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Nonlinear topological states in the Su–Schrieffer–Heeger model

https://doi.org/10.17586/2220-8054-2017-8-6-695-700

Аннотация

Topological photonics offers unique functionalities in light manipulation at the nanoscale by means of the so-called topological states which are robust against various forms of disorder. One of the simplest one-dimensional models supporting topological states is the Su–Schrieffer–Heeger model. In this paper, we review the physics of the Su–Schrieffer–Heeger model and its nonlinear counterparts exhibiting self-induced, tunable and many-particle edge states. We discuss the robustness of these states, highlighting their rich potential for nanophotonic and quantum optics applications.

Об авторах

M. A. Gorlach
ITMO University
Россия

Kronverkskiy, 49, St. Petersburg, 197101



A. P. Slobozhanyuk
ITMO University
Россия

Kronverkskiy, 49, St. Petersburg, 197101



Список литературы

1. Lu L., Joannopoulos J.D., Soljačić M. Topological photonics. Nature Photonics, 2014, 8 (5), P. 821–829.

2. Lu L., Joannopoulos J.D., Soljačić M. Topological states in photonic systems. Nature Physics, 2016, 12 (7), P. 626–629.

3. Khanikaev A.B., Shvets G. Two-dimensional topological photonics, Nature Photonics, 2017, 11, P. 763–773.

4. Leykam D., Chong Y.D. Edge solitons in nonlinear-photonic topological insulators. Physical Review Letters, 2016, 117 (14), P. 143901.

5. Chen B.G., Upadhyaya N., Vitelli V. Nonlinear conduction via solitons in a topological mechanical insulator. Proceedings of the National Academy of Sciences of the United States of America, 2014, 111 (36), P. 13004–13009.

6. Gulevich D.R., Yudin D., et al. Exploring nonlinear topological states of matter with excition-polaritons: Edge solitons in kagome lattice. Scientific Reports, 2017, 7 (1), P. 1780.

7. Hadad Y., Khanikaev A.B., Alu A. Self-induced topological transitions and edge states supported by the nonlinear staggered potentials. Physical Review B, 2016, 93 (15), P. 155112.

8. Hadad Y., Vitelli V., Alu A. Solitons and Propagating Domain Walls in Topological Resonator Arrays. ACS Photonics, 2017, 4 (8), P. 1974–1979.

9. Di Liberto M., Recati A., Carusotto I., Menotti C. Two-body physics in the Su–Schrieffer–Heeger model. Physical Review A, 2016, 94 (6), P. 062704.

10. Gorlach M.A., Poddubny A.N. Topological edge states of bound photon pairs. Physical Review A, 2017, 95 (5), P. 053866.

11. Su W.P., Schrieffer J.R., Heeger A.A. Solitons in polyacetylene. Physical Review Letters, 1979, 42 (25), P. 1698–1701.

12. Heeger A.J., Kivelson S., Schrieffer J.R., Su W.P. Solitons in conducting polymers. Reviews of Modern Physics, 1988, 60 (3), P. 781–850.

13. Malkova N., Hromada I., et al. Observation of optical Shockley-like surface states in photonic superlattices. Optics Letters, 2009, 34 (11), P. 1633–1635.

14. Schomerus H. Topologically protected midgap states in complex photonic lattices. Optics Letters, 2013, 38 (11), P. 1912–1914.

15. Slobozhanyuk A.P., Poddubny A.N., et al. Subwavelength topological edge states in optically resonant dielectric structures. Physical Review Letters, 2015, 114 (12), P. 123901.

16. Poli C., Bellec M., et al. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nature Communications, 2015, 6, P. 7710.

17. Blanco-Redondo A., Andonegui I., et al. Topological Optical Waveguiding in Silicon and the Transition between Topological and Trivial Defect States. Physical Review Letters, 2016, 116 (16), P. 163901.

18. Slobozhanyuk A.P., Poddubny A.N., et al. Enhanced photonic spin Hall effect with subwavelength topological edge states. Laser & Photonic Reviews, 2016, 10 (4), P. 656–664.

19. Kruk S., Slobozhanyuk A., et al. Edge States and Topological Phase Transitions in Chains of Dielectric Nanoparticles. Small, 2017, 13 (11), P. 1603190.

20. Poddubny A., Miroshnichenko A., Slobozhanyuk A., Kivshar Y. Topological Majorana States in Zigzag Chains of Plasmonic Nanoparticles. ACS Photonics, 2014, 1 (2), P. 101–105.

21. Ling C.W., Xiao M., et al. Topological edge plasmon modes between diatomic chains of plasmonic nanoparticles. Optics Express, 2015, 23 (3), P. 2021–2031.

22. Cheng Q., Pan Y., Wang Q., Li T., Zhu S. Topologically protected interface mode in plasmonic waveguide arrays. Laser & Photonics Reviews, 2015, 9 (4), P. 392–398.

23. Sinev I.S., Mukhin I.S., et al. Mapping plasmonic topological states at the nanoscale. Nanoscale, 2015, 7 (28), P. 11904–11908.

24. St-Jean P., Goblot V., et al. Lasing in topological edge states of a one-dimensional lattice. Nature Photonics, 2017, 11 (10), P. 651–656.

25. Kane C.L., Lubensky T.C. Topological boundary modes in isostatic lattices. Nature Physics, 2014, 10, P. 39–45.

26. Zak J. Berry’s Phase for Energy Bands in Solids. Physical Review Letters, 1989, 62 (23), P. 2747–2750.

27. Winkler K., Thalhammer G., et al. Repulsively bound atom pairs in an optical lattice. Nature, 2006, 441 (7095), P. 853–856.

28. Valiente M., Petrosyan D. Two-particle states in the Hubbard model. Journal of Physics B, 2008, 41 (16), P. 161002.

29. Zhang J.M., Braak D., Kollar M. Bound states in the continuum realized in the one-dimensional two-particle Hubbard model with an impurity. Physical Review Letters, 2012, 109 (11), P. 116405.

30. Zhang J.M., Braak D., Kollar M. Bound states in the one-dimensional two-particle Hubbard model with an impurity. Physical Review A, 2013, 87 (12), P. 023613.

31. Pinto R.A., Nguenang J.P., Flach S. Boundary effects on quantum q-breathers in a Bose-Hubbard chain. Physica D, 2009, 238 (5), P. 581–588.

32. Longhi S., Della Valle G. Tamm–Hubbard surface states in the continuum. Journal of Physics: Condensed Matter, 2013, 25 (23), P. 235601.


Рецензия

Для цитирования:


Gorlach M.A., Slobozhanyuk A.P. Nonlinear topological states in the Su–Schrieffer–Heeger model. Наносистемы: физика, химия, математика. 2017;8(6):695-700. https://doi.org/10.17586/2220-8054-2017-8-6-695-700

For citation:


Gorlach M.A., Slobozhanyuk A.P. Nonlinear topological states in the Su–Schrieffer–Heeger model. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(6):695-700. https://doi.org/10.17586/2220-8054-2017-8-6-695-700

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ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)