Breakdown of Dirac dynamics in honeycomb lattices due to nonlinear interactions
Open accessAbstract
We study the dynamics of coherent waves in nonlinear honeycomb lattices and show that nonlinearity breaks down the Dirac dynamics. As an example, we demonstrate that even a weak nonlinearity has major qualitative effects on one of the hallmarks of honeycomb lattices: conical diffraction. Under linear conditions, a circular input wave packet associated with the Dirac point evolves into a ring, but even a weak nonlinearity alters the evolution such that the emerging beam possesses triangular symmetry, and populates Bloch modes outside of the Dirac cone. Our results are presented in the context of optics, but we propose a scheme to observe equivalent phenomena in Bose-Einstein condensates.
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Many works have remarked that the Hermiticity of the underlying Hamiltonian can be relaxed and a consistent quantum theory can be constructed for a broader class of Hamiltonians, in particular those possessing parity-time (PT) symmetry.
“Indeed, many works have remarked that the Hermiticity of the underlying Hamiltonian can be relaxed, and that a a consistent quantum theory can be constructed for a broader class of Hamiltonians [85,86,87,88], in particular those possessing parity-time ( PT ) symmetry.”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [86]
The Abstract (p. 1) concerns nonlinear wave dynamics in honeycomb lattices, and the conclusion (p. 9) concerns the breakdown of the Dirac approximation. Searches for relaxed Hermiticity, consistent quantum theory, and parity-time (PT) symmetry found no passage in our copy addressing the attributed claim. (LLM, conf=0.75)
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Cites
Two-dimensional gas of massless Dirac fermions in graphene
Novoselov, K. S., Geim, A. K., Morozov, S. V., Jiang, D., Katsnelson, M. I., Grigorieva, I. V., Dubonos, S. V., & Firsov, A. A. (2005) · Nature · doi:10.1038/nature04233 · Cited by 21,611 · see citing works
Chiral tunnelling and the Klein paradox in graphene
Katsnelson, M. I., Novoselov, K. S., & Geim, A. K. (2006) · Nature Physics · doi:10.1038/nphys384 · Cited by 3,896 · see citing works
Quantum interference and Klein tunnelling in graphene heterojunctions
Young, A. F., & Kim, P. (2009) · Nature Physics · doi:10.1038/nphys1198 · Cited by 1,183 · see citing works
Conical Diffraction and Gap Solitons in Honeycomb Photonic Lattices
Peleg, O., Bartal, G., Freedman, B., Manela, O., Segev, M., & Christodoulides, D. N. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.103901 · Cited by 378 · see citing works
Self-citationExtremal transmission at the Dirac point of a photonic band structure
Sepkhanov, R. A., Bazaliy, Y. B., & Beenakker, C. W. J. (2007) · Physical Review A · doi:10.1103/physreva.75.063813 · Cited by 250 · see citing works
Theory of electron Zitterbewegung in graphene probed by femtosecond laser pulses
Rusin, T. M., & Zawadzki, W. (2009) · Physical Review B · doi:10.1103/physrevb.80.045416 · Cited by 133 · see citing works
Conical diffraction in honeycomb lattices
Ablowitz, M. J., Nixon, S. D., & Zhu, Y. (2009) · Physical Review A · doi:10.1103/physreva.79.053830 · Cited by 109 · see citing works
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Szameit, A., Rechtsman, M. C., Bahat-Treidel, O., & Segev, M. (2011) · Physical Review A · doi:10.1103/physreva.84.021806 · Cited by 280 · see citing works
Self-citationClassical simulation of relativistic quantum mechanics in periodic optical structures
Longhi, S. (2011) · Applied Physics B · doi:10.1007/s00340-011-4628-7 · Cited by 72 · see citing works
Pseudospin and nonlinear conical diffraction in Lieb lattices
Leykam, D., Bahat-Treidel, O., & Desyatnikov, A. S. (2012) · Physical Review A · doi:10.1103/physreva.86.031805 · Cited by 62 · see citing works
Self-citationNonlinear wave dynamics in honeycomb lattices
Bahat-Treidel, O., & Segev, M. (2011) · Physical Review A · doi:10.1103/physreva.84.021802 · Cited by 26 · see citing works
Self-citation
- Authors
- Bahat-Treidel, O., Peleg, O., Segev, M., & Buljan, H.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2010-07-26
- Volume
- 82
- Issue
- 1
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2058404058
- Cited by
- 44
- References
- 7
- Citations by year
- 2026: 2 · 2024: 1 · 2021: 1 · 2020: 2 · 2018: 1 · 2017: 1 · 2016: 3 · 2015: 6 · 2014: 5 · 2013: 5 · 2012: 7
- FWCI
- 4.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Photonic Systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- honeycomb lattice, Dirac cones, nonlinear optics, conical diffraction, Dirac point, weak nonlinearity, Bloch modes, Bose-Einstein condensate, wave packet evolution
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