992) 12947,

M. Methfessel, M. Van Schilfgaarde, and R.A. Casali, Springer, 2000, 535 114-147, 3.

E. Bott, M. Methfessel, W. Krabs, and P. C. Schmidt, Nonsingular Hankel functions as a new basis for electronic structure calculations, J. Math. Phys. 39 (1998) 3393,

P. E. Blochl, O. Jepsen and O. K. Andersen, Improved tetrahedron method for Brillouin-zone integrations. Physical Review B, 49 (1994) 16223,

I. Galanakis, P. Mavropoulos and P. H. Dederichs, Electronic structure and Slater-Pauling behaviour in half-metallic Heusler alloys calculated from first principles, Journal of Physics D: Applied Physics, 39 (2006) 765.

F. Birch, Finite strain isotherm and velocities for single-crystal and polycrystalline NaCl at high pressures and 300 K, Journal of Geophysical Research: Solid Earth, 83 (1978) 1257-1268.

M. Labidi, S. Ghemid, H. Meradji, S. Labidi, and F. E. H. Hassan, Density functional calculations of Pb1-xCaxSySe1-y alloys lattice matched to different substrates. Journal of Physics and Chemistry of Solids, 73 (2012) 608,

P. Pyykko, Relativistic effects in chemistry: more common than you thought, Annual review of physical chemistry, 63 (2012) 45-64.

T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang and C. Fang, Catalogue of topological electronic materials. Nature, 566 (2019) 475,

O. P. Giannozzi et al., Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys. Condens. Matter, 29 (2017) 465901,

Y. Gillet et al, Ab Initio Approach to Second-order Resonant Raman Scattering Including Exciton-Phonon Interaction, Sci. Rep. 7 (2017) 7344,

S. Baroni, S. de Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys 73 (2001) 515,




How to Cite

A. Youcef, “Topologically nontrivial phase in Na2CuX (X= As, Sb, Sn and Bi) full Heusler compounds: Insights from DFT-based computer simulation”, Rev. Mex. Fís., vol. 69, no. 2 Mar-Apr, pp. 020501 1–, Mar. 2023.