- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Millisecond-Coherent 2D Nuclear Shells around VB− Defects in hBN

G. V. Mamin1, E. V. Dmitrieva1, F. F. Murzakhanov1, I. N. Gracheva1, K. L. Franzke2, T. Biktagirov3, W. G. Schmidt3, U. Gerstmann2,*, and V. A. Soltamov2,†

  • *Contact author: uwe.gerstmann@upb.de
  • †Contact author: victrosoltamov@gmail.com
PDF

Phys. Rev. Lett. 137, 186701 – Published 26 October, 2026

DOI: https://doi.org/10.1103/nmsz-9p3k

Abstract

We demonstrate an essentially two-dimensional (2D) driven central-spin regime based on negatively charged boron vacancy (VB−) defects in the dense nuclear quadrupolar lattice of hexagonal boron nitride (hBN). At 3 T magnetic field, the B11 bath collapses into classes of planar, equidistant nuclei. Electron-nuclear double resonance spectroscopy and ab initio calculations show that the electron spin density is in fact localized in the defective boron nitride layer exclusively, and that this 2D geometry reduces the electron-nuclear spin Hamiltonian to a function of discrete shell coordinates within the nanometer-scale vicinity of the defect. Even the deviations from bulklike quadrupole coupling of B11 reveals an abrupt truncation across the van der Waals gap. VB−:hBN is thus established as a platform of discrete 2D nuclear shells, enabling shell-selective coherent control of B11 nuclei with T2n*≈100  μs and shell-dependent Hahn-echo coherence times T2n spanning 0.33–1.44 ms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, Science 316, 1312 (2007).
  2. D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. Zhou, Nat. Photonics 12, 516 (2018).
  3. S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, Nature (London) 543, 221 (2017).
  4. F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Rev. Mod. Phys. 85, 961 (2013).
  5. G. Burkard, T. D. Ladd, A. Pan, J. M. Nichol, and J. R. Petta, Rev. Mod. Phys. 95, 025003 (2023).
  6. B. Urbaszek, X. Marie, T. Amand, O. Krebs, P. Voisin, P. Malentinsky, A. Hogele, and A. Imamoǧlu, Rev. Mod. Phys. 85, 79 (2013).
  7. M. H. Appel, A. Ghorbal, N. Shofer, L. Zaporski, S. Manna, S. F. Covre da Silva, U. Haeusler, C. Le Gall, A. Rastelli, D. A. Gangloff, and M. Atatüre, Nat. Phys. 21, 368 (2025).
  8. E. Hesselmeier, P. Kuna, W. Knolle, F. Kaiser, N. T. Son, M. Ghezellou, J. Ul-Hassan, V. Vorobyov, and J. Wrachtrup, Phys. Rev. Lett. 132, 180804 (2024).
  9. H. Edlbauer, J. Wang, A. M. S.-E. Huq, I. Thorvaldson, M. T. Jones, S. H. Misha, W. J. Pappas, C. M. Moehle, Y.-L. Hsueh, and H. Bornemann et al., Nature (London) 648, 569 (2025).
  10. C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, Phys. Rev. X 9, 031045 (2019).
  11. W. M. Witzel and S. Das Sarma, Phys. Rev. B 74, 035322 (2006).
  12. A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961).
  13. I. A. Merkulov, A. L. Efros, and M. Rosen, Phys. Rev. B 65, 205309 (2002).
  14. A. V. Khaetskii, D. Loss, and L. Glazman, Phys. Rev. Lett. 88, 186802 (2002).
  15. R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, Science 320, 352 (2008).
  16. A. Gottscholl, M. Kianinia, V. Soltamov, S. Orlinskii, G. Mamin, C. Bradac, C. Kasper, K. Krambrock, A. Sperlich, M. Toth, I. Aharonovich, and V. Dyakonov, Nat. Mater. 19, 540 (2020).
  17. N. Chejanovsky, A. Mukherjee, J. Geng, Y.-C. Chen, Y. Kim, A. Denisenko, A. Finkler, T. Taniguchi, K. Watanabe, D. B. R. Dasari, A. Auburger, A. Gali, J. H. Smet, and J. Wrachtrup, Nat. Mater. 20, 1079 (2021).
  18. H. L. Stern, M. Gilardoni, and Q. Gu et al., Nat. Mater. 23, 1379 (2024).
  19. X. Gao, S. Vaidya, and K. Li et al., Nature (London) 643, 943 (2025).
  20. V. Ivády, G. Barcza, G. Thiering, S. Li, H. Hamdi, J.-P. Chou, O. Legeza, and A. Gali, npj Comput. Mater. 6, 41 (2020).
  21. I. N. Gracheva, F. F. Murzakhanov, G. V. Mamin, M. A. Sadovnikova, B. F. Gabbasov, E. N. Mokhov, and M. R. Gafurov, J. Phys. Chem. C 127, 3634 (2023).
  22. W. Lee, V. S. Liu, Z. Zhang, S. Kim, R. Gong, X. Du, K. Pham, T. Poirier, Z. Hao, J. H. Edgar, P. Kim, C. Zu, E. J. Davis, and N. Y. Yao, Phys. Rev. Lett. 134, 096202 (2025).
  23. G. V. Mamin, E. V. Dmitrieva, F. F. Murzakhanov, I. N. Gracheva, E. N. Mokhov, I. I. Vlasov, M. R. Gafurov, U. Gerstmann, and V. A. Soltamov, Appl. Phys. Lett. 127, 024001 (2025).
  24. X. Gao, S. Vaidya, K. Li, P. Ju, B. Jiang, Z. Xu, A. E. Llacsahuanga Allcca, K. Shen, T. Taniguchi, K. Watanabe, S. A. Bhave, Y. P. Chen, Y. Ping, and T. Li, Nat. Mater. 21, 1024 (2022).
  25. S. Ru, Z. Jiang, H. Liang, J. Kenny, H. Cai, X. Lyu, R. Cernansky, F. Zhou, Y. Yang, K. Watanabe, T. Taniguchi, F. Li, T. S. Koh, X. Liu, F. Jelezko, A. A. Bettiol, and W. Gao, Phys. Rev. Lett. 132, 266801 (2024).
  26. A. Tibiássy, C. J. Patrickson, T. Poirier, J. H. Edgar, B. Lopez-Rodriguez, V. Ivady, and I. J. Luxmoore, Adv. Funct. Mater. 36, e24710 (2026).
  27. M. Ye, H. Seo, and G. Galli, npj Comput. Mater. 5, 44 (2019).
  28. J. Lee, H. Kim, H. Park, and H. Seo, Adv. Funct. Mater. 36, e2511274 (2026).
  29. F. T. Tabesh, S. Rahimi-Keshari, and M. Abdi, Quantum Sci. Technol. 10, 035064 (2025).
  30. A. Tárkányi and V. Ivády, Adv. Funct. Mater. 36, 2511300 (2026).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/nmsz-9p3k for the pulse sequences used in the ESE, ENDOR, and nuclear spin echo measurements, details of the DFT calculations, the calculated spin density, the fitting parameters of the nuclear Rabi oscillations, and the derivation of the 2D dipolar hyperfine lattice sum, which includes Refs. [32–40].
  32. S. Blügel, H. Akai, R. Zeller, and P. H. Dederichs, Phys. Rev. B 35, 3271 (1987).
  33. P. Giannozzi et al., J. Phys. Condens. Matter 21, 395502 (2009).
  34. P Giannozzi et al., J. Phys. Condens. Matter 29, 465901 (2017).
  35. J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003).
  36. S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).
  37. I. Lovchinsky, J. D. Sanchez-Yamagishi, E. K. Urbach, S. Choi, S. Fang, T. I. Andersen, K. Watanabe, T. Taniguchi, A. Bylinskii, E. Kaxiras, P. Kim, H. Park, and M. D. Lukin, Science 355, 503 (2017).
  38. G. Jeschke, W. Hoffbauer, and M. Jansen, Solid State Nucl. Magn. Reson. 12, 1 (1998).
  39. A. H. Silver and P. J. Bray, J. Chem. Phys. 32, 288 (1960).
  40. K. L. Franzke, W. G. Schmidt, and U. Gerstmann, J. Phys. Conf. Ser. 2701, 012094 (2024).
  41. E. R. Davies, Phys. Lett. 47A, 1 (1974).
  42. W. B. Mims, Proc. R. Soc. A 283, 452 (1965).
  43. F. F. Murzakhanov, B. V. Yavkin, G. V. Mamin, S. B. Orlinskii, I. E. Mumdzhi, I. N. Gracheva, B. F. Gabbasov, A. N. Smirnov, V. Y. Davydov, and V. A. Soltamov, Nanomater. Nanotechnol. 11, 1373 (2021).
  44. A. J. Healey, P. Singh, and I. O. Robertson et al., Mater. Quantum Technol. 4, 035701 (2024).
  45. R. Gong, G. He, X. Gao, P. Ju, Z. Liu, B. Ye, E. A. Henriksen, T. Li, and C. Zu, Nat. Commun. 14, 3299 (2023).
  46. E. J. Davis, B. Ye, F. Machado, S. A. Meynell, W. Wu, T. Mittiga, W. Schenken, M. Joos, B. Kobrin, Y. Lyu, Z. Wang, D. Bluvstein, S. Choi, C. Zu, A. C. Bleszynski Jayich, and N. Y. Yao, Nat. Phys. 19, 836 (2023).
  47. C. Gemperle, A. Schweiger, and R. R. Ernst, Chem. Phys. Lett. 145, 1 (1988).
  48. H.-J. Lim, S. Welinski, A. Ferrier, P. Goldner, and J. J. L. Morton, Phys. Rev. B 97, 064409 (2018).
  49. J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. L. Morton, F. A. Zwanenburg, D. N. Jamieson, A. S. Dzurak, and A. Morello, Nature (London) 496, 334 (2013).
  50. E. A. Chekhovich, M. Hopkinson, M. S. Skolnick, and A. I. Tartakovskii, Nat. Commun. 6, 6348 (2015).
  51. H. E. Dyte, S. Manna, S. F. Covre da Silva, A. Rastelli, and E. A. Chekhovich, Nat. Commun. 17, 239 (2026).
  52. Y. Nakamura, S. Nishimura, T. Iwasaki, S. Nakaharai, S. Ogawa, Y. Morita, K. Watanabe, T. Taniguchi, K. Sasaki, and K. Kobayashi, Phys. Rev. B 111, 195404 (2025).

Outline

Information

Phys. Rev. Lett. 137, 186701– Published 26 October, 2026
  • Received 23 May 2026
  • Accepted 28 September 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation