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Coupling quantum dots to elastic waves in a phononic crystal waveguide

Jakub Rosiński1,*, Michał Gawełczyk1, Matthias Weiß2, Hubert J. Krenner2, and Paweł Machnikowski1,†

  • *Contact author: jakub.rosinski@pwr.edu.pl
  • †Contact author: pawel.machnikowski@pwr.edu.pl
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Phys. Rev. Applied 26, 024038 – Published 17 August, 2026

DOI: https://doi.org/10.1103/h7tj-bt38

Abstract

We present a comprehensive study of quantum dot (QD) coupling to various phononic modes in a phononic waveguide (WG), combining multiband k·p and configuration-interaction (CI) QD state simulations with finite-element WG mode modeling. We consider self-assembled Stranski-Krastanov InGaAs/GaAs as well as local droplet-etched GaAs/AlGaAs structures. Using k·p-CI calculations, we quantify the strain and piezoelectric responses of InAs and GaAs QDs. By systematically isolating volumetric/shear deformation-potential and piezoelectric channels, we demonstrate how mode symmetries dictate distinct coupling mechanisms. We identify the dominant coupling channels and characterize their observable signatures in the QD response. We predict strong linear energy shifts under volumetric strain and quadratic behavior under shear strain, especially in GaAs QDs. The piezoelectric effect is dominated by polarizability, which also leads to a quadratic response. The simulations show energy modulations up to 0.7 meV for an acoustic wave with 0.1 nm amplitude. The quadratic response to shear strain and piezoelectric field leads to frequency doubling in the QD response to a mechanical wave and to nonharmonic time traces when linear and quadratic effects contribute to a similar degree. The deep understanding of QD-acoustic couplings opens pathways to the optimal design of QD and WG structures, as well as to improved engineering of acousto-optic quantum interfaces.

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References (94)

  1. L. Rayleigh, On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc. s1-17, 4 (1885).
  2. H. Lamb, On waves in an elastic plate, Proc. R. Soc. A 93, 114 (1917).
  3. P. Delsing et al., The 2019 surface acoustic waves roadmap, J. Phys. D 52, 353001 (2019).
  4. G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, Quantum technologies with hybrid systems, Proc. Natl. Acad. Sci. U.S.A. 112, 3866 (2015).
  5. M. Schleier-Smith, Editorial: Hybridizing quantum physics and engineering, Phys. Rev. Lett. 117, 100001 (2016).
  6. M. J. A. Schütz, Universal quantum transducers based on surface acoustic waves, in Quantum Dots for Quantum Information Processing: Controlling and Exploiting the Quantum Dot Environment (Springer International Publishing, Cham, 2017), pp. 143–196.
  7. N. Lauk, N. Sinclair, S. Barzanjeh, J. P. Covey, M. Saffman, M. Spiropulu, and C. Simon, Perspectives on quantum transduction, Quantum Sci. Technol. 5, 020501 (2020).
  8. K. J. Satzinger, Y. P. Zhong, H.-S. Chang, G. A. Peairs, A. Bienfait, M.-H. Chou, A. Y. Cleland, C. R. Conner, É. Dumur, J. Grebel, I. Gutierrez, B. H. November, R. G. Povey, S. J. Whiteley, D. D. Awschalom, D. I. Schuster, and A. N. Cleland, Quantum control of surface acoustic-wave phonons, Nature (London) 563, 661 (2018).
  9. M. V. Gustafsson, T. Aref, A. F. Kockum, M. K. Ekström, G. Johansson, and P. Delsing, Propagating phonons coupled to an artificial atom, Science 346, 207 (2014).
  10. J. R. Gell, M. B. Ward, R. J. Young, R. M. Stevenson, P. Atkinson, D. Anderson, G. A. C. Jones, D. A. Ritchie, and A. J. Shields, Modulation of single quantum dot energy levels by a surface-acoustic-wave, Appl. Phys. Lett. 93, 081115 (2008).
  11. S. Völk, F. J. R. Schülein, F. Knall, D. Reuter, A. D. Wieck, T. A. Truong, H. Kim, P. M. Petroff, A. Wixforth, and H. J. Krenner, Enhanced sequential carrier capture into individual quantum dots and quantum posts controlled by surface acoustic waves, Nano Lett. 10, 3399 (2010).
  12. M. Metcalfe, S. M. Carr, A. Muller, G. S. Solomon, and J. Lawall, Resolved sideband emission of InAs/GaAs quantum dots strained by surface acoustic waves, Phys. Rev. Lett. 105, 037401 (2010).
  13. R. Blattmann, H. J. Krenner, S. Kohler, and P. Hänggi, Entanglement creation in a quantum-dot–nanocavity system by Fourier-synthesized acoustic pulses, Phys. Rev. A 89, 012327 (2014).
  14. F. J. R. Schülein, E. Zallo, P. Atkinson, O. G. Schmidt, R. Trotta, A. Rastelli, A. Wixforth, and H. J. Krenner, Fourier synthesis of radiofrequency nanomechanical pulses with different shapes, Nat. Nanotechnol. 10, 512 (2015).
  15. M. Weiß and H. J. Krenner, Interfacing quantum emitters with propagating surface acoustic waves, J. Phys. D 51, 373001 (2018).
  16. M. Weiß, D. Wigger, M. Nägele, K. Müller, J. J. Finley, T. Kuhn, P. Machnikowski, and H. J. Krenner, Optomechanical wave mixing by a single quantum dot, Optica 8, 291 (2021).
  17. D. Wigger, K. Gawarecki, and P. Machnikowski, Remote phonon control of quantum dots and other artificial atoms, Adv. Quantum Technol. 4, 2000128 (2021).
  18. M. Choquer, M. Weiß, E. D. Nysten, M. Lienhart, P. Machnikowski, D. Wigger, H. J. Krenner, and G. Moody, Quantum control of optically active artificial atoms with surface acoustic waves, IEEE Trans. Quantum Eng. 3, 1 (2022).
  19. S. J. Whiteley, G. Wolfowicz, C. P. Anderson, A. Bourassa, H. Ma, M. Ye, G. Koolstra, K. J. Satzinger, M. V. Holt, F. J. Heremans, A. N. Cleland, D. I. Schuster, G. Galli, and D. D. Awschalom, Spin–phonon interactions in silicon carbide addressed by Gaussian acoustics, Nat. Phys. 15, 490 (2019).
  20. S. Maity, L. Shao, S. Bogdanović, S. Meesala, Y.-I. Sohn, N. Sinclair, B. Pingault, M. Chalupnik, C. Chia, L. Zheng, K. Lai, and M. Lončar, Coherent acoustic control of a single silicon vacancy spin in diamond, Nat. Commun. 11, 193 (2020).
  21. D. A. Golter, T. Oo, M. Amezcua, K. A. Stewart, and H. Wang, Optomechanical quantum control of a nitrogen-vacancy center in diamond, Phys. Rev. Lett. 116, 143602 (2016).
  22. S. Lazić, A. Espinha, S. Pinilla Yanguas, C. Gibaja, F. Zamora, P. Ares, M. Chhowalla, W. S. Paz, J. J. P. Burgos, A. Hernández-Mínguez, P. V. Santos, and H. P. van der Meulen, Dynamically tuned non-classical light emission from atomic defects in hexagonal boron nitride, Commun. Phys. 2, 113 (2019).
  23. A. Hernández-Mínguez, A. V. Poshakinskiy, M. Hollenbach, P. V. Santos, and G. V. Astakhov, Acoustically induced coherent spin trapping, Sci. Adv. 7, eabj5030 (2021).
  24. S. D. Patel, K. Parto, M. Choquer, N. Lewis, S. Umezawa, L. Hellman, D. Polishchuk, and G. Moody, Surface acoustic wave cavity optomechanics with atomically thin h-BN and WSe2 single-photon emitters, PRX Quantum 5, 010330 (2024).
  25. A. Bienfait, K. J. Satzinger, Y. P. Zhong, H.-S. Chang, M.-H. Chou, C. R. Conner, É. Dumur, J. Grebel, G. A. Peairs, R. G. Povey, and A. N. Cleland, Phonon-mediated quantum state transfer and remote qubit entanglement, Science 364, 368 (2019).
  26. S. Hermelin, S. Takada, M. Yamamoto, S. Tarucha, A. D. Wieck, L. Saminadayar, C. Bäuerle, and T. Meunier, Electrons surfing on a sound wave as a platform for quantum optics with flying electrons, Nature (London) 477, 435 (2011).
  27. R. P. G. McNeil, M. Kataoka, C. J. B. Ford, C. H. W. Barnes, D. Anderson, G. A. C. Jones, I. Farrer, and D. A. Ritchie, On-demand single-electron transfer between distant quantum dots, Nature (London) 477, 439 (2011).
  28. S. Takada, H. Edlbauer, H. V. Lepage, J. Wang, P.-A. Mortemousque, G. Georgiou, C. H. W. Barnes, C. J. B. Ford, M. Yuan, P. V. Santos, X. Waintal, A. Ludwig, A. D. Wieck, M. Urdampilleta, T. Meunier, and C. Bäuerle, Sound-driven single-electron transfer in a circuit of coupled quantum rails, Nat. Commun. 10, 4557 (2019).
  29. B. Jadot, P.-A. Mortemousque, E. Chanrion, V. Thiney, A. Ludwig, A. D. Wieck, M. Urdampilleta, C. Bäuerle, and T. Meunier, Distant spin entanglement via fast and coherent electron shuttling, Nat. Nanotechnol. 16, 570 (2021).
  30. V. Narayanamurti, H. L. Störmer, M. A. Chin, A. C. Gossard, and W. Wiegmann, Selective transmission of high-frequency phonons by a superlattice: The “dielectric” phonon filter, Phys. Rev. Lett. 43, 2012 (1979).
  31. R. Martínez-Sala, J. Sancho, J. V. Sánchez, V. Gómez, J. Llinares, and F. Meseguer, Sound attenuation by sculpture, Nature (London) 378, 241 (1995).
  32. S. Benchabane, A. Khelif, J.-Y. Rauch, L. Robert, and V. Laude, Evidence for complete surface wave band gap in a piezoelectric phononic crystal, Phys. Rev. E 73, 065601(R) (2006).
  33. M. Sigalas and E. N. Economou, Band structure of elastic waves in two dimensional systems, Solid State Commun. 86, 141 (1993).
  34. S. Mohammadi, A. A. Eftekhar, W. D. Hunt, and A. Adibi, High-Q micromechanical resonators in a two-dimensional phononic crystal slab, Appl. Phys. Lett. 94, 051906 (2009).
  35. S. Benchabane, O. Gaiffe, G. Ulliac, R. Salut, Y. Achaoui, and V. Laude, Observation of surface-guided waves in holey hypersonic phononic crystal, Appl. Phys. Lett. 98, 171908 (2011).
  36. P. H. Otsuka, K. Nanri, O. Matsuda, M. Tomoda, D. M. Profunser, I. A. Veres, S. Danworaphong, A. Khelif, S. Benchabane, V. Laude, and O. B. Wright, Broadband evolution of phononic-crystal-waveguide eigenstates in real-and k-spaces, Sci. Rep. 3, 3351 (2013).
  37. M. Ghasemi Baboly, C. M. Reinke, B. A. Griffin, I. El-Kady, and Z. C. Leseman, Acoustic waveguiding in a silicon carbide phononic crystals at microwave frequencies, Appl. Phys. Lett. 112, 103504 (2018).
  38. R. Pourabolghasem, R. Dehghannasiri, A. A. Eftekhar, and A. Adibi, Waveguiding effect in the gigahertz frequency range in pillar-based phononic-crystal slabs, Phys. Rev. Appl. 9, 014013 (2018).
  39. J. M. García, T. Mankad, P. O. Holtz, P. J. Wellman, and P. M. Petroff, Electronic states tuning of InAs self-assembled quantum dots, Appl. Phys. Lett. 72, 3172 (1998).
  40. M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots, Phys. Rev. B 65, 195315 (2002).
  41. R. Trotta, P. Atkinson, J. D. Plumhof, E. Zallo, R. O. Rezaev, S. Kumar, S. Baunack, J. R. Schröter, A. Rastelli, and O. G. Schmidt, Nanomembrane quantum-light-emitting diodes integrated onto piezoelectric actuators, Adv. Mater. 24, 2668 (2012).
  42. H. Drexler, D. Leonard, W. Hansen, J. P. Kotthaus, and P. M. Petroff, Spectroscopy of quantum levels in charge-tunable InGaAs quantum dots, Phys. Rev. Lett. 73, 2252 (1994).
  43. H. J. Krenner, E. C. Clark, T. Nakaoka, M. Bichler, C. Scheurer, G. Abstreiter, and J. J. Finley, Optically probing spin and charge interactions in a tunable artificial molecule, Phys. Rev. Lett. 97, 076403 (2006).
  44. C. L. Salter, R. M. Stevenson, I. Farrer, C. A. Nicoll, D. A. Ritchie, and A. J. Shields, An entangled-light-emitting diode, Nature 465, 594 (2010).
  45. J. Zhang, J. S. Wildmann, F. Ding, R. Trotta, Y. Huo, E. Zallo, D. Huber, A. Rastelli, and O. G. Schmidt, High yield and ultrafast sources of electrically triggered entangled-photon pairs based on strain-tunable quantum dots, Nat. Commun. 6, 10067 (2015).
  46. H. J. Krenner, C. E. Pryor, J. He, and P. M. Petroff, A semiconductor exciton memory cell based on a single quantum nanostructure, Nano Lett. 8, 1750 (2008).
  47. D. Wigger, M. Weiß, M. Lienhart, K. Müller, J. J. Finley, T. Kuhn, H. J. Krenner, and P. Machnikowski, Resonance-fluorescence spectral dynamics of an acoustically modulated quantum dot, Phys. Rev. Res. 3, 033197 (2021).
  48. P. Imany, Z. Wang, R. A. DeCrescent, R. C. Boutelle, C. A. McDonald, T. Autry, S. Berweger, P. Kabos, S. W. Nam, R. P. Mirin, and K. L. Silverman, Quantum phase modulation with acoustic cavities and quantum dots, Optica 9, 501 (2022).
  49. M. Weiß, S. Kapfinger, T. Reichert, J. J. Finley, A. Wixforth, M. Kaniber, and H. J. Krenner, Surface acoustic wave regulated single photon emission from a coupled quantum dot–nanocavity system, Appl. Phys. Lett. 109, 033105 (2016).
  50. S. G. Carter, A. S. Bracker, M. K. Yakes, M. K. Zalalutdinov, M. Kim, C. S. Kim, C. Czarnocki, M. Scheibner, and D. Gammon, Sensing flexural motion of a photonic crystal membrane with InGaAs quantum dots, Appl. Phys. Lett. 111, 183101 (2017).
  51. A. Vogele, M. M. Sonner, B. Mayer, X. Yuan, M. Weiß, E. D. Nysten, S. F. Covre da Silva, A. Rastelli, and H. J. Krenner, Quantum dot optomechanics in suspended nanophononic strings, Adv. Quantum Technol. 3, 1900102 (2020).
  52. C. Spinnler, G. N. Nguyen, Y. Wang, M. Erbe, A. Javadi, L. Zhai, S. Scholz, A. D. Wieck, A. Ludwig, P. Lodahl, L. Midolo, and R. J. Warburton, Quantum dot coupled to a suspended-beam mechanical resonator: From the unresolved- to the resolved-sideband regime, Phys. Rev. Appl. 21, 034046 (2024).
  53. C. Spinnler, G. N. Nguyen, Y. Wang, L. Zhai, A. Javadi, M. Erbe, S. Scholz, A. D. Wieck, A. Ludwig, P. Lodahl, L. Midolo, and R. J. Warburton, A single-photon emitter coupled to a phononic-crystal resonator in the resolved-sideband regime, Nat. Commun. 15, 9509 (2024).
  54. I. Yeo, A. Gloppe, E. Dupont-Ferrier, P. Verlot, N. S. Malik, E. Dupuy, J. Claudon, A. Aufféves, G. Nogues, S. Seidelin, O. Arcizet, and M. Richard, Strain-mediated coupling in a quantum dot–mechanical oscillator hybrid system, Nat. Nanotechnol. 9, 106 (2014).
  55. S. G. Carter, A. S. Bracker, G. W. Bryant, M. Kim, C. S. Kim, M. K. Zalalutdinov, M. K. Yakes, C. Czarnocki, J. Casara, M. Scheibner, and D. Gammon, Spin-mechanical coupling of an InAs quantum dot embedded in a mechanical resonator, Phys. Rev. Lett. 121, 246801 (2018).
  56. X. Yuan, M. Schwendtner, R. Trotta, Y. Huo, J. Martín-Sánchez, G. Piredda, H. Huang, J. Edlinger, C. Diskus, O. G. Schmidt, B. Jakoby, H. J. Krenner, and A. Rastelli, A frequency-tunable nanomembrane mechanical oscillator with embedded quantum dots, Appl. Phys. Lett. 115, 181902 (2019).
  57. R. Tanos, H. Tlili, Y. Curé, M. Finazzer, A. Artioli, S. Kotal, Y. Genuist, P. Verlot, J. Bleuse, J.-M. Gérard, and J. Claudon, High-order nanowire resonances for high-frequency, large-coupling-strength quantum dot hybrid nanomechanics, ACS Photonics 11, 1352 (2024).
  58. G. Modica, R. Zhu, R. Horvath, G. Beaudoin, I. Sagnes, and R. Braive, Slow propagation of 2 GHz acoustical waves in a suspended GaAs phononic waveguide on insulator, Appl. Phys. Lett. 117, 193501 (2020).
  59. A. H. Safavi-Naeini and O. Painter, Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab, Opt. Express 18, 14926 (2010).
  60. C. Brendel, V. Peano, O. Painter, and F. Marquardt, Snowflake phononic topological insulator at the nanoscale, Phys. Rev. B 97, 020102 (2018).
  61. D. Hatanaka and H. Yamaguchi, Real-space characterization of cavity-coupled waveguide systems in hypersonic phononic crystals, Phys. Rev. Appl. 13, 024005 (2020).
  62. P.-L. Ardelt, K. Gawarecki, K. Müller, A. M. Waeber, A. Bechtold, K. Oberhofer, J. M. Daniels, F. Klotz, M. Bichler, T. Kuhn, H. J. Krenner, P. Machnikowski, and J. J. Finley, Coulomb mediated hybridization of excitons in coupled quantum dots, Phys. Rev. Lett. 116, 077401 (2016).
  63. X. Yuan, S. F. Covre da Silva, D. Csontosová, H. Huang, C. Schimpf, M. Reindl, J. Lu, Z. Ni, A. Rastelli, and P. Klenovský, GaAs quantum dots under quasiuniaxial stress: Experiment and theory, Phys. Rev. B 107, 235412 (2023).
  64. C. Schimpf et al., Optical and magnetic response by design in GaAs quantum dots, PRX Quantum 6, 040309 (2025).
  65. H. Ren, T. Shah, H. Pfeifer, C. Brendel, V. Peano, F. Marquardt, and O. Painter, Topological phonon transport in an optomechanical system, Nat. Commun. 13, 3476 (2022).
  66. R. G. Povey, M.-H. Chou, G. Andersson, C. R. Conner, J. Grebel, Y. J. Joshi, J. M. Miller, H. Qiao, X. Wu, H. Yan et al., Two-dimensional optomechanical crystal resonator in gallium arsenide, Phys. Rev. Appl. 21, 014015 (2024).
  67. O. Florez, G. Arregui, M. Albrechtsen, R. C. Ng, J. Gomis-Bresco, S. Stobbe, C. M. Sotomayor-Torres, and P. D. García, Engineering nanoscale hypersonic phonon transport, Nat. Nanotechnol. 17, 947 (2022).
  68. S. Mohammadi, A. A. Eftekhar, A. Khelif, and A. Adibi, Simultaneous two-dimensional phononic and photonic band gaps in opto-mechanical crystal slabs, Opt. Express 18, 9164 (2010).
  69. B. A. Auld, Acoustic Fields and Waves in Solids (John Wiley & Sons, New York, 1973).
  70. D. Yudistira, Y. Pennec, B. Djafari Rouhani, S. Dupont, and V. Laude, Non-radiative complete surface acoustic wave bandgap for finite-depth holey phononic crystal in lithium niobate, Appl. Phys. Lett. 100, 061912 (2012).
  71. COMSOL multiphysics, https://www.comsol.com/.
  72. M. M. de Lima and P. V. Santos, Modulation of photonic structures by surface acoustic waves, Rep. Prog. Phys. 68, 1639 (2005).
  73. T. B. Bahder, Eight-band k·p model of strained zinc-blende crystals, Phys. Rev. B 41, 11992 (1990).
  74. G. W. Bryant, Electronic structure of ultrasmall quantum-well boxes, Phys. Rev. Lett. 59, 1140 (1987).
  75. K. Gawarecki, P. Machnikowski, and T. Kuhn, Electron states in a double quantum dot with broken axial symmetry, Phys. Rev. B 90, 085437 (2014).
  76. K. Gawarecki, Spin-orbit coupling and magnetic-field dependence of carrier states in a self-assembled quantum dot, Phys. Rev. B 97, 235408 (2018).
  77. B. Krummheuer, V. M. Axt, and T. Kuhn, Coupled polarization and acoustic-phonon dynamics after optical excitation of quantum dots near surfaces, Phys. Rev. B 72, 245336 (2005).
  78. J. Pustiowski, K. Müller, M. Bichler, G. Koblmüller, J. J. Finley, A. Wixforth, and H. J. Krenner, Independent dynamic acousto-mechanical and electrostatic control of individual quantum dots in a LiNbO3-GaAs hybrid, Appl. Phys. Lett. 106, 121106 (2015).
  79. D. Wigger, T. Czerniuk, D. E. Reiter, M. Bayer, and T. Kuhn, Systematic study of the influence of coherent phonon wave packets on the lasing properties of a quantum dot ensemble, New J. Phys. 19, 073001 (2017).
  80. E. D. Nysten, Y. H. Huo, H. Yu, G. F. Song, A. Rastelli, and H. J. Krenner, Multi-harmonic quantum dot optomechanics in fused LiNbO3-(Al)GaAs hybrids, J. Phys. D 50, 43LT01 (2017).
  81. O. Madelung, Introduction to Solid-State Theory, Springer Series in Solid-State Sciences, Vol. 2 (Springer, Berlin, 1978).
  82. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors: Physics and Materials Properties, 3rd ed. (Springer, Berlin, 2005).
  83. See Supplemental Material at http://link.aps.org/supplemental/10.1103/h7tj-bt38 for the numerical values of all components of the dipole moment and quadrupole tensor as a function of the electric field.
  84. M. Weiß, J. B. Kinzel, F. J. R. Schülein, M. Heigl, D. Rudolph, S. Morkötter, M. Döblinger, M. Bichler, G. Abstreiter, J. J. Finley, G. Koblmüller, A. Wixforth, and H. J. Krenner, Dynamic acoustic control of individual optically active quantum dot-like emission centers in heterostructure nanowires, Nano Lett. 14, 2256 (2014).
  85. A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, J. Chan, S. Gröblacher, and O. Painter, Two-dimensional phononic-photonic band gap optomechanical crystal cavity, Phys. Rev. Lett. 112, 153603 (2014).

  86. http://wcss.pl.

  87. M. Gawełczyk, Partial data for “Coupling quantum dots to elastic waves in a phononic crystal waveguide”, RepOD, v1, 10.18150/ZJNP5D (2026).
  88. I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, Band parameters for III–V compound semiconductors and their alloys, J. Appl. Phys. 89, 5815 (2001).
  89. R. G. Veprek, S. Steiger, and B. Witzigmann, Ellipticity and the spurious solution problem of k·p envelope equations, Phys. Rev. B 76, 165320 (2007).
  90. S. Birner, The multi-band k·p hamiltonian for heterostructures: parameters and applications, in Multi-Band Effective Mass Approximations: Advanced Mathematical Models and Numerical Techniques, edited by M. Ehrhardt-T. Koprucki (Springer International Publishing, Cham, 2014), pp. 193–244.
  91. M. A. Caro, S. Schulz, and E. P. O’Reilly, Origin of nonlinear piezoelectricity in III-V semiconductors: Internal strain and bond ionicity from hybrid-functional density functional theory, Phys. Rev. B 91, 075203 (2015).
  92. R. Winkler, Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, Springer Tracts in Modern Physics, Vol.191 (Springer, Berlin, 2003).
  93. S. Adachi, GaAs, AlAs, and AlxGa1−xAs: Material parameters for use in research and device applications, J. Appl. Phys. 58, R1 (1985).
  94. A. V. Korovin, Y. Pennec, M. Stocchi, D. Mencarelli, L. Pierantoni, T. Makkonen, J. Ahopelto, and B. Djafari Rouhani, Conversion between surface acoustic waves and guided modes of a quasi-periodic structured nanobeam, J. Phys. D 52, 32LT01 (2019).

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Phys. Rev. Applied 26, 024038– Published 17 August, 2026
  • Received 17 January 2026
  • Revised 8 July 2026
  • Accepted 13 July 2026
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