Pd₂ZrIn Heusler Superconductor: Structural Disorder, Electronic Structure, Superconducting Ground State, and First-Principles Research Gaps - A Review

Authors

  • Priscilla Obiageli Osuhor University of Delta, Agbor Author

DOI:

https://doi.org/10.70882/josrar.2026.v3i2.285

Keywords:

Heusler compounds, Pd₂ZrIn, Superconductivity, van Hove singularity, Muon spin relaxation, Density functional theory, Antisite disorder

Abstract

The full-Heusler compound Pd2ZrIn (space group Fm3̄m, No. 225) belongs to a family of palladium-based Heusler superconductors alongside Pd2ZrAl, Pd2HfAl, and Pd2HfIn whose occurrence of superconductivity was originally predicted from electronic-structure calculations and subsequently confirmed by resistivity and magnetic-susceptibility measurements. This review synthesizes the currently available experimental and first-principles literature on Pd2ZrIn, covering its crystal structure and characteristic B2-type antisite disorder, the van Hove scenario invoked to rationalize its occurrence of superconductivity, and the detailed superconducting ground state recently established by muon spin relaxation and rotation (μSR) measurements namely bulk type-II superconductivity with Tc ≈ 2.2 K, a fully gapped, nodeless s-wave order parameter [Δ(0) ≈ 0.33 meV], and preserved time-reversal symmetry. Pd2ZrIn is placed in the broader context of the valence-electron-count (VEC) systematics that organize known Heusler superconductors, and is compared with isostructural and closely related compounds (Pd2ZrAl, Pd2HfAl, ZrPd2Sn, LiPd2Si, MgPd2Sb, ScAu2Al). Although the original 2009 work included electronic-structure calculations for the Pd₂ZrAl/Pd₂HfAl/Pd₂ZrIn/Pd₂HfIn family, the literature located for this review does not provide a dedicated, comprehensive Pd₂ZrIn-specific first-principles treatment of its equilibrium structural parameters, elastic/mechanical response, disorder-dependent electronic structure, phonon dispersion, Eliashberg spectral function α²F(ω), and ab initio electron–phonon coupling. These quantities therefore remain well-defined targets for a focused DFT/DFPT investigation. This review identifies these gaps and outlines a computational framework by which they could be addressed.

References

Carnicom, E. M., Xie, W., Yang, Z., Górnicka, K., Kong, T., Klimczuk, T., & Cava, R. J. (2019). Importance of specific heat characterization when reporting new superconductors: An example of superconductivity in LiGa₂Rh. Chemistry of Materials, 31(6), 2164–2173.

Dshemuchadse, J., & Steurer, W. (2015). Some statistics on intermetallic compounds. Inorganic Chemistry, 54(3), 1120–1128.

Galanakis, I., Dederichs, P. H., & Papanikolaou, N. (2002). Origin and properties of the gap in the half-ferromagnetic Heusler alloys. Physical Review B, 66(13), 134428.

Graf, T., Felser, C., & Parkin, S. S. P. (2011). Simple rules for the understanding of Heusler compounds. Progress in Solid State Chemistry, 39(1), 1–50.

Górnicka, K., Gui, X., Chamorro, J. R., McQueen, T. M., Cava, R. J., Klimczuk, T., & Winiarski, M. J. (2024). Superconductivity–electron count relationship in Heusler phases—the case of LiPd₂Si. Chemistry of Materials, 36(4), 1870–1879.

Górnicka, K., Kuderowicz, G., Carnicom, E. M., Kutorasiński, K., Wiendlocha, B., Cava, R. J., & Klimczuk, T. (2020). Soft-mode enhanced type-I superconductivity in LiPd₂Ge. Physical Review B, 102(2), 024507.

Górnicka, K., Kuderowicz, G., Winiarski, M. J., Wiendlocha, B., & Klimczuk, T. (2021). Superconductivity in LiGa₂Ir Heusler type compound with VEC = 16. Scientific Reports, 11, 16517.

Heusler, F. (1903). Über magnetische Manganlegierungen. Verhandlungen der Deutschen Physikalischen Gesellschaft, 5, 219.

Klimczuk, T., Wang, C. H., Gofryk, K., Ronning, F., Winterlik, J., Fecher, G. H., Griveau, J.-C., Colineau, E., Felser, C., Thompson, J. D., Cava, R. J., & Steglich, F. (2012). Superconductivity in the Heusler family of intermetallics. Physical Review B, 85(17), 174505.

Kuderowicz, G., & Wiendlocha, B. (2023). Strong-coupling superconductivity of the Heusler-type compound ScAu₂Al: Ab-initio studies. Physical Review B, 108(22), 224501.

Mahdjouba, K., Yahia, B., Fares, F., Abdelilah, F. M., & Mohammed, B. (2024). Exploring Heusler superconducting properties for Ni₂ZrAl and Ni₂ZrGa Heusler compounds: First principal insight. Physica B: Condensed Matter, 689, 416180. https://doi.org/10.1016/j.physb.2024.416180

Matthias, B. T. (1955). Empirical relation between superconductivity and the number of valence electrons per atom. Physical Review, 97(1), 74–76.

McMillan, W. L. (1968). Transition temperature of strong-coupled superconductors. Physical Review, 167(2), 331–344.

Su, H., Du, F., Li, R., Luo, S., Chen, Y., Liu, J., Chen, Y., Cao, C., Smidman, M., & Yuan, H. (2022). Structural phase transitions and superconductivity in the Heusler intermetallics XPd₂Sn (X = Ti, Zr, Hf). Physical Review B, 106(13), 134517. https://doi.org/10.1103/PhysRevB.106.134517

Wiendlocha, B., Winiarski, M. J., Muras, M., Zvoriste-Walters, C., Griveau, J.-C., Heathman, S., Gazda, M., & Klimczuk, T. (2015). Pressure effects on the superconductivity of the HfPd₂Al Heusler compound: Experimental and theoretical study. Physical Review B, 91(2), 024509. https://doi.org/10.1103/PhysRevB.91.024509

Winiarski, M. J., Kuderowicz, G., Górnicka, K., Litzbarski, L. S., Stolecka, K., Wiendlocha, B., Cava, R. J., & Klimczuk, T. (2021). MgPd₂Sb: A Mg-based Heusler-type superconductor. Physical Review B, 103(21), 214501.

Winterlik, J., Fecher, G. H., Thomas, A., & Felser, C. (2009). Superconductivity in palladium-based Heusler compounds. Physical Review B, 79(6), 064508.

Yadav, K., Divakaran, A. M., Nakamura, J. G., Takeuchi, T., & Mukherjee, K. (2026). Unveiling the superconducting ground state of Heusler alloy Pd₂ZrIn via muon spin relaxation and rotation measurement [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2604.19283

Abstract

Downloads

Published

2026-08-25

How to Cite

Osuhor, P. O. (2026). Pd₂ZrIn Heusler Superconductor: Structural Disorder, Electronic Structure, Superconducting Ground State, and First-Principles Research Gaps - A Review. Journal of Science Research and Reviews, 3(2), 118-124. https://doi.org/10.70882/josrar.2026.v3i2.285