Physics:Semi-Dirac fermion

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Short description: Class of fermionic quasiparticles

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. More precisely, they disperse linearly along a given direction in momentum space, and quadratically in the orthogonal direction[1]. 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 [2][3]. These excitations have been experimentally observed in a wide range of physical contexts from cold atoms trapped in optical lattices[4], to the nodal line semi-metal zirconium silicon sulfide (ZrSiS), which is the first unambiguous detection in solids[5]. Different approaches have been taken to generalizations, such as considering arbitrary numbers of quadratically and linearly dispersing dimensions [6], or replacing the quadratic term with an arbitrary even power law [7]. 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 [8].

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[9]. 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[10].

See also

References

  1. ↑ 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" (in en). The European Physical Journal B 72 (4): 509–520. doi:10.1140/epjb/e2009-00383-0. ISSN 1434-6036. https://doi.org/10.1140/epjb/e2009-00383-0. 
  2. ↑ Kotov, Valeri N.; Uchoa, Bruno; Sushkov, Oleg P. (2021-01-06). "Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition" (in en). Physical Review B 103 (4). doi:10.1103/PhysRevB.103.045403. ISSN 2469-9950. https://link.aps.org/doi/10.1103/PhysRevB.103.045403. 
  3. ↑ Banerjee, S.; Pickett, W. E. (2012-08-15). "Phenomenology of a semi-Dirac semi-Weyl semimetal" (in en). Physical Review B 86 (7). doi:10.1103/PhysRevB.86.075124. ISSN 1098-0121. https://link.aps.org/doi/10.1103/PhysRevB.86.075124. 
  4. ↑ 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" (in en). Nature 483 (7389): 302–305. doi:10.1038/nature10871. ISSN 1476-4687. https://www.nature.com/articles/nature10871. 
  5. ↑ Shao, Yinming; Moon, Seongphill; Rudenko, A. N.; Wang, Jie; Herzog-Arbeitman, Jonah; Ozerov, Mykhaylo; Graf, David; Sun, Zhiyuan et al. (2024-12-05). "Semi-Dirac Fermions in a Topological Metal" (in en). Physical Review X 14 (4). doi:10.1103/PhysRevX.14.041057. ISSN 2160-3308. https://link.aps.org/doi/10.1103/PhysRevX.14.041057. 
  6. ↑ Sur, Shouvik; Roy, Bitan (2019-11-12). "Unifying Interacting Nodal Semimetals: A New Route to Strong Coupling" (in en). Physical Review Letters 123 (20). doi:10.1103/PhysRevLett.123.207601. ISSN 0031-9007. https://link.aps.org/doi/10.1103/PhysRevLett.123.207601. 
  7. ↑ Elsayed, Mohamed M.; Uchoa, Bruno; Kotov, Valeri N. (2025-04-15). "Coulomb interactions in systems of generalized semi-Dirac fermions" (in en). Physical Review B 111 (16). doi:10.1103/PhysRevB.111.165127. ISSN 2469-9950. https://link.aps.org/doi/10.1103/PhysRevB.111.165127. 
  8. ↑ 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. doi:10.1088/1361-648X/adf0d4. ISSN 0953-8984. https://iopscience.iop.org/article/10.1088/1361-648X/adf0d4. 
  9. ↑ Huang, Huaqing; Liu, Zhirong; Zhang, Hongbin; Duan, Wenhui; Vanderbilt, David (2015-10-28). "Emergence of a Chern-insulating state from a semi-Dirac dispersion" (in en). Physical Review B 92 (16). doi:10.1103/PhysRevB.92.161115. ISSN 1098-0121. https://link.aps.org/doi/10.1103/PhysRevB.92.161115. 
  10. ↑ Elsayed, Mohamed M.; Lakoba, Taras I.; Kotov, Valeri N. (2026-03-28), Interacting type-II semi-Dirac quasiparticles, arXiv, doi:10.48550/arXiv.2601.21098, arXiv:2601.21098, http://arxiv.org/abs/2601.21098, retrieved 2026-04-17 




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