- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Coupled topological interface states and phonon molecules in GaAs/AlAs superlattices

S. Sandeep, O. Colmegna, C. Xiang, E. R. Cardozo de Oliveira, K. Papatryfonos, M. Morassi, A. Lemaitre, and N. D. Lanzillotti-Kimura*

  • *Contact author: daniel.kimura@cnrs.fr
PDF

Phys. Rev. B 114, 225302 – Published 22 October, 2026

DOI: https://doi.org/10.1103/m86k-4m6v

Abstract

Topological interface states in one-dimensional superlattices provide spatially localized phonon modes protected by the topology of the underlying band structure. In GaAs/AlAs distributed Bragg reflectors (DBRs), such states can be engineered through band inversion between superlattices with opposite Zak phases within the Su-Schrieffer-Heeger framework. Here, we demonstrate topological phonon molecules and extended chains formed by coupled nanophononic interface states. By concatenating three superlattices with alternating topology, we realize two coupled interface states that hybridize into symmetric and antisymmetric modes, whose splitting can be tuned over tens of gigahertz by varying the reflectivity of the central DBR. Extending this concept, we engineer chains of up to N=6 coupled interface states that form narrow topological minibands while remaining strongly localized at the interfaces. We experimentally observe these coupled states in molecular-beam-epitaxy-grown GaAs/AlAs heterostructures using time-domain pump-probe transient reflectivity measurements, and reproduce their behavior using transfer-matrix calculations and a simple analytical model for the mode splitting. These results establish topological interface states as a robust platform for engineering coupled phononic systems and tunable nanophononic architectures in the GHz regime.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (78)

  1. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  2. J. Asbóth, L. Oroszlány, and A. Pályi, A Short Course on Topological Insulators, Lecture Notes in Physics (Springer, Cham, 2016), Vol. 919.
  3. L. Eek, A. Moustaj, M. Röntgen, V. Pagneux, V. Achilleos, and C. M. Smith, Emergent non-Hermitian models, Phys. Rev. B 109, 045122 (2024).
  4. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
  5. N. V. Hauff, H. Le Jeannic, P. Lodahl, S. Hughes, and N. Rotenberg, Chiral quantum optics in broken-symmetry and topological photonic crystal waveguides, Phys. Rev. Res. 4, 023082 (2022).
  6. M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, Imaging topological edge states in silicon photonics, Nat. Photon. 7, 1001 (2013).
  7. M. Xiao, Z. Q. Zhang, and C. T. Chan, Surface impedance and bulk band geometric phases in one-dimensional systems, Phys. Rev. X 4, 021017 (2014).
  8. L. Lu, J. D. Joannopoulos, and M. Soljačić, Topological photonics, Nat. Photon. 8, 821 (2014).
  9. A. B. Khanikaev and G. Shvets, Two-dimensional topological photonics, Nat. Photon. 11, 763 (2017).
  10. A. Rodriguez, K. Papatryfonos, E. R. C. de Oliveira, and N. D. Lanzillotti-Kimura, Topological nanophononic interface states using high-order bandgaps in the one-dimensional Su-Schrieffer-Heeger model, Phys. Rev. B 108, 205301 (2023).
  11. M. Esmann, F. R. Lamberti, A. Lemaître, and N. D. Lanzillotti-Kimura, Topological acoustics in coupled nanocavity arrays, Phys. Rev. B 98, 161109(R) (2018).
  12. G. Arregui, O. Ortíz, M. Esmann, C. M. Sotomayor-Torres, C. Gomez-Carbonell, O. Mauguin, B. Perrin, A. Lemaître, P. D. García, and N. D. Lanzillotti-Kimura, Coherent generation and detection of acoustic phonons in topological nanocavities, APL Photon. 4, 030805 (2019).
  13. C. Brendel, V. Peano, O. Painter, and F. Marquardt, Snowflake phononic topological insulator at the nanoscale, Phys. Rev. B 97, 020102(R) (2018).
  14. R. Süsstrunk and S. D. Huber, Observation of phononic helical edge states in a mechanical topological insulator, Science 349, 47 (2015).
  15. E. Prodan and C. Prodan, Topological phonon modes and their role in dynamic instability of microtubules, Phys. Rev. Lett. 103, 248101 (2009).
  16. J. Doster, T. Shah, T. Fösel, P. Paulitschke, F. Marquardt, and E. M. Weig, Observing polarization patterns in the collective motion of nanomechanical arrays, Nat. Commun. 13, 2478 (2022).
  17. J. Kettler, N. Vaish, L. M. de Lépinay, B. Besga, P.-L. de Assis, O. Bourgeois, A. Auffèves, M. Richard, J. Claudon, J.-M. Gérard, B. Pigeau, O. Arcizet, P. Verlot, and J.-P. Poizat, Inducing micromechanical motion by optical excitation of a single quantum dot, Nat. Nanotechnol. 16, 283 (2021).
  18. G. Ma, M. Xiao, and C. T. Chan, Topological phases in acoustic and mechanical systems, Nat. Rev. Phys. 1, 281 (2019).
  19. M. Xiao, G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, Geometric phase and band inversion in periodic acoustic systems, Nat. Phys. 11, 240 (2015).
  20. D. Zhao, M. Xiao, C. W. Ling, C. T. Chan, and K. H. Fung, Topological interface modes in local resonant acoustic systems, Phys. Rev. B 98, 014110 (2018).
  21. L.-Y. Zheng, V. Achilleos, O. Richoux, G. Theocharis, and V. Pagneux, Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network, Phys. Rev. Appl. 12, 034014 (2019).
  22. X. Zhang, M. Xiao, Y. Cheng, M.-H. Lu, and J. Christensen, Topological sound, Commun. Phys. 27, 1 (2018).
  23. C. He, X. Ni, H. Ge, X.-C. Sun, Y.-B. Chen, M.-H. Lu, X.-P. Liu, and Y.-F. Chen, Acoustic topological insulator and robust one-way sound transport, Nat. Phys. 12, 1124 (2016).
  24. S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016).
  25. D. Lee, N. D. Lanzillotti-Kimura, J. Li, and J. Rho, Elastic topological interface states and voltage feeder by breaking inversion symmetry on thin plates, Phys. Rev. B 106, 104107 (2022).
  26. P. St-Jean, A. Dauphin, P. Massignan, B. Real, O. Jamadi, M. Milicevic, A. Lemaître, A. Harouri, L. Le Gratiet, I. Sagnes, S. Ravets, J. Bloch, and A. Amo, Measuring topological invariants in a polaritonic analog of graphene, Phys. Rev. Lett. 126, 127403 (2021).
  27. N. Pernet, P. St-Jean, D. D. Solnyshkov, G. Malpuech, N. Carlon Zambon, Q. Fontaine, B. Real, O. Jamadi, A. Lemaître, M. Morassi, L. Le Gratiet, T. Baptiste, A. Harouri, I. Sagnes, A. Amo, S. Ravets, and J. Bloch, Gap solitons in a one-dimensional driven-dissipative topological lattice, Nat. Phys. 18, 678 (2022).
  28. D. L. Chafatinos, A. S. Kuznetsov, S. Anguiano, A. E. Bruchhausen, A. A. Reynoso, K. Biermann, P. V. Santos, and A. Fainstein, Polariton-driven phonon laser, Nat. Commun. 11, 4552 (2020).
  29. A. S. Kuznetsov, D. H. O. Machado, K. Biermann, and P. V. Santos, Electrically driven microcavity exciton-polariton optomechanics at 20 GHz, Phys. Rev. X 11, 021020 (2021).
  30. S. Klembt, T. H. Harder, O. A. Egorov, K. Winkler, R. Ge, M. A. Bandres, M. Emmerling, L. Worschech, T. C. H. Liew, M. Segev, C. Schneider, and S. Höfling, Exciton-polariton topological insulator, Nature (London) 562, 552 (2018).
  31. Q. Song, M. Odeh, J. Zúñiga-Pérez, B. Kanté, and P. Genevet, Plasmonic topological metasurface by encircling an exceptional point, Science 373, 1133 (2021).
  32. D. Malz, J. Knolle, and A. Nunnenkamp, Topological magnon amplification, Nat. Commun. 10, 3937 (2019).
  33. Y. Jin, D. Torrent, B. D. Rouhani, L. He, Y. Xiang, F.-Z. Xuan, Z. Gu, H. Xue, J. Zhu, Q. Wu, G. Huang, P. D. García, G. Arregui, Y. Chen, S. Guenneau, M. Wegener, M. Kadic, Y. Liu, J. Li, Y.-S. Wang, et al., The 2024 phononic crystals roadmap, J. Phys. D: Appl. Phys. 58, 113001 (2025).
  34. Z. Wang, L. Ye, Z. Pu, Q. Ma, H. He, J. Lu, W. Deng, X. Huang, M. Ke, and Z. Liu, Higher-order topological transport protected by boundary Chern number in phononic crystals, Commun. Phys. 7, 193 (2024).
  35. P. H. Otsuka, M. Tomoda, D. Hatanaka, H. Yamaguchi, K. Tsuruta, and O. Matsuda, Imaging valley-vortex edge modes in a phononic crystal at ultrahigh frequencies, J. Appl. Phys. 137, 235104 (2025).
  36. Z.-D. Zhang, S.-Y. Yu, M.-H. Lu, and Y.-F. Chen, Gigahertz surface acoustic wave topological rainbow in nanoscale phononic crystals, Phys. Rev. Lett. 133, 267001 (2024).
  37. X. Xi, I. Chernobrovkin, J. Košata, M. B. Kristensen, E. Langman, A. S. Sørensen, O. Zilberberg, and A. Schliesser, A soft-clamped topological waveguide for phonons, Nature (London) 642, 947 (2025).
  38. X.-B. Xu, M. Oudich, Y. Zeng, J.-Z. Zhang, Y.-H. Yang, J.-Q. Wang, W. Wang, L. Sun, G.-C. Guo, Y. Jing, and C.-L. Zou, Gigahertz topological phononic circuits based on micrometre-scale unsuspended waveguide arrays, Nat. Electron. 8, 689 (2025).
  39. M. Esmann and N. D. Lanzillotti-Kimura, A topological view on optical and phononic Fabry–Perot microcavities through the Su–Schrieffer–Heeger model, Appl. Sci. 8, 527 (2018).
  40. M. Esmann, F. R. Lamberti, P. Senellart, I. Favero, O. Krebs, L. Lanco, C. Gomez Carbonell, A. Lemaître, and N. D. Lanzillotti-Kimura, Topological nanophononic states by band inversion, Phys. Rev. B 97, 155422 (2018).
  41. Priya, E. R. C. de Oliveira, and N. D. Lanzillotti-Kimura, Perspectives on high-frequency nanomechanics, nanoacoustics, and nanophononics, Appl. Phys. Lett. 122, 140501 (2023).
  42. C. Xiang, E. R. C. de Oliveira, S. Sandeep, K. Papatryfonos, M. Morassi, L. L. Gratiet, A. Harouri, I. Sagnes, A. Lemaitre, O. Ortiz, M. Esmann, and N. D. Lanzillotti-Kimura, Interference of ultrahigh frequency acoustic phonons from distant quasi-continuous sources, arXiv:2407.06821.
  43. O. Ortiz, F. Pastier, A. Rodriguez, Priya, A. Lemaître, C. Gomez-Carbonell, I. Sagnes, A. Harouri, P. Senellart, V. Giesz, M. Esmann, and N. D. Lanzillotti-Kimura, Fiber-integrated microcavities for efficient generation of coherent acoustic phonons, Appl. Phys. Lett. 117, 183102 (2020).
  44. O. Ortíz, M. Esmann, and N. D. Lanzillotti-Kimura, Phonon engineering with superlattices: Generalized nanomechanical potentials, Phys. Rev. B 100, 085430 (2019).
  45. N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing, Sci. Adv. 6, eaaw4137 (2020).
  46. K. Papatryfonos, D. Saladukha, K. Merghem, S. Joshi, F. Lelarge, S. Bouchoule, D. Kazazis, S. Guilet, L. Le Gratiet, T. J. Ochalski, G. Huyet, A. Martinez, and A. Ramdane, Laterally coupled distributed feedback lasers emitting at 2 µm with quantum dash active region and high-duty-cycle etched semiconductor gratings, J. Appl. Phys. 121, 053101 (2017).
  47. J. Wang, Y. Bai, H. Liu, Z. Cheng, M. Tang, S. Chen, J. Wu, K. Papatryfonos, Z. Liu, Y. Huang, and X. Ren, Optimization of 1.3µm inas/gaas quantum dot lasers epitaxially grown on silicon: taking the optical loss of metamorphic epilayers into account, Laser Phys. 28, 126206 (2018).
  48. P. Delsing, A. N. Cleland, M. J. A. Schuetz, J. Knörzer, G. Giedke, J. I. Cirac, K. Srinivasan, M. Wu, K. C. Balram, C. Bäuerle, T. Meunier, C. J. B. Ford, P. V. Santos, E. Cerda-Méndez, H. Wang, H. J. Krenner, E. D. S. Nysten, M. Weiß, G. R. Nash, L. Thevenard, et al., The 2019 surface acoustic waves roadmap, J. Phys. D: Appl. Phys. 52, 353001 (2019).
  49. P. Torres, J. Iniguez, and R. Rurali, Giant electrophononic response in PbTiO3 by strain engineering, Phys. Rev. Lett. 123, 185901 (2019).
  50. C. Li, H. Ma, T. Li, J. Dai, M. A. J. Rasel, A. Mattoni, A. Alatas, M. G. Thomas, Z. W. Rouse, A. Shragai, S. P. Baker, B. J. Ramshaw, J. P. Feser, D. B. Mitzi, and Z. Tian, Remarkably weak anisotropy in thermal conductivity of two-dimensional hybrid perovskite butylammonium lead iodide crystals, Nano Lett. 21, 3708 (2021).
  51. F. Bencivenga, R. Mincigrucci, F. Capotondi, L. Foglia, D. Naumenko, A. A. Maznev, E. Pedersoli, A. Simoncig, F. Caporaletti, V. Chiloyan, R. Cucini, F. Dallari, R. A. Duncan, T. D. Frazer, G. Gaio, A. Gessini, L. Giannessi, S. Huberman, H. Kapteyn, J. Knobloch, et al., Nanoscale transient gratings excited and probed by extreme ultraviolet femtosecond pulses, Sci. Adv. 5, eaaw5805 (2019).
  52. Y. Chu, P. Kharel, T. Yoon, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator, Nature (London) 563, 666 (2018).
  53. D. D. Bühler, M. Weiß, A. Crespo-Poveda, E. D. S. Nysten, J. J. Finley, K. Müller, P. V. Santos, M. M. de Lima, and H. J. Krenner, On-chip generation and dynamic piezo-optomechanical rotation of single photons, Nat. Commun. 13, 6998 (2022).
  54. C. Meng, G. A. Brawley, S. Khademi, E. M. Bridge, J. S. Bennett, and W. P. Bowen, Measurement-based preparation of multimode mechanical states, Sci. Adv. 8, eabm7585 (2022).
  55. I. Mahboob, K. Nishiguchi, H. Okamoto, and H. Yamaguchi, Phonon-cavity electromechanics, Nat. Phys. 8, 387 (2012).
  56. B. Stiller, M. Merklein, C. Wolff, K. Vu, P. Ma, S. J. Madden, and B. J. Eggleton, Coherently refreshing hypersonic phonons for light storage, Optica 7, 492 (2020).
  57. K. Papatryfonos, J. Girard, M. Tang, H. Deng, A. J. Seeds, C. David, G. Rodary, H. Liu, and D. R. Selviah, Low‐defect quantum dot lasers directly grown on silicon exhibiting low threshold current and high output power at elevated temperatures, Adv. Photon. Res. 6, 2400082 (2025).
  58. O. Ortiz, P. Priya, A. Rodriguez, A. Lemaître, M. Esmann, and N. D. Lanzillotti-Kimura, Topological optical and phononic interface mode by simultaneous band inversion, Optica 8, 598 (2021).
  59. A. Fainstein, N. D. Lanzillotti-Kimura, B. Jusserand, and B. Perrin, Strong optical-mechanical coupling in a vertical GaAs/AlAs microcavity for subterahertz phonons and near-infrared light, Phys. Rev. Lett. 110, 037403 (2013).
  60. K. Papatryfonos, A. Rodriguez, E. R. C. de Oliveira, and N. D. Lanzillotti-Kimura, High-order topological states using alignment of different band gaps in 1D superlattices, Proc. SPIE, 12991, 1299107 (2024).
  61. M. Esmann, F. R. Lamberti, A. Harouri, L. Lanco, I. Sagnes, I. Favero, G. Aubin, C. Gomez-Carbonell, A. Lemaître, O. Krebs, P. Senellart, and N. D. Lanzillotti-Kimura, Brillouin scattering in hybrid optophononic Bragg micropillar resonators at 300 GHz, Optica 6, 854 (2019).
  62. K. Papatryfonos, T. Angelova, A. Brimont, B. Reid, S. Guldin, P. R. Smith, M. Tang, K. Li, A. J. Seeds, H. Liu, and D. R. Selviah, Refractive indices of MBE-grown AlxGa(1−x)As ternary alloys in the transparent wavelength region, AIP Adv. 11, 025327 (2021).
  63. J. P. Mathew, J. del Pino, and E. Verhagen, Synthetic gauge fields for phonon transport in a nano-optomechanical system, Nat. Nanotechnol. 15, 198 (2020).
  64. S. Arora, T. Bauer, R. Barczyk, E. Verhagen, and L. Kuipers, Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths, Light: Sci. Applic. 10, 9 (2021).
  65. N. D. Lanzillotti-Kimura, A. Fainstein, C. A. Balseiro, and B. Jusserand, Phonon engineering with acoustic nanocavities: Theoretical considerations on phonon molecules, band structures, and acoustic Bloch oscillations, Phys. Rev. B 75, 024301 (2007).
  66. N. D. Lanzillotti-Kimura, A. Fainstein, B. Perrin, B. Jusserand, O. Mauguin, L. Largeau, and A. Lemaître, Bloch oscillations of THz acoustic phonons in coupled nanocavity structures, Phys. Rev. Lett. 104, 197402 (2010).
  67. C. Schmidt, A. Palatnik, M. Sudzius, S. Meister, and K. Leo, Coupled topological interface states, Phys. Rev. B 103, 085412 (2021).
  68. R. Sharma, S. Jena, and D. V. Udupa, Coupling of topological interface states in 1D photonic crystal, Opt. Mater. (Amsterdam) 137, 113508 (2023).
  69. A. Fainstein and B. Jusserand, Raman scattering in resonant cavities, in Light Scattering in Solid IX, edited by M. Cardona and R. Merlin (Springer, Berlin, 2006), Vol. 108, pp. 17–110.
  70. N. D. Lanzillotti-Kimura, A. Fainstein, B. Perrin, and B. Jusserand, Theory of coherent generation and detection of THz acoustic phonons using optical microcavities, Phys. Rev. B 84, 064307 (2011).
  71. M. F. Pascual-Winter, A. Fainstein, B. Jusserand, B. Perrin, and A. Lemaître, Spectral responses of phonon optical generation and detection in superlattices, Phys. Rev. B 85, 235443 (2012).
  72. M. F. Pascual Winter, G. Rozas, A. Fainstein, B. Jusserand, B. Perrin, A. Huynh, P. O. Vaccaro, and S. Saravanan, Selective optical generation of coherent acoustic nanocavity modes, Phys. Rev. Lett. 98, 265501 (2007).
  73. A. Mlayah, J.-R. Huntzinger, and N. Large, Raman-Brillouin light scattering in low-dimensional systems: Photoelastic model versus quantum model, Phys. Rev. B 75, 245303 (2007).
  74. J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila, and J. Ahopelto, Inelastic light scattering by longitudinal acoustic phonons in thin silicon layers: From membranes to silicon-on-insulator structures, Phys. Rev. B 77, 045420 (2008).
  75. B. Jusserand, Selective resonant interaction between confined excitons and folded acoustic phonons in GaAs/AlAs multi-quantum wells, Appl. Phys. Lett. 103, 093112 (2013).
  76. B. Jusserand, A. N. Poddubny, A. V. Poshakinskiy, A. Fainstein, and A. Lemaitre, Polariton resonances for ultrastrong coupling cavity optomechanics in GaAs / AlAs multiple quantum wells, Phys. Rev. Lett. 115, 267402 (2015).
  77. S. Sandeep, O. Colmegna, C. Xiang, E. R. C. de Oliveira, K. Papatryfonos, M. Morassi, A. Lemaitre, and N. D. Lanzillotti-Kimura, Data set of coupled topological interface states and phonon molecules in GaAs/AlAs superlattices [Dataset], Zenodo, 2026, doi: https://doi.org/10.5281/zenodo.21997281.
  78. S. Tamura and J. P. Wolfe, Acoustic-phonon transmission in quasiperiodic superlattices, Phys. Rev. B 36, 3491 (1987).

Outline

Information

Phys. Rev. B 114, 225302– Published 22 October, 2026
  • Received 29 April 2026
  • Revised 12 August 2026
  • Accepted 12 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation