Semi-Dirac fermion

In condensed matter physics, semi-Dirac fermions are a class of quasiparticles that can exhibit both massless (like light) and massive (like conventional particles) behavior depending on the direction of propagation[1]. More precisely, they disperse linearly along a given direction in momentum space, and quadratically in the orthogonal direction.[2] This exotic electronic structure can emerge at the critical point of a topological phase transition from semimetal to insulator wherein two Dirac cones coalesce, giving rise to a semi-Dirac point. Note that the Berry phases annihilate, resulting in topologically trivial quasiparticles. The fundamental anisotropy leads to a variety of unique properties and novel phenomena.[3][4] These excitations have been experimentally observed in a wide range of physical contexts from cold atoms trapped in optical lattices,[5] to the nodal line semi-metal zirconium silicon sulfide (ZrSiS), which is the first unambiguous detection in solids.[6] Different approaches have been taken to generalizations, such as considering arbitrary numbers of quadratically and linearly dispersing dimensions,[7] or replacing the quadratic term with an arbitrary even power law.[8] For the latter, an interacting microscopic model has been proposed as the first theoretical realization of the higher-order quartic semi-Dirac fermions in two-dimensions.[9]

There are also type-II semi-Dirac fermions, which were proposed as a model to explain the coexisting non-trivial topological, and semi-Dirac, behavior in titanium/vanadium oxide heterostructures.[10] These excitations occur at the merger of three Dirac cones, leaving a finite Berry phase and the associated topological properties. The critical spectrum possesses semi-Dirac character in the sense that it is linear and parabolic along the principal axes, but displays a different admixture of momentum components for an arbitrary direction of motion. Moreover the system remains semimetallic following the transition, with both Dirac and type-II semi-Dirac properties appearing at different Fermi levels. Long-range Coulomb interactions have been shown to drive the system to this electronic phase[11].

See also

References

  1. ↑ Uchoa, Bruno; Elsayed, Mohamed M.; Kotov, Valeri N.; Shao, Yinming; Basov, Dmitri N. (2026-07-22), Colloquium: Semi-Dirac Fermions in Quantum Matter, arXiv, doi:10.48550/arXiv.2607.20627, arXiv:2607.20627, retrieved 2026-08-20
  2. ↑ Montambaux, G.; Piéchon, F.; Fuchs, J.-N.; Goerbig, M. O. (2009-12-01). "A universal Hamiltonian for motion and merging of Dirac points in a two-dimensional crystal". The European Physical Journal B. 72 (4): 509–520. arXiv:0907.0500. Bibcode:2009EPJB...72..509M. doi:10.1140/epjb/e2009-00383-0. ISSN 1434-6036.
  3. ↑ Kotov, Valeri N.; Uchoa, Bruno; Sushkov, Oleg P. (2021-01-06). "Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition". Physical Review B. 103 (4) 045403. arXiv:2008.04326. Bibcode:2021PhRvB.103d5403K. doi:10.1103/PhysRevB.103.045403. ISSN 2469-9950.
  4. ↑ Banerjee, S.; Pickett, W. E. (2012-08-15). "Phenomenology of a semi-Dirac semi-Weyl semimetal". Physical Review B. 86 (7) 075124. arXiv:1207.5760. Bibcode:2012PhRvB..86g5124B. doi:10.1103/PhysRevB.86.075124. ISSN 1098-0121.
  5. ↑ Tarruell, Leticia; Greif, Daniel; Uehlinger, Thomas; Jotzu, Gregor; Esslinger, Tilman (March 2012). "Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice". Nature. 483 (7389): 302–305. arXiv:1111.5020. Bibcode:2012Natur.483..302T. doi:10.1038/nature10871. ISSN 1476-4687. PMID 22422263.
  6. ↑ Shao, Yinming; Moon, Seongphill; Rudenko, A. N.; Wang, Jie; Herzog-Arbeitman, Jonah; Ozerov, Mykhaylo; Graf, David; Sun, Zhiyuan; Queiroz, Raquel; Lee, Seng Huat; Zhu, Yanglin; Mao, Zhiqiang; Katsnelson, M. I.; Bernevig, B. Andrei; Smirnov, Dmitry (2024-12-05). "Semi-Dirac Fermions in a Topological Metal". Physical Review X. 14 (4) 041057. arXiv:2311.03735. Bibcode:2024PhRvX..14d1057S. doi:10.1103/PhysRevX.14.041057. ISSN 2160-3308.
  7. ↑ Sur, Shouvik; Roy, Bitan (2019-11-12). "Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling". Physical Review Letters. 123 (20) 207601. arXiv:1812.05615. Bibcode:2019PhRvL.123t7601S. doi:10.1103/PhysRevLett.123.207601. ISSN 0031-9007. PMID 31809112.
  8. ↑ Elsayed, Mohamed M.; Uchoa, Bruno; Kotov, Valeri N. (2025-04-15). "Coulomb interactions in systems of generalized semi-Dirac fermions". Physical Review B. 111 (16) 165127. arXiv:2410.22572. Bibcode:2025PhRvB.111p5127E. doi:10.1103/PhysRevB.111.165127. ISSN 2469-9950.
  9. ↑ Elsayed, Mohamed M; Kotov, Valeri N (2025-08-08). "Microscopic lattice model for quartic semi-Dirac fermions in two dimensions". Journal of Physics: Condensed Matter. 37 (31): 315501. arXiv:2505.06479. Bibcode:2025JPCM...37E5501E. doi:10.1088/1361-648X/adf0d4. ISSN 0953-8984. PMID 40669491.
  10. ↑ Huang, Huaqing; Liu, Zhirong; Zhang, Hongbin; Duan, Wenhui; Vanderbilt, David (2015-10-28). "Emergence of a Chern-insulating state from a semi-Dirac dispersion". Physical Review B. 92 (16) 161115. arXiv:1507.01742. Bibcode:2015PhRvB..92p1115H. doi:10.1103/PhysRevB.92.161115. ISSN 1098-0121.
  11. ↑ Elsayed, Mohamed M.; Lakoba, Taras I.; Kotov, Valeri N. (2026-07-30). "Interacting type-II semi-Dirac quasiparticles". Physical Review Research. 8 (3): 033128. doi:10.1103/6ktq-2nn6.
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