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Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice

Gulevich, D. R., Yudin, D., Skryabin, D. V., Iorsh, I. V., Shelykh, I. A.·2017·Scientific Reports
DOI 10.1038/s41598-017-01646-yPMC PMC5431788
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Abstract

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator – material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes – topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.

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Figure 1 (a) A strip of kagome lattice. The strip is infinite along x but has a finite extent along the y axis. The sites marked by black form a unit cell of the strip. The bottom boundary of the strip with a row of uncoupled sites supports the dispersion of topological edge mode with the group velocity changing sign within the bulk gap as shown in Figure b. (b) Band structure for exciton-polaritons in a strip of kagome lattice. Dispersion of edge states with reversed group velocity and a well defined minimum and maximum lying within the bulk gap appears for a certain range of values of the magnetic field and TE-TM splitting at the lower boundary made of sites without the nearest neighbor hopping (the bottom one in Figure a): in this example, Ω = 0.3 and δJ = 0.15 in normalized units. The red and blue dots mark the regions where nonlinear solutions in the form of bright and dark solitons are sought. The band structure beyond the edge of the first Brillouin zone at π/2 is shown for better display of the topological edge state dispersions.
Figure 1 (a) A strip of kagome lattice. The strip is infinite along x but has a finite extent along the y axis. The sites marked by black form a unit cell of the strip. The bottom boundary of the strip with a row of uncoupled sites supports the dispersion of topological edge mode with the group velocity changing sign within the bulk gap as shown in Figure b. (b) Band structure for exciton-polaritons in a strip of kagome lattice. Dispersion of edge states with reversed group velocity and a well defined minimum and maximum lying within the bulk gap appears for a certain range of values of the magnetic field and TE-TM splitting at the lower boundary made of sites without the nearest neighbor hopping (the bottom one in Figure a): in this example, Ω = 0.3 and δJ = 0.15 in normalized units. The red and blue dots mark the regions where nonlinear solutions in the form of bright and dark solitons are sought. The band structure beyond the edge of the first Brillouin zone at π/2 is shown for better display of the topological edge state dispersions.CC BY · PubMed Central
Figure 2 Simulation of collision of dark and grey solitons excited on the TEM propagating along the lower boundary of the kagome lattice strip in Fig. 1a. The TEM is excited at quasimomentum k e = 1.59, E(k e) = −1.09 at δJ = 0.15, Ω = 0.3, in the vicinity of the blue spot on Fig. 1b. At t = 0 initial conditions in the form of dark (18) (on the left) and grey (19) soliton (on the right) with η = 0.25 have been taken upon applying the transformation (15) with v = 0.042. The grey soliton parameter θ was taken to be 0.4π. At t > 0 the dark and grey move with constant velocities until the scattering act occurs at t ≈ 900, following which the dark and grey solitons exchange sides.
Figure 2 Simulation of collision of dark and grey solitons excited on the TEM propagating along the lower boundary of the kagome lattice strip in Fig. 1a. The TEM is excited at quasimomentum k e = 1.59, E(k e) = −1.09 at δJ = 0.15, Ω = 0.3, in the vicinity of the blue spot on Fig. 1b. At t = 0 initial conditions in the form of dark (18) (on the left) and grey (19) soliton (on the right) with η = 0.25 have been taken upon applying the transformation (15) with v = 0.042. The grey soliton parameter θ was taken to be 0.4π. At t > 0 the dark and grey move with constant velocities until the scattering act occurs at t ≈ 900, following which the dark and grey solitons exchange sides.CC BY · PubMed Central

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Research works printed but not linked: 50

  1. Kane, C. L. & Mele, E. J. Quantum spin hall effect in graphene. Phys. Rev. Lett. 95, 226801, doi:10.1103/PhysRevLett.95.226801 (2005). · DOI · Paper page
  2. Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin hall effect and topological phase transition in hgte quantum wells. Science 314, 1757–61, doi:10.1126/science.1133734 (2006). · DOI · Paper page
  3. Raghu, S. & Haldane, F. D. M. Analogs of quantum-hall-effect edge states in photonic crystals. Phys. Rev. A 78, 033834, doi:10.1103/PhysRevA.78.033834 (2008). · DOI · Paper page
  4. Haldane, F. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904, doi:10.1103/PhysRevLett.100.013904 (2008). · DOI · Paper page
  5. Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nature Physics 7, 907–912, doi:10.1038/nphys2063 (2011). · DOI · Paper page
  6. Fang, K., Yu, Z. & Fan, S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nature Photonics 6, 782–787, doi:10.1038/nphoton.2012.236 (2012). · DOI · Paper page
  7. Khanikaev, A. B. et al. Photonic topological insulators. Nature Materials 12, 233–239, doi:10.1038/nmat3520 (2013). · DOI · Paper page
  8. Lu, L., Joannopoulos, J. D. & Soljačic′, M. Topological photonics. Nature Photonics 8, 821–829, doi:10.1038/nphoton.2014.248 (2014). · DOI · Paper page
  9. Carusotto, I. & Ciuti, C. Quantum fluids of light. Reviews of Modern Physics 85, 299–366, doi:10.1103/RevModPhys.85.299 (2013). · DOI · Paper page
  10. Cerda-Méndez, E. A. et al. Polariton condensation in dynamic acoustic lattices. Phys. Rev. Lett. 105, 116402, doi:10.1103/PhysRevLett.105.116402 (2010). · DOI
  11. Kim, N. Y. et al. Exciton–polariton condensates near the dirac point in a triangular lattice. New Journal of Physics 15, 035032, doi:10.1088/1367-2630/15/3/035032 (2013). · DOI
  12. Baboux, F. et al. Bosonic condensation and disorder-induced localization in a flat band. Phys. Rev. Lett. 116, 066402, doi:10.1103/PhysRevLett.116.066402 (2016). · DOI
  13. Liew, T., Shelykh, I. & Malpuech, G. Polaritonic devices. Physica E 43, 1543–1568, doi:10.1016/j.physe.2011.04.003 (2011). · DOI
  14. D. Sanvitto, D. & Kéna-Cohen, S. The road towards polaritonic devices. Nature Materials 15, 1061–1073, doi:10.1038/nmat4668 (2016). · DOI
  15. Karzig, T., Bardyn, C.-E., Lindner, N. H. & Refael, G. Topological polaritons. Phys. Rev. X 5, 031001, doi:10.1103/PhysRevX.5.031001 (2015). · DOI
  16. Bardyn, C.-E., Karzig, T., Refael, G. & Liew, T. C. H. Topological polaritons and excitons in garden-variety systems. Phys. Rev. B 91, 161413, doi:10.1103/PhysRevB.91.161413 (2015). · DOI
  17. Nalitov, A. V., Solnyshkov, D. D. & Malpuech, G. Polariton ℤ topological insulator. Phys. Rev. Lett. 114, 116401, doi:10.1103/PhysRevLett.114.116401 (2015). · DOI
  18. Yi, K. & Karzig, T. Topological polaritons from photonic dirac cones coupled to excitons in a magnetic field. Phys. Rev. B 93, 104303, doi:10.1103/PhysRevB.93.104303 (2016). · DOI
  19. Bardyn, C.-E., Karzig, T., Refael, G. & Liew, T. C. H. Chiral bogoliubov excitations in nonlinear bosonic systems. Phys. Rev. B 93, 020502, doi:10.1103/PhysRevB.93.020502 (2016). · DOI · Paper page
  20. Janot, A., Rosenow, B. & Refael, G. Topological polaritons in a quantum spin hall cavity. Phys. Rev. B 93, 161111, doi:10.1103/PhysRevLett.111.230403 (2016). · DOI
  21. Gulevich, D. R., Yudin, D., Iorsh, I. V. & Shelykh, I. A. Kagome lattice from an exciton-polariton perspective. Phys. Rev. B 94, 115437, doi:10.1103/PhysRevB.94.115437 (2016). · DOI
  22. Lumer, Y., Plotnik, Y., Rechtsman, M. C. & Segev, M. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905, doi:10.1103/PhysRevLett.111.243905 (2013). · DOI
  23. Ostrovskaya, E. A., Abdullaev, J., Fraser, M. D., Desyatnikov, A. S. & Kivshar, Y. S. Self-localization of polariton condensates in periodic potentials. Phys. Rev. Lett. 110, 170407, doi:10.1103/PhysRevLett.110.170407 (2013). · DOI
  24. Hadad, Y., Khanikaev, A. B. & Alù, A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials. Phys. Rev. B 93, 155112, doi:10.1103/PhysRevB.93.155112 (2016). · DOI
  25. Bleu, O., Solnyshkov, D. D. & Malpuech, G. Interacting quantum fluid in a polariton chern insulator. Phys. Rev. B 93, 085438, doi:10.1103/PhysRevLett.118.023901 (2016). · DOI · Paper page
  26. Kartashov, Y. V. & Skryabin, D. V. Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling. Opt. Lett. 41, 5043–5046, doi:10.1364/OL.41.005043 (2016). · DOI
  27. Gulevich, D. R., Skryabin, D. V., Alodjants, A. P. & Shelykh, I. A. Topological spin meissner effect in spinor exciton-polariton condensate: Constant amplitude solutions, half-vortices, and symmetry breaking. Phys. Rev. B 94, 115407, doi:10.1103/PhysRevB.94.115407 (2016). · DOI
  28. Ablowitz, M. J., Curtis, C. W. & Ma, Y.-P. Linear and nonlinear traveling edge waves in optical honeycomb lattices. Phys. Rev. A 90, 023813, doi:10.1103/PhysRevA.90.023813 (2014). · DOI
  29. Leykam, D. & Chong, Y. D. Edge solitons in nonlinear-photonic topological insulators. Phys. Rev. Lett. 117, 143901, doi:10.1103/PhysRevLett.117.143901 (2016). · DOI · Paper page
  30. Kartashov, Y. V. & Skryabin, D. V. Modulational instability and solitary waves in polariton topological insulators. Optica 3, 1228, doi:10.1364/OPTICA.3.001228 (2016). · DOI
  31. Cerda-Méndez, E. A. et al. Exciton-polariton gap solitons in two-dimensional lattices. Phys. Rev. Lett. 111, 146401, doi:10.1103/PhysRevLett.111.146401 (2013). · DOI
  32. Solnyshkov, D. D., Bleu, O., Teklu, B. & Malpuech, G. Chirality of topological gap solitons in bosonic dimer chains. Phys. Rev. Lett. 118, 023901, doi:10.1103/PhysRevLett.118.023901 (2017). · DOI
  33. Rajaraman, R. Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory (Elsevier Science, 1987).
  34. de Vasconcellos, S. M. et al. Spatial, spectral, and polarization properties of coupled micropillar cavities. Appl. Phys. Lett. 99, 101103, doi:10.1063/1.3632111 (2011). · DOI
  35. Nalitov, A. V., Malpuech, G., Terças, H. & Solnyshkov, D. D. Spin-orbit coupling and the optical spin hall effect in photonic graphene. Phys. Rev. Lett. 114, 026803, doi:10.1103/PhysRevLett.114.026803 (2015). · DOI
  36. Sala, V. G. et al. Spin-orbit coupling for photons and polaritons in microstructures. Phys. Rev. X 5, 011034 (2015).
  37. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067, doi:10.1103/RevModPhys.82.3045 (2010). · DOI · Paper page
  38. Fruchart, M. & Carpentier, D. An introduction to topological insulators. Comptes Rendus Physique 14, 779–815, doi:10.1016/j.crhy.2013.09.013 Topological insulators/Isolants topologiquesTopological insulators/Isolants topologiques (2013). · DOI
  39. Vladimirova, M. et al. Polarization controlled nonlinear transmission of light through semiconductor microcavities. Phys. Rev. B 79, 115325, doi:10.1103/PhysRevB.79.115325 (2009). · DOI
  40. Landau, L. D. & Lifshitz, L. M. Quantum Mechanics, Third Edition: Non-Relativistic Theory (Volume 3) (Pregamon Press, 1977).
  41. Ablowitz, M. J. Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons (Cambridge University Press, 2011). · DOI
  42. Milićević, M. et al. Edge states in polariton honeycomb lattices. 2D Materials 2, 034012, doi:10.1088/2053-1583/2/3/034012 (2015). · DOI · Paper page
  43. Galbiati, M. et al. Polariton condensation in photonic molecules. Phys. Rev. Lett. 108, 126403, doi:10.1103/PhysRevLett.108.126403 (2012). · DOI
  44. Abbarchi, M. et al. Macroscopic quantum self-trapping and josephson oscillations of exciton polaritons. Nature Physics 9, 275–279, doi:10.1038/nphys2609 (2013). · DOI
  45. Dufferwiel, S. et al. Tunable polaritonic molecules in an open microcavity system. Applied Physics Letters 107, 201106, doi:10.1063/1.4936092 (2015). · DOI
  46. Kuwata-Gonokami, M. et al. Parametric scattering of cavity polaritons. Phys. Rev. Lett. 79, 1341–1344, doi:10.1103/PhysRevLett.79.1341 (1997). · DOI
  47. Savvidis, P. G. et al. Angle-resonant stimulated polariton amplifier. Phys. Rev. Lett. 84, 1547–1550, doi:10.1103/PhysRevLett.84.1547 (2000). · DOI
  48. Ciuti, C., Schwendimann, P. & Quattropani, A. Parametric luminescence of microcavity polaritons. Phys. Rev. B 63, 041303–5, doi:10.1103/PhysRevLett.84.1752 (2001). · DOI
  49. Dasbach, G., Schwab, M., Bayer, M. & Forchel, A. Parametric polariton scattering in microresonators with three-dimensional optical confinement. Phys. Rev. B 64, 201309, doi:10.1103/PhysRevB.64.201309 (2001). · DOI
  50. Tartakovskii, A. I. et al. Polariton parametric scattering processes in semiconductor microcavities observed in continuous wave experiments. Phys. Rev. B 65, 081308, doi:10.1103/PhysRevB.65.081308 (2002). · DOI

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Metadata

Authors
Gulevich, D. R., Yudin, D., Skryabin, D. V., Iorsh, I. V., & Shelykh, I. A.
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2017-05-11
Volume
7
Issue
1
ISSN
2045-2322
DOI
10.1038/s41598-017-01646-y
PMC
PMC5431788
Cited by
87
References
6
Language
en
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