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Chin. Phys. B, 2026, Vol. 35(5): 057102    DOI: 10.1088/1674-1056/ae27b7
Special Issue: SPECIAL TOPIC — John Tse: Pioneer in high-pressure materials science
SPECIAL TOPIC — John Tse: Pioneer in high-pressure materials science Prev   Next  

Superconducting and dynamically stable polymorphs of elemental calcium predicted under high pressure

Akinwumi Akinpelu and Yansun Yao†
Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada
Abstract  Compressed calcium undergoes successive structural transitions under high pressure. In this study, high-pressure polymorphs of elemental calcium were investigated using a machine-learned interatomic potential combined with a sensible random structure search. Two new energetically favourable and dynamically stable phases were predicted, crystallizing in the $P$-$42_{1}c$ and $P$-$31c$ space groups at high pressure. Both structures are predicted to be metallic and likely exhibit phonon-mediated superconductivity. Using the Allen-Dynes modified McMillan equation, the superconducting critical temperatures ($T_{\rm c}$) were estimated to be 26 K for the $P$-$42_{1}c$ phase at 200 GPa and 31 K for the $P$-$31c$ phase at 250 GPa, which are comparable to the highest experimentally observed $T_{\rm c}$ for calcium (29 K at 216 GPa). These relatively high $T_{\rm c}$ values are attributed to strong electron-phonon coupling between partially occupied d states and moderate-frequency phonon modes. These findings provide further insight into the complex polymorphism and superconductivity of elemental calcium under extreme conditions.
Keywords:  crystal structure prediction      phase changes      high pressure      material science      superconductivity  
Received:  31 October 2025      Revised:  30 November 2025      Accepted manuscript online:  04 December 2025
PACS:  71.20.Dg (Alkali and alkaline earth metals)  
  71.20.-b (Electron density of states and band structure of crystalline solids)  
  74.62.Fj (Effects of pressure)  
  61.50.Ks (Crystallographic aspects of phase transformations; pressure effects)  
Fund: Project supported by the Information and Communications Technology group and the High-Performance Computing Training and Research Facilities at the University of Saskatchewan for the use of the Plato cluster computing resource, as well as computing clusters provided by West Grid and Digital Research Alliance of Canada. This project was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
Corresponding Authors:  Yansun Yao     E-mail:  yansun.yao@usask.ca

Cite this article: 

Akinwumi Akinpelu and Yansun Yao Superconducting and dynamically stable polymorphs of elemental calcium predicted under high pressure 2026 Chin. Phys. B 35 057102

[1] Grochala W, Hoffmann R, Feng J and Ashcroft N W 2007 Angew. Chem. Int. Ed. 46 3620
[2] Ahuja R, Eriksson O, Wills J M and Johansson B 1995 Phys. Rev. Lett. 75 3473
[3] Hamlin J J 2015 Physica C 514 59
[4] Olijnyk H and Holzapfel W B 1984 Phys. Lett. A 100 191
[5] Yabuuchi T, Nakamoto Y, Shimizu K and Kikegawa T 2005 J. Phys. Soc. Jpn. 74 2391
[6] Teweldeberhan A M and Bonev S A 2008 Phys. Rev. B 78 140101
[7] Gao G, Xie Y, Cui T, Ma Y, Zhang L and Zou G 2008 Solid State Commun. 146 181
[8] Yao Y, Martoňák R, Patchkovskii S and Klug D D 2010 Phys. Rev. B 82 094107
[9] Yao Y, Klug D D, Sun J and Martoňák R 2009 Phys. Rev. Lett. 103 055503
[10] Li B, Ding Y, Yang W, Wang L, Zou B, Shu J, Sinogeikin S, Park C, Zou G and Mao H K 2012 Proc. Natl. Acad. Sci. USA 109 16459
[11] Fujihisa H, Nakamoto Y, Shimizu K, Yabuuchi T and Gotoh Y 2008 Phys. Rev. Lett. 101 095503
[12] Yao Y, Tse J S, Song Z, Klug D D, Sun J and Le Page Y 2008 Phys. Rev. B 78 054506
[13] Ishikawa T, Ichikawa A, Nagara H, Geshi M, Kusakabe K and Suzuki N 2008 Phys. Rev. B 77 020101
[14] Nakamoto Y, Sakata M, Shimizu K, Fujihisa H, Matsuoka T, Ohishi Y and Kikegawa T 2010 Phys. Rev. B 81 140106
[15] Fujihisa H, Nakamoto Y, Sakata M, Shimizu K, Matsuoka T, Ohishi Y, Yamawaki H, Takeya S and Gotoh Y 2013 Phys. Rev. Lett. 110 235501
[16] Oganov A R, Ma Y, Xu Y, Errea I, Bergara A and Lyakhov A O 2010 Proc. Natl. Acad. Sci. USA 107 7646
[17] Arapan S, Mao H K and Ahuja R 2008 Proc. Natl. Acad. Sci. USA 105 20627
[18] Ishikawa T, Nagara H, Suzuki N, Tsuchiya T and Tsuchiya J 2010 Phys. Rev. B 81 092104
[19] Sakata M, Nakamoto Y, Shimizu K, Matsuoka T and Ohishi Y 2011 Phys. Rev. B 83 220512
[20] Ying J, Liu S, Lu Q, Wen X, Gui Z, Zhang Y, Wang X, Sun J and Chen X 2023 Phys. Rev. Lett. 130 256002
[21] Pickard C J 2022 Phys. Rev. B 106 014102
[22] Salzbrenner P T, Joo S H, Conway L J, Cooke P I C, Zhu B, Matraszek M P, Witt W C and Pickard C J 2023 J. Chem. Phys. 159 144801
[23] Pickard C J and Needs R J 2006 Phys. Rev. Lett. 97 045504
[24] Pickard C J and Needs R J 2011 J. Phys.: Condens. Matter 23 053201
[25] Kim S W, Conway L J, Pickard C J, Pascut G L and Monserrat B 2023 Nat. Commun. 14 7360
[26] Ferreira P P, Conway L J, Cucciari A, Di Cataldo S, Giannessi F, Kogler E, Eleno L T F, Pickard C J, Heil C and Boeri L 2023 Nat. Commun. 14 5367
[27] Dolui K, Conway L J, Heil C, Strobel T A, Prasankumar R P and Pickard C J 2024 Phys. Rev. Lett. 132 166001
[28] Bhullar M, Akinpelu A and Yao Y 2024 Comput. Mater. Today 3 100009
[29] Akinpelu A, Bhullar M, Wang H and Yao Y 2025 Commun. Chem. 8 177
[30] Hohenberg P and Kohn W 1964 Phys. Rev. 136 B864
[31] Kohn W and Sham L J 1965 Phys. Rev. 140 A1133
[32] https://www.mtg.msm.cam.ac.uk/Codes/AIRSS
[33] https://www.mtg.msm.cam.ac.uk/Codes/EDDP
[34] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[35] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[36] Monkhorst H J and Pack J D 1976 Phys. Rev. B 13 5188
[37] Blöchl P E 1994 Phys. Rev. B 50 17953
[38] Baroni S, de Gironcoli S, Dal Corso A and Giannozzi P 2001 Rev. Mod. Phys. 73 515
[39] Togo A, Oba F and Tanaka I 2008 Phys. Rev. B 78 134106
[40] Bader R F W 1991 Chem. Rev. 91 893
[41] Otero-de-la-Roza A, Johnson E R and Lu?ana V 2014 Comput. Phys. Commun. 185 1007
[42] Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti G L, Cococcioni M, Dabo I 2009 J. Phys.: Condens. Matter 21 395502
[43] Vanderbilt D 1990 Phys. Rev. B 41 7892
[44] McMillan W L 1968 Phys. Rev. 167 331
[45] Allen P B and Dynes R C 1975 Phys. Rev. B 12 905
[46] Momma K and Izumi F 2011 J. Appl. Crystallogr. 44 1272
[47] Becke A D and Edgecombe K E 1990 J. Chem. Phys. 92 5397
[48] Racioppi S and Zurek E 2025 Acta Cryst. B 81 256
[49] Racioppi S, Storm C V, McMahonMI and Zurek E 2023 Angew. Chem. Int. Ed. 62 e202310802
[50] Bader R F W and Esseén H 1984 J. Chem. Phys. 80 1943
[51] Bader R F W, MacDougall P J and Lau C D 1984 J. Am. Chem. Soc. 106 1594
[52] Yao Y, Yong X, Tse J S and Greschner M J 2014 J. Phys. Chem. C 118 29591
[53] Kasinathan D, Kuneš J, Lazicki A, Rosner H, Yoo C S, Scalettar R T and Pickett W E 2006 Phys. Rev. Lett. 96 047004
[54] Tse J S, Yao Y and Tanaka K 2007 Phys. Rev. Lett. 98 117004
[55] Simon A 1997 Angew. Chem. Int. Ed. 36 1788
[56] Majumdar A, Tse J S and Yao Y 2017 Angew. Chem. Int. Ed. 56 11390
[57] Yao Y, Tse J S, Tanaka K, Marsiglio F and Ma Y 2009 Phys. Rev. B 79 054524
[58] Matsuoka T, Nakamoto Y and Shimizu K 2006 J. Phys. Soc. Jpn. 75 083703
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