Chiral phase transitions; Chiral phasis; Crystal chirality; Displacive transitions; First principle calculations; Parent structure; Pseudosymmetry; Soft-phonon mode; Space Groups; Structural relationship; Electronic, Optical and Magnetic Materials; Condensed Matter Physics
Abstract :
[en] We present an algorithm that integrates pseudosymmetry search with first-principles calculations to systematically identify achiral parent structures and establish potential chiral displacive transitions linking them to their corresponding chiral phases within the 22 enantiomorphic space groups. This approach enables a robust exploration of structural relationships, offering new insights into symmetry-driven properties. Our workflow streamlines the discovery of displacive chiral phase transitions driven by soft phonon modes, providing insights into the mechanisms of structural chirality in inorganic materials. We apply this methodology on the chiral phases of TeO2, Na2SeO9, Sr2As2O7, As2O5, Rb2Be2O3, and CaTe2O3. Demonstrating that some do not have a minimal supergroup that allows for an achiral phase; some can have a minimal supergroup, still, no unstable phonon mode exists in the achiral phase; and somewhere the minimal supergroup exists with a soft phonon mode connecting the identified achiral phase and the chiral phase through small continuous displacements.
Research Center/Unit :
Q-MAT - Quantum Materials - ULiège
Disciplines :
Physics
Author, co-author :
Gomez Ortiz, Fernando ; Université de Liège - ULiège > Département de physique > Physique théorique des matériaux
Romero, Aldo ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures ; Department of Physics and Astronomy, West Virginia University, Morgantown, United States
Bousquet, Eric ; Université de Liège - ULiège > Département de physique > Physique théorique des matériaux
Language :
English
Title :
Pathways to crystal chirality: An algorithm to identify displacive chiral phase transitions
Publication date :
17 July 2025
Journal title :
Physical Review. B
ISSN :
2469-9950
eISSN :
2469-9969
Publisher :
American Physical Society
Volume :
112
Issue :
1
Pages :
1 - 11
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
F.R.S.-FNRS - Fonds de la Recherche Scientifique Waalse Gewest EU - European Union NSF - National Science Foundation NASA - National Aeronautics and Space Administration
Funding text :
We acknowledge helpful discussions with Luis Elcoro, administrator of the Bilbao Crystallographic Server. F.G.-O. acknowledges financial support from MSCA-PF 101148906 funded by the European Union and the Fonds de la Recherche Scientifique (FNRS) through the FNRS-CR 1.B.227.25F grant. F.G.-O. and E.B. acknowledge the Fonds de la Recherche Scientifique (FNRS) for financial support, the PDR project CHRYSALID No. 40003544 and the Consortium des \u00C9quipements de Calcul Intensif (C\u00C9CI), funded by the F.R.S.-FNRS under Grant No. 2.5020.11 and the Tier-1 Lucia supercomputer of the Walloon Region, infrastructure financed by the Walloon Region under the Grant No. 1910247. F.G.-O. and E.B. also acknowledge support from the European Union\u2019s Horizon 2020 research and innovation program under Grant No. 964931 (TSAR).We also thank the Pittsburgh Supercomputer Center (Bridges2) and San Diego Supercomputer Center (Expanse) through allocation DMR140031 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which National Science Foundation supports Grants No. 2138259, No. 2138286, No. 2138307, No. 2137603, and No. 2138296. We also recognize the computational resources provided by the WVU Research Computing Dolly Sods HPC cluster, which is funded in part by NSF OAC-2117575. We also recognize the support of the West Virginia High Education Policy Commission under the call Research Challenge Grand Program 2022, Award No. RCG 23-007 and NASA EPSCoR Award No. 80NSSC22M0173
[1] M. Nespolo, M. I. Aroyo, and B. Souvignier, Crystallographic shelves: Space-group hierarchy explained, J. Appl. Crystallogr. 51, 1481 (2018).
[2] B. Souvignier, Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6, Acta Crystallogr. A: Found. Crystallogr. 59, 210 (2003).
[3] E. Bousquet, M. Fava, Z. Romestan, F. Gómez-Ortiz, E. E. McCabe, and A. H. Romero, Structural chirality and related properties in periodic inorganic solids: Review and perspectives, J. Phys.: Condens. Matter 37, 163004 (2025).
[4] G. H. Fecher, J. Kübler, and C. Felser, Chirality in the solid state: Chiral crystal structures in chiral and achiral space groups, Materials 15, 5812 (2022).
[5] D. Avnir, Chiral minerals, Minerals 14, 995 (2024).
[6] L. Sohncke, Entwickelung einer Theorie der Krystallstruktur (BG Teubner, Leipzig, 1879).
[7] P. Le Guennec, On the concept of chirality, J. Math. Chem. 23, 429 (1998).
[8] H. Flack and G. Bernardinelli, Absolute structure and absolute configuration, Acta Crystallogr. A: Found. Crystallogr. 55, 908 (1999).
[9] H. D. Flack, Chiral and achiral crystal structures, Helv. Chim. Acta 86, 905 (2003).
[10] F. Arago, Mémoire sur la polarisation colorée, OEuvres complètes de François Arago (1811).
[11] L. Pasteur, Sur les relations qui peuvent exister entre la forme crystalline, la composition chimique et le sens de la polarization rotatoire, Ann. Chim. Phys. 24, 442 (1848).
[12] T. Verbiest, S. V. Elshocht, M. Kauranen, L. Hellemans, J. Snauwaert, C. Nuckolls, T. J. Katz, and A. Persoons, Strong enhancement of nonlinear optical properties through supramolecular chirality, Science 282, 913 (1998).
[13] L. D. Barron, L. Hecht, I. H. McColl, and E.W. Blanch, Raman optical activity comes of age, Mol. Phys. 102, 731 (2004).
[14] L. Zhang and Q. Niu, Chiral phonons at high-symmetry points in monolayer hexagonal lattices, Phys. Rev. Lett. 115, 115502 (2015).
[15] H. Zhu, J. Yi, M.-Y. Li, J. Xiao, L. Zhang, C.-W. Yang, R. A. Kaindl, L.-J. Li, Y. Wang, and X. Zhang, Observation of chiral phonons, Science 359, 579 (2018).
[16] C. P. Romao and D. M. Juraschek, Phonon-induced geometric chirality, ACS Nano 18, 29550 (2024).
[17] T. Wang, H. Sun, X. Li, and L. Zhang, Chiral phonons: Prediction, verification, and application, Nano Lett. 24, 4311 (2024).
[18] S. Dalum and P. Hedegård, Theory of chiral induced spin selectivity, Nano Lett. 19, 5253 (2019).
[19] J. Junquera, Y. Nahas, S. Prokhorenko, L. Bellaiche, J. Íñiguez, D. G. Schlom, L.-Q. Chen, S. Salahuddin, D. A. Muller, L. W. Martin, and R. Ramesh, Topological phases in polar oxide nanostructures, Rev. Mod. Phys. 95, 025001 (2023).
[20] G. Chang, B. J. Wieder, F. Schindler, D. S. Sanchez, I. Belopolski, S.-M. Huang, B. Singh, D. Wu, T.-R. Chang, T. Neupert et al., Topological quantum properties of chiral crystals, Nat. Mater. 17, 978 (2018).
[21] L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
[22] I. Mazin et al., Altermagnetism—A new punch line of fundamental magnetism, Phys. Rev. X 12, 040002 (2022).
[23] D. S. Sanchez, I. Belopolski, T. A. Cochran, X. Xu, J.-X. Yin, G. Chang, W. Xie, K. Manna, V. Süß, C.-Y. Huang et al., Topological chiral crystals with helicoid-arc quantum states, Nature (Lond.) 567, 500 (2019).
[24] J. Hlinka, Eight types of symmetrically distinct vectorlike physical quantities, Phys. Rev. Lett. 113, 165502 (2014).
[25] M. Uwaha, Introduction to the BCF theory, Prog. Cryst. Growth Charact. Mater. 62, 58 (2016).
[26] H. Katsuno and M. Uwaha, Mechanism of chirality conversion by periodic change of temperature: Role of chiral clusters, Phys. Rev. E 93, 013002 (2016).
[27] C. Viedma, Chiral symmetry breaking during crystallization: Complete chiral purity induced by nonlinear autocatalysis and recycling, Phys. Rev. Lett. 94, 065504 (2005).
[28] G. H. Wagnière and G. L. Rikken, Chirality and magnetism II: Free electron on an infinite helix, inverse faraday effect and inverse magnetochiral effect, Chem. Phys. Lett. 502, 126 (2011).
[29] M. Fava, E. McCabe, A. H. Romero, and E. Bousquet, Phonondriven mechanism for the chiral phase transition of K3NiO2, Phys. Rev. B 111, 174102 (2025).
[30] M. T. Dove, Theory of displacive phase transitions in minerals, Am. Mineral. 82, 213 (1997).
[31] M. Isobe and Y. Ueda, Observation of phase transition from metal to spin-singlet insulator in MgTi2O4 with s = 1/2 pyrochlore lattice, J. Phys. Soc. Jpn. 71, 1848 (2002).
[32] M. Schmidt, W. Ratcliff, P. G. Radaelli, K. Refson, N. M. Harrison, and S. W. Cheong, Spin singlet formation in MgTi2O4: Evidence of a helical dimerization pattern, Phys. Rev. Lett. 92, 056402 (2004).
[33] A. W. Schlueter, R. A. Jacobson, and R. E. Rundle, A redetermination of the crystal structure of CsCuCl3, Inorg. Chem. 5, 277 (1966).
[34] I. Maki and T. Sugimura, Metasilicates in the ternary system Na2O–CaO–SiO2, J. Ceram. Assoc. Jpn. 76, 144 (1968).
[35] R. X. Fischer and E. Tillmanns, Revised data for combeite, Na2Ca2Si3O9, Acta Crystallogr. Sect. C 43, 1852 (1987).
[36] H. Ohsato, Y. Takéuchi, and I. Maki, Structural study of the phase transition of Na4Ca4[Si6O18], Acta Crystallogr. Sect. B 46, 125 (1990).
[37] T. Yamada and H. Koizumi, Czochralski growth of Ag4P2O7 crystals, J. Cryst. Growth 64, 558 (1983).
[38] M. Fava, W. Lafargue-Dit-Hauret, A. H. Romero, and E. Bousquet, Ferroelectricity and chirality in the Pb5Ge3O11 crystal, Phys. Rev. B 109, 024113 (2024).
[39] E. Wachter, E. C. Glazer, S. Parkin, and C. P. Brock, An exceptional 5:4 enantiomeric structure, Acta Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 72, 223 (2016).
[40] C. P. Brock, High-z structures of organic molecules: Their diversity and organizing principles, Acta Crystallogr. B Struct. Sci. Cryst. Eng. Mater. 72, 807 (2016).
[41] A. Jain, Y. Shin, and K. A. Persson, Computational predictions of energy materials using density functional theory, Nat. Rev. Mater. 1, 15004 (2016).
[42] K. T. Butler, J. M. Frost, J. M. Skelton, K. L. Svane, and A. Walsh, Computational materials design of crystalline solids, Chem. Soc. Rev. 45, 6138 (2016).
[43] E. Kroumova, M. I. Aroyo, J. M. Pérez-Mato, J. M. Igartua, and S. Ivantchev, Systematic search of displacive ferroelectrics, Ferroelectrics 241, 295 (2000).
[44] E. Kroumova, M. I. Aroyo, and J. M. Perez-Mato, Prediction of new displacive ferroelectrics through systematic pseudosymmetry search. Results for materials with Pba2 and Pmc21 symmetry, Acta Crystallogr. Sect. B 58, 921 (2002).
[45] C. Capillas, M. I. Aroyo, and J. M. Perez-Mato, Search for new Pna21 ferroelectrics, Ferroelectrics 301, 203 (2004).
[46] J. M. Igartua, M. I. Aroyo, E. Kroumova, and J. M. Perez-Mato, Search for Pnma materials with high-temperature structural phase transitions, Acta Crystallogr B 55, 177 (1999).
[47] J. M. Igartua, M. I. Aroyo, and J. M. Perez-Mato, Systematic search of materials with high-temperature structural phase transitions: Application to space group P212121, Phys. Rev. B 54, 12744 (1996).
[48] E. Kroumova, M. I. Aroyo, J. M. Perez-Mato, S. Ivantchev, J. M. Igartua, and H. Wondratschek, PSEUDO: A program for a pseudosymmetry search, J. Appl. Crystallogr. 34, 783 (2001).
[49] D. Dummit and R. Foote, Abstract Algebra (Wiley, New York, 2003).
[50] C. Capillas, E. S. Tasci, G. de la Flor, D. Orobengoa, J. M. Perez-Mato, and M. I. Aroyo, A new computer tool at the Bilbao crystallographic server to detect and characterize pseudosymmetry, Z. Krist. 226, 186 (2011).
[51] M. I. Aroyo, J. M. Perez-Mato, C. Capillas, E. Kroumova, S. Ivantchev, G. Madariaga, A. Kirov, and H. Wondratschek, Bilbao crystallographic server: I. Databases and crystallographic computing programs, Z. Krist. 221, 15 (2006).
[52] M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato, and H. Wondratschek, Bilbao Crystallographic Server. II. Representations of crystallographic point groups and space groups, Acta Crystallogr. Sect. A 62, 115 (2006).
[53] H. Wondratschek and U. Müller, International Tables for Crystallography, Vol. A1: Symmetry Relations Between Space Groups, International Tables for Crystallography (Springer, Netherlands, Dordrecht, 2010).
[54] H. Wondratschek, Splitting of Wyckoff positions (orbits), Mineral. Petrol. 48, 87 (1993).
[55] D. Zagorac, H. Müller, S. Ruehl, J. Zagorac, and S. Rehme, Recent developments in the inorganic crystal structure database: Theoretical crystal structure data and related features, J. Appl. Crystallogr. 52, 918 (2019).
[56] J. Leciejewicz, The crystal structure of tellurium dioxide. A redetermination by neutron diffraction, Zeitschr. Kristallog. Crystall. Mater. 116, 345 (1961).
[57] P. A. Thomas, The crystal structure and absolute optical chirality of paratellurite, α-TeO2, J. Phys. C 21, 4611 (1988).
[58] K. Peng, W. Ren, Y. Wu, H. Ru, S. Lu, A. Chen, P. Wang, X. Fang, H. Li, L. Chi, S. Ding, L. Wang, Y. Wang, and F. Li, Observation of metallic TeO2 thin film with rutile structure on fete surface, J. Mater. Sci. 57, 10225 (2022).
[59] F. Gómez-Ortiz, M. Fava, E. E. McCabe, A. H. Romero, and E. Bousquet, Structural chirality measurements and computation of handedness in periodic solids, Phys. Rev. B 110, 174112 (2024).
[60] F. Gómez-Ortiz, Helicity computation (2024), https://github. com/Gomez-OrtizF/Helicity_Computation_Crystals/.
[61] F. Edhokkar, A. Hadrich, M. Graia, and T. Mhiri, Synthesis and crystal structure of Sr2As2O7 from single-crystal data, IOP Conf. Ser.: Mater. Sci. Eng. 28, 012017 (2012).
[62] A. Mbarek and F. Edhokkar, The P43 enantiomorph of Sr2As2O7, Acta Crystallogr. E 69, i84 (2013).
[63] M. Project, Data retrieved from the materials project for Na2 SeO9 (mp-1211530) (2023), database version v2023.11.1, https://next-gen.materialsproject.org/materials/mp-1211530.
[64] M. Jansen, Über eine neue modifikation von As2O5/On a new modification of As2O5, Zeitschr. Naturforsch. B 34, 10 (1979).
[65] M. Project, Data retrieved from the materials project for Rb2 Be2 O3 (mp-771976) (2023), database version v2023.11.1, https://next-gen.materialsproject.org/materials/mp-771976.
[66] B. Stöger, M. Weil, E. Zobetz, and G. Giester, Polymorphism of CaTeO3 and solid solutions Cax Sr1-xTeO3, Acta Crystallogr. Sect. B 65, 167 (2009).
[67] X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet, J.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet, N. Brouwer, F. Bruneval, G. Brunin, T. Cavignac, J.-B. Charraud, W. Chen, M. Côté, S. Cottenier, J. Denier, G. Geneste, P. Ghosez, M. Giantomassi, Y. Gillet, O. Gingras, D. R. Hamann, G. Hautier, X. He, N. Helbig, N. Holzwarth, Y. Jia, F. Jollet, W. Lafargue-Dit-Hauret, K. Lejaeghere, M. A. Marques, A. Martin, C. Martins, H. P. Miranda, F. Naccarato, K. Persson, G. Petretto, V. Planes, Y. Pouillon, S. Prokhorenko, F. Ricci, G.-M. Rignanese, A. H. Romero, M. M. Schmitt, M. Torrent, M. J. van Setten, B. Van Troeye, M. J. Verstraete, G. Zérah, and J. W. Zwanziger, The ABINIT project: Impact, environment and recent developments, Comput. Phys. Commun. 248, 107042 (2020).
[68] D. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
[69] M. J. Van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rignanese, The pseudodojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018).
[70] X. Gonze and C. Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55, 10355 (1997).
