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Electronic states, spin-orbit coupling, and magnetism induced by 60∘ dislocations in germanium

Veronica Regazzoni, Fabrizio Rovaris, Anna Marzegalli, Francesco Montalenti, and Emilio Scalise*

  • *Contact author: emilio.scalise@unimib.it

Phys. Rev. B 114, 245201 – Published 5 October, 2026

DOI: https://doi.org/10.1103/n1dx-1k1b

Abstract

Defects in semiconductors have recently attracted renewed interest owing to their potential in novel quantum applications. Here we investigate the electronic and magnetic properties induced by 60° dislocations in Ge. Using large-scale density functional theory calculations, we determine the band structure for both the shuffle and glide sets in their lowest-energy configurations. The band structure for the shuffle set reveals defect-induced dispersive bands localized within the band gap near the Γ point, whereas for the glide set we observe strong overlap with the conduction band. Defect-induced band splitting evident away from Γ reveals Rashba-Dresselhaus spin-orbit coupling, an effect previously reported only for screw dislocations. Remarkably, we find evidence that specific dislocation arrangements can stabilize antiferromagnetic ordering with sizable local magnetic moments and considerable exchange splitting between opposite spin states. These results uncover rich physics in Ge dislocations through the combination of spin-orbit coupling and magnetic ordering, potentially enabling novel defect-based functionalities in Ge devices.

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References (64)

  1. G. Scappucci, C. Kloeffel, F. A. Zwanenburg, D. Loss, M. Myronov, J.-J. Zhang, S. De Franceschi, G. Katsaros, and M. Veldhorst, The germanium quantum information route, Nat. Rev. Mater. 6, 926 (2021).
  2. T. Koch, C. Godfrin, V. Adam, J. Ferrero, D. Schroller, N. Glaeser, S. Kubicek, R. Li, R. Loo, S. Massar, G. Simion, D. Wan, K. De Greve, and W. Wernsdorfer, Industrial 300 mm wafer processed spin qubits in natural silicon/silicon-germanium, npj Quantum Inf. 11, 59 (2025).
  3. Y. Shimura, C. Godfrin, A. Hikavyy, R. Li, J. Aguilera, G. Katsaros, P. Favia, H. Han, D. Wan, K. De Greve, and R. Loo, Compressively strained epitaxial Ge layers for quantum computing applications, Mater. Sci. Semicond. Process. 174, 108231 (2024).
  4. J. W. Matthews and A. E. Blakeslee, Defects in epitaxial multilayers: I. Misfit dislocations, J. Cryst. Growth 27, 118 (1974).
  5. R. People and J. C. Bean, Calculation of critical layer thickness versus lattice mismatch for GexSi1−x/Si strained-layer heterostructures, Appl. Phys. Lett. 47, 322 (1985).
  6. V. Ivády, J. Davidsson, N. Delegan, A. L. Falk, P. V. Klimov, S. J. Whiteley, S. O. Hruszkewycz, M. V. Holt, F. Joseph Heremans, N. T. Son, D. D. Awschalom, I. A. Abrikosov, and A. Gali, Stabilization of point-defect spin qubits by quantum wells, Nat. Commun. 10, 5607 (2019).
  7. D. Barragan-Yani and L. Wirtz, Assessing the potential of perfect screw dislocations in SiC for solid-state quantum technologies, Phys. Rev. Res. 6, L022055 (2024).
  8. J. A. Steele, P. J. Strohbeen, C. Verdi, A. Baktash, A. Danilenko, Y.-H. Chen, J. van Dijk, F. H. Knudsen, A. Leblanc, D. Perconte, L. Wang, E. Demler, S. Salmani-Rezaie, P. Jacobson, and J. Shabani, Superconductivity in substitutional Ga-hyperdoped Ge epitaxial thin films, Nat. Nanotechnol. 20, 1757 (2025).
  9. S. Polat Genlik, R. C. Myers, and M. Ghazisaeidi, Dislocations as natural quantum wires in diamond, Phys. Rev. Mater. 7, 024601 (2023).
  10. V. Krivobok, S. Nikolaev, S. Chentsov, E. Onishchenko, A. Pruchkina, V. Bagaev, A. Silina, and N. Smirnova, Two types of isolated (quantum) emitters related to dislocations in crystalline CdZnTe, J. Lumin. 200, 240 (2018).
  11. X. Li, B. Han, R. Zhu, R. Shi, M. Wu, Y. Sun, Y. Li, B. Liu, L. Wang, J. Zhang, C. Tan, P. Gao, and X. Bai, Dislocation-tuned ferroelectricity and ferromagnetism of the BiFeO3/SrRuO3 interface, Proc. Natl. Acad. Sci. USA 120, e2213650120 (2023).
  12. Y. Liang, D. Yi, T. Nan, S. Liu, L. Zhao, Y. Zhang, H. Chen, T. Xu, M. Dai, J.-M. Hu, B. Xu, J. Shi, W. Jiang, R. Yu, and Y.-H. Lin, Field-free spin-orbit switching of perpendicular magnetization enabled by dislocation-induced in-plane symmetry breaking, Nat. Commun. 14, 5458 (2023).
  13. C. Zhang, V. W.-z. Yu, Y. Jin, J. Nagura, S. P. Genlik, M. Ghazisaeidi, and G. Galli, Towards dislocation-driven quantum interconnects, npj Comput. Mater. 12, 77 (2026).
  14. E. A. Fitzgerald, Jr., The Properties, Control and Elimination of Misfit Dislocations in Semiconductor Heterostructures (Cornell University, Ithaca, NY, 1989).
  15. J. P. Hirth, J. Lothe, and T. Mura, Theory of dislocations, J. Appl. Mech. 50, 476 (1983).
  16. P. Humble and R. H. J. Hannink, Plastic deformation of diamond at room temperature, Nature (London) 273, 37 (1978).
  17. P. Mooney, Strain relaxation and dislocations in SiGe/Si structures, Mater. Sci. Eng.: R: Rep. 17, 105 (1996).
  18. Y. B. Bolkhovityanov and L. V. Sokolov, Ge-on-Si films obtained by epitaxial growing: Edge dislocations and their participation in plastic relaxation, Semicond. Sci. Technol. 27, 043001 (2012).
  19. F. Rovaris, M. H. Zoellner, P. Zaumseil, M. A. Schubert, A. Marzegalli, L. Di Gaspare, M. De Seta, T. Schroeder, P. Storck, G. Schwalb, C. Richter, T. U. Schülli, G. Capellini, and F. Montalenti, Misfit-dislocation distributions in heteroepitaxy: From mesoscale measurements to individual defects and back, Phys. Rev. Appl. 10, 054067 (2018).
  20. A. Marzegalli, M. Brunetto, M. Salvalaglio, F. Montalenti, G. Nicotra, M. Scuderi, C. Spinella, M. De Seta, and G. Capellini, Onset of plastic relaxation in the growth of Ge on Si(001) at low temperatures: Atomic-scale microscopy and dislocation modeling, Phys. Rev. B 88, 165418 (2013).
  21. F. K. LeGoues, B. S. Meyerson, and J. F. Morar, Anomalous strain relaxation in SiGe thin films and superlattices, Phys. Rev. Lett. 66, 2903 (1991).
  22. T. Wang, Y. Zhang, and S. Chua, Dislocation evolution in epitaxial multilayers and graded composition buffers, Acta Mater. 49, 1599 (2001).
  23. E. A. Fitzgerald, M. T. Currie, S. B. Samavedam, T. A. Langdo, G. Taraschi, V. Yang, C. W. Leitz, and M. T. Bulsara, Dislocations in relaxed SiGe/Si heterostructures, Phys. Status Solidi A 171, 227 (1999).
  24. O. Skibitzki, M. H. Zoellner, F. Rovaris, M. A. Schubert, Y. Yamamoto, L. Persichetti, L. Di Gaspare, M. De Seta, R. Gatti, F. Montalenti, and G. Capellini, Reduction of threading dislocation density beyond the saturation limit by optimized reverse grading, Phys. Rev. Mater. 4, 103403 (2020).
  25. R. D. Arroyo, F. Isa, G. Isella, R. Erni, H. von Känel, P. Gröning, and M. D. Rossell, Effect of thermal annealing on the interface quality of Ge/Si heterostructures, Scr. Mater. 170, 52 (2019).
  26. F. Rovaris, F. Isa, R. Gatti, A. Jung, G. Isella, F. Montalenti, and H. von Känel, Three-dimensional SiGe/Si heterostructures: Switching the dislocation sign by substrate under-etching, Phys. Rev. Mater. 1, 073602 (2017).
  27. J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
  28. J. E. Peralta, J. Heyd, G. E. Scuseria, and R. L. Martin, Spin-orbit splittings and energy band gaps calculated with the Heyd-Scuseria-Ernzerhof screened hybrid functional, Phys. Rev. B 74, 073101 (2006).
  29. A. D. Becke and E. R. Johnson, A simple effective potential for exchange, J. Chem. Phys. 124, 221101 (2006).
  30. F. Tran, P. Blaha, and K. Schwarz, Band gap calculations with Becke–Johnson exchange potential, J. Phys.: Condens. Matter 19, 196208 (2007).
  31. F. Tran and P. Blaha, Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential, Phys. Rev. Lett. 102, 226401 (2009).
  32. E. Scalise, L. Barbisan, A. Sarikov, F. Montalenti, L. Miglio, and A. Marzegalli, The origin and nature of killer defects in 3C-SiC for power electronic applications by a multiscale atomistic approach, J. Mater. Chem. C 8, 8380 (2020).
  33. E. M. T. Fadaly, A. Marzegalli, Y. Ren, L. Sun, A. Dijkstra, D. de Matteis, E. Scalise, A. Sarikov, M. De Luca, R. Rurali, I. Zardo, J. E. M. Haverkort, S. Botti, L. Miglio, E. P. A. M. Bakkers, and M. A. Verheijen, Unveiling planar defects in hexagonal Group IV materials, Nano Lett. 21, 3619 (2021).
  34. L. Hu, H. Huang, Z. Wang, W. Jiang, X. Ni, Y. Zhou, V. Zielasek, M. G. Lagally, B. Huang, and F. Liu, Ubiquitous spin-orbit coupling in a screw dislocation with high spin coherency, Phys. Rev. Lett. 121, 066401 (2018).
  35. 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).
  36. 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).
  37. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  38. G. I. Csonka, J. P. Perdew, A. Ruzsinszky, P. H. T. Philipsen, S. Lebègue, J. Paier, O. A. Vydrov, and J. G. Ángyán, Assessing the performance of recent density functionals for bulk solids, Phys. Rev. B 79, 155107 (2009).
  39. G.-X. Zhang, A. M. Reilly, A. Tkatchenko, and M. Scheffler, Performance of various density-functional approximations for cohesive properties of 64 bulk solids, New J. Phys. 20, 063020 (2018).
  40. J. P. Perdew, A. Ruzsinszky, J. Tao, V. N. Staroverov, G. E. Scuseria, and G. I. Csonka, Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits, J. Chem. Phys. 123, 062201 (2005).
  41. C. Rödl, J. Furthmüller, J. R. Suckert, V. Armuzza, F. Bechstedt, and S. Botti, Accurate electronic and optical properties of hexagonal germanium for optoelectronic applications, Phys. Rev. Mater. 3, 034602 (2019).
  42. A. Marzegalli, F. Montalenti, and E. Scalise, Polytypic quantum wells in Si and Ge: Impact of 2D hexagonal inclusions on electronic band structure, Nanoscale Horiz. 9, 2320 (2024).
  43. C. Kittel, Introduction to Solid State Physics, 8th ed. (John Wiley & Sons, Hoboken, NJ, 2005).
  44. O. Rubel, A. Bokhanchuk, S. J. Ahmed, and E. Assmann, Unfolding the band structure of disordered solids: From bound states to high-mobility Kane fermions, Phys. Rev. B 90, 115202 (2014).
  45. L.-W. Wang, L. Bellaiche, S.-H. Wei, and A. Zunger, “Majority representation” of alloy electronic states, Phys. Rev. Lett. 80, 4725 (1998).
  46. W. Cai, V. V. Bulatov, J. Chang, J. Li, and S. Yip, Anisotropic elastic interactions of a periodic dislocation array, Phys. Rev. Lett. 86, 5727 (2001).
  47. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  48. L. Pizzagalli, J. Godet, J. Guénolé, and S. Brochard, Dislocation cores in silicon: New aspects from numerical simulations, in Journal of Physics: Conference Series Vol. 281 (IOP Publishing, Bristol, England, 2011), p. 012002.
  49. J. Hornstra, Dislocations in the diamond lattice, J. Phys. Chem. Solids 5, 129 (1958).
  50. D. Hull and D. J. Bacon, Introduction to Dislocations (Elsevier, Amsterdam, 2011), Vol. 37.
  51. L. Barbisan, A. Marzegalli, and F. Montalenti, Atomic-scale insights on the formation of ordered arrays of edge dislocations in Ge/Si (001) films via molecular dynamics simulations, Sci. Rep. 12, 3235 (2022).
  52. Z. Zhang, X. Zou, V. H. Crespi, and B. I. Yakobson, Intrinsic magnetism of grain boundaries in two-dimensional metal dichalcogenides, ACS Nano 7, 10475 (2013).
  53. I. I. Naumov and P. Dev, One-dimensional magnetism and Rashba-like effects in zigzag bismuth nanoribbons, Phys. Rev. Mater. 7, 026204 (2023).
  54. T. Arguirov, M. Kittler, M. Oehme, N. V. Abrosimov, O. F. Vyvenko, E. Kasper, and J. Schulze, Luminescence from germanium and germanium on silicon, Solid State Phenom. 205, 383 (2014).
  55. M. Kittler, T. Arguirov, M. Oehme, Y. Yamamoto, B. Tillack, and N. V. Abrosimov, Photoluminescence study of Ge containing crystal defects, Phys. Status Solidi A 208, 754 (2011).
  56. F. Pezzoli, F. Isa, G. Isella, C.V. Falub, T. Kreiliger, M. Salvalaglio, R. Bergamaschini, E. Grilli, M. Guzzi, H. von Känel, and L. Miglio, Ge crystals on Si show their light, Phys. Rev. Appl. 1, 044005 (2014).
  57. K. Tanaka, M. Suezawa, and I. Yonenaga, Photoluminescence spectra of deformed Si-Ge alloy, J. Appl. Phys. 80, 6991 (1996).
  58. P. Grillot, S. Ringel, and E. Fitzgerald, Effect of composition on deep levels in heteroepitaxial GexSi1−x layers and evidence for dominant intrinsic recombination-generation in relaxed Ge layers on Si, J. Electron. Mater. 25, 1028 (1996).
  59. G. S. Hubbard and E. E. Haller, Electrical properties of dislocations in ultra-pure germanium, J. Electron. Mater. 9, 51 (1980).
  60. C. Claeys and E. Simoen, Extended Defects in Germanium: Fundamental and Technological Aspects (Springer, Berlin, 2009).
  61. V. Regazzoni, F. Rovaris, A. Marzegalli, and E. Scalise, Atomistic structures of the 60° dislocations in 3C germanium, Zenodo, 2026, 10.5281/zenodo.22796437.
  62. C. Wilhelmer, D. Waldhoer, L. Cvitkovich, D. Milardovich, M. Waltl, and T. Grasser, Over-and undercoordinated atoms as a source of electron and hole traps in amorphous silicon nitride (a-Si3N4), Nanomaterials 13, 2286 (2023).
  63. R. Atta-Fynn, P. Biswas, P. Ordejón, and D. A. Drabold, Systematic study of electron localization in an amorphous semiconductor, Phys. Rev. B 69, 085207 (2004).
  64. T. Ogawa, K. Tsuruta, and H. Iyetomi, An ab initio analysis of electronic states associated with a silicon vacancy in cubic symmetry, Solid State Commun. 151, 1605 (2011).

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