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Unified ab initio quantum-electrodynamical density functional theory for cavity-modified electron-phonon-photon coupling in solids

Benshu Fan1,*, I-Te Lu1,†, Michael Ruggenthaler1,‡, and Angel Rubio1,2,§

  • *Contact author: benshu.fan@mpsd.mpg.de
  • †Contact author: i-te.lu@mpsd.mpg.de
  • ‡Contact author: michael.ruggenthaler@mpsd.mpg.de
  • §Contact author: angel.rubio@mpsd.mpg.de
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Phys. Rev. B 114, 105111 – Published 10 August, 2026

DOI: https://doi.org/10.1103/fxd5-59hv

Abstract

Quantum-electrodynamical density-functional theory (QEDFT) provides a first-principles framework for describing materials coupled to quantized electromagnetic fields. While QEDFT has successfully captured cavity-induced modifications of electronic structures in atoms and molecules, a fully self-consistent and accurate framework to simulate and predict the structural, phonon-related, polarization, and optical response of periodic solids in optical cavities has remained elusive. Here, we introduce a unified QEDFT approach that combines collective light-matter coupling parameter in the electronic ground state, density-functional perturbation theory for phonons, and real-time time-dependent QEDFT for optical excitations. This framework enables ab initio calculations of cavity-modified electronic and phononic dispersions, Born effective charges, dielectric tensors, and both resonant and nonresonant optical absorption spectra. Using wurtzite gallium nitride (GaN) in an optical cavity as a case study, we demonstrate that the quantized vacuum field reshapes electronic, phononic, and polarization properties, producing experimentally accessible signatures in the dielectric function and absorption spectra. These results establish QEDFT as a general first-principles platform for predicting and exploring cavity-modified quantum materials.

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References (110)

  1. J. Flick, M. Ruggenthaler, H. Appel, and A. Rubio, Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry, Proc. Natl. Acad. Sci. USA 114, 3026 (2017).
  2. M. Ruggenthaler, N. Tancogne-Dejean, J. Flick, H. Appel, and A. Rubio, From a quantum-electrodynamical light–matter description to novel spectroscopies, Nat. Rev. Chem. 2, 0118 (2018).
  3. M. A. Sentef, M. Ruggenthaler, and A. Rubio, Cavity quantum-electrodynamical polaritonically enhanced electron-phonon coupling and its influence on superconductivity, Sci. Adv. 4, eaau6969 (2018).
  4. Q.-D. Jiang and F. Wilczek, Quantum atmospherics for materials diagnosis, Phys. Rev. B 99, 201104(R) (2019).
  5. Y. Ashida, A. İmamoğlu, J. Faist, D. Jaksch, A. Cavalleri, and E. Demler, Quantum electrodynamic control of matter: Cavity-enhanced ferroelectric phase transition, Phys. Rev. X 10, 041027 (2020).
  6. H. Hübener, U. De Giovannini, C. Schäfer, J. Andberger, M. Ruggenthaler, J. Faist, and A. Rubio, Engineering quantum materials with chiral optical cavities, Nat. Mater. 20, 438 (2021).
  7. F. J. Garcia-Vidal, C. Ciuti, and T. W. Ebbesen, Manipulating matter by strong coupling to vacuum fields, Science 373, eabd0336 (2021).
  8. S. Latini, D. Shin, S. A. Sato, C. Schäfer, U. De Giovannini, H. Hübener, and A. Rubio, The ferroelectric photo ground state of SrTiO3: Cavity materials engineering, Proc. Natl. Acad. Sci. USA 118, e2105618118 (2021).
  9. F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Appl. Phys. Rev. 9, 011312 (2022).
  10. E. Viñas Boström, A. Sriram, M. Claassen, and A. Rubio, Controlling the magnetic state of the proximate quantum spin liquid α−RuCl3 with an optical cavity, npj Comput. Mater. 9, 202 (2023).
  11. H. Hübener, E. V. Boström, M. Claassen, S. Latini, and A. Rubio, Quantum materials engineering by structured cavity vacuum fluctuations, Mater. Quantum Technol. 4, 023002 (2024).
  12. I.-T. Lu, D. Shin, M. K. Svendsen, H. Hübener, U. De Giovannini, S. Latini, M. Ruggenthaler, and A. Rubio, Cavity-enhanced superconductivity in MgB2 from first-principles quantum electrodynamics (QEDFT), Proc. Natl. Acad. Sci. USA 121, e2415061121 (2024).
  13. I.-T. Lu, D. Shin, M. K. Svendsen, S. Latini, H. Hübener, M. Ruggenthaler, and A. Rubio, Cavity engineering of solid-state materials without external driving, Adv. Opt. Photon. 17, 441 (2025).
  14. Q.-D. Jiang, Harnessing vacuum fluctuations to shape electronic and photonic behavior, npj Nanophoton. 2, 46 (2025).
  15. A. de la Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, and M. A. Sentef, Colloquium: Nonthermal pathways to ultrafast control in quantum materials, Rev. Mod. Phys. 93, 041002 (2021).
  16. J. Bloch, A. Cavalleri, V. Galitski, M. Hafezi, and A. Rubio, Strongly correlated electron–photon systems, Nature (London) 606, 41 (2022).
  17. C. Bao, P. Tang, D. Sun, and S. Zhou, Light-induced emergent phenomena in 2D materials and topological materials, Nat. Rev. Phys. 4, 33 (2022).
  18. Y. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, Observation of Floquet-Bloch states on the surface of a topological insulator, Science 342, 453 (2013).
  19. E. J. Sie, C. M. Nyby, C. Pemmaraju, S. J. Park, X. Shen, J. Yang, M. C. Hoffmann, B. Ofori-Okai, R. Li, A. H. Reid, et al., An ultrafast symmetry switch in a Weyl semimetal, Nature (London) 565, 61 (2019).
  20. M. Henstridge, M. Först, E. Rowe, M. Fechner, and A. Cavalleri, Nonlocal nonlinear phononics, Nat. Phys. 18, 457 (2022).
  21. S. Ito, M. Schüler, M. Meierhofer, S. Schlauderer, J. Freudenstein, J. Reimann, D. Afanasiev, K. Kokh, O. Tereshchenko, J. Güdde, et al., Build-up and dephasing of Floquet–Bloch bands on subcycle timescales, Nature (London) 616, 696 (2023).
  22. S. Zhou, C. Bao, B. Fan, H. Zhou, Q. Gao, H. Zhong, T. Lin, H. Liu, P. Yu, P. Tang, et al., Pseudospin-selective Floquet band engineering in black phosphorus, Nature (London) 614, 75 (2023).
  23. S. Zhou, C. Bao, B. Fan, F. Wang, H. Zhong, H. Zhang, P. Tang, W. Duan, and S. Zhou, Floquet engineering of black phosphorus upon below-gap pumping, Phys. Rev. Lett. 131, 116401 (2023).
  24. B. Fan, U. De Giovannini, H. Hübener, S. Zhou, W. Duan, A. Rubio, and P. Tang, Floquet optical selection rules in black phosphorus, Sci. Adv. 11, eadw2744 (2025).
  25. O. Neufeld, M. E. Tzur, G. Lerner, O. Kfir, A. Fleischer, and O. Cohen, Light symmetry, chirality, and their role in nonlinear optics and ultrafast phenomena, Adv. Opt. Photon. 18, 160 (2026).
  26. A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nat. Rev. Phys. 1, 19 (2019).
  27. T. S. Haugland, E. Ronca, E. F. Kjønstad, A. Rubio, and H. Koch, Coupled cluster theory for molecular polaritons: Changing ground and excited states, Phys. Rev. X 10, 041043 (2020).
  28. B. Munkhbat, A. Canales, B. Küçüköz, D. G. Baranov, and T. O. Shegai, Tunable self-assembled Casimir microcavities and polaritons, Nature (London) 597, 214 (2021).
  29. L. Konecny, V. P. Kosheleva, H. Appel, M. Ruggenthaler, and A. Rubio, Relativistic linear response in quantum-electrodynamical density functional theory, Phys. Rev. X 15, 031052 (2025).
  30. G. Kipp, H. M. Bretscher, B. Schulte, D. Herrmann, K. Kusyak, M. W. Day, S. Kesavan, T. Matsuyama, X. Li, S. M. Langner, et al., Cavity electrodynamics of van der Waals heterostructures, Nat. Phys. 21, 1926 (2025).
  31. J. Galego, C. Climent, F. J. Garcia-Vidal, and J. Feist, Cavity Casimir-Polder forces and their effects in ground-state chemical reactivity, Phys. Rev. X 9, 021057 (2019).
  32. X. Li, A. Mandal, and P. Huo, Cavity frequency-dependent theory for vibrational polariton chemistry, Nat. Commun. 12, 1315 (2021).
  33. C. Schäfer, J. Flick, E. Ronca, P. Narang, and A. Rubio, Shining light on the microscopic resonant mechanism responsible for cavity-mediated chemical reactivity, Nat. Commun. 13, 7817 (2022).
  34. W. Ahn, J. F. Triana, F. Recabal, F. Herrera, and B. S. Simpkins, Modification of ground-state chemical reactivity via light–matter coherence in infrared cavities, Science 380, 1165 (2023).
  35. Y. Ke, Z. Song, and Q.-D. Jiang, Vacuum-induced symmetry breaking of chiral enantiomer formation in chemical reactions, Phys. Rev. Lett. 131, 223601 (2023).
  36. F. Appugliese, J. Enkner, G. L. Paravicini-Bagliani, M. Beck, C. Reichl, W. Wegscheider, G. Scalari, C. Ciuti, and J. Faist, Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect, Science 375, 1030 (2022).
  37. A. Rubio, A new Hall for quantum protection, Science 375, 976 (2022).
  38. J. Enkner, L. Graziotto, F. Appugliese, V. Rokaj, J. Wang, M. Ruggenthaler, C. Reichl, W. Wegscheider, A. Rubio, and J. Faist, Testing the renormalization of the von Klitzing constant by cavity vacuum fields, Phys. Rev. X 14, 021038 (2024).
  39. J. Enkner, L. Graziotto, D. Boriçi, F. Appugliese, C. Reichl, G. Scalari, N. Regnault, W. Wegscheider, C. Ciuti, and J. Faist, Tunable vacuum-field control of fractional and integer quantum Hall phases, Nature (London) 641, 884 (2025).
  40. G. Jarc, S. Y. Mathengattil, A. Montanaro, F. Giusti, E. M. Rigoni, R. Sergo, F. Fassioli, S. Winnerl, S. Dal Zilio, D. Mihailovic, et al., Cavity-mediated thermal control of metal-to-insulator transition in 1T-TaS2, Nature (London) 622, 487 (2023).
  41. F. Schlawin, A. Cavalleri, and D. Jaksch, Cavity-mediated electron-photon superconductivity, Phys. Rev. Lett. 122, 133602 (2019).
  42. J. B. Curtis, Z. M. Raines, A. A. Allocca, M. Hafezi, and V. M. Galitski, Cavity quantum Eliashberg enhancement of superconductivity, Phys. Rev. Lett. 122, 167002 (2019).
  43. I. Keren, T. A. Webb, S. Zhang, J. Xu, D. Sun, B. S. Kim, D. Shin, S. S. Zhang, J. Zhang, G. Pereira, et al., Cavity-altered superconductivity, Nature (London) 650, 864 (2026).
  44. A. Chakraborty, M. Pini, M. Zündel, and F. Piazza, Controlling collective phenomena via the quantum state of interaction mediators: Changing the criticality of photon-mediated superconductivity via Fock states of light, PRX Quantum 6, 020341 (2025).
  45. H. Xu, A. Baydin, Q. Yi, I.-T. Lu, N. Zhu, T. E. Kritzell, J. Doumani, D. Kim, F. Tay, A. Rubio, et al., Vacuum-dressed superconductivity in NbN observed in a high-Q terahertz cavity, arXiv:2601.08191.
  46. E. T. Jaynes and F. W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE 51, 89 (1963).
  47. J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Modifying chemical landscapes by coupling to vacuum fields, Angew. Chem. Int. Ed 51, 1592 (2012).
  48. T. W. Ebbesen, Hybrid light–matter states in a molecular and material science perspective, Acc. Chem. Res. 49, 2403 (2016).
  49. A. Mandal, M. A. Taylor, B. M. Weight, E. R. Koessler, X. Li, and P. Huo, Theoretical advances in polariton chemistry and molecular cavity quantum electrodynamics, Chem. Rev. 123, 9786 (2023).
  50. M. Ruggenthaler, D. Sidler, and A. Rubio, Understanding polaritonic chemistry from ab initio quantum electrodynamics, Chem. Rev. 123, 11191 (2023).
  51. D. Sidler, M. Ruggenthaler, and A. Rubio, Collectively-modified intermolecular electron correlations: The connection of polaritonic chemistry and spin glass physics: Focus review, Chem. Rev. 126, 4 (2026).
  52. M. Ruggenthaler, J. Flick, C. Pellegrini, H. Appel, I. V. Tokatly, and A. Rubio, Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory, Phys. Rev. A 90, 012508 (2014).
  53. M. Ruggenthaler, Ground-state quantum-electrodynamical density-functional theory, arXiv:1509.01417.
  54. C. Schäfer, F. Buchholz, M. Penz, M. Ruggenthaler, and A. Rubio, Making ab initio QED functional(s): Nonperturbative and photon-free effective frameworks for strong light–matter coupling, Proc. Natl. Acad. Sci. USA 118, e2110464118 (2021).
  55. I.-T. Lu, M. Ruggenthaler, N. Tancogne-Dejean, S. Latini, M. Penz, and A. Rubio, Electron-photon exchange-correlation approximation for quantum-electrodynamical density-functional theory, Phys. Rev. A 109, 052823 (2024).
  56. F. Buchholz, I. Theophilou, S. E. Nielsen, M. Ruggenthaler, and A. Rubio, Reduced density-matrix approach to strong matter-photon interaction, ACS Photonics 6, 2694 (2019).
  57. F. Buchholz, I. Theophilou, K. J. Giesbertz, M. Ruggenthaler, and A. Rubio, Light–matter hybrid-orbital-based first-principles methods: The influence of polariton statistics, J. Chem. Theory Comput. 16, 5601 (2020).
  58. T. Schnappinger, D. Sidler, M. Ruggenthaler, A. Rubio, and M. Kowalewski, Cavity Born–Oppenheimer Hartree–Fock ansatz: Light–matter properties of strongly coupled molecular ensembles, J. Phys. Chem. Lett. 14, 8024 (2023).
  59. G. Thiam, R. Rossi, H. Koch, L. Belpassi, and E. Ronca, A comprehensive theory for relativistic polaritonic chemistry: A four-component ab initio treatment of molecular systems coupled to quantum fields, JACS Au 5, 3775 (2025).
  60. J. McTague and J. J. Foley, Non-Hermitian cavity quantum electrodynamics–configuration interaction singles approach for polaritonic structure with ab initio molecular Hamiltonians, J. Chem. Phys. 156, 154103 (2022).
  61. N. Vu, D. Mejia-Rodriguez, N. P. Bauman, A. Panyala, E. Mutlu, N. Govind, and J. J. Foley IV, Cavity quantum electrodynamics complete active space configuration interaction theory, J. Chem. Theory Comput. 20, 1214 (2024).
  62. U. Mordovina, C. Bungey, H. Appel, P. J. Knowles, A. Rubio, and F. R. Manby, Polaritonic coupled-cluster theory, Phys. Rev. Res. 2, 023262 (2020).
  63. P. M. M. de Melo and A. Marini, Unified theory of quantized electrons, phonons, and photons out of equilibrium: A simplified ab initio approach based on the generalized Baym-Kadanoff ansatz, Phys. Rev. B 93, 155102 (2016).
  64. J. Yang, Q. Ou, Z. Pei, H. Wang, B. Weng, Z. Shuai, K. Mullen, and Y. Shao, Quantum-electrodynamical time-dependent density functional theory within Gaussian atomic basis, J. Chem. Phys. 155, 064107 (2021).
  65. D. M. Welakuh, J. Flick, M. Ruggenthaler, H. Appel, and A. Rubio, Frequency-dependent Sternheimer linear-response formalism for strongly coupled light–matter systems, J. Chem. Theory Comput. 18, 4354 (2022).
  66. C. Pellegrini, J. Flick, I. V. Tokatly, H. Appel, and A. Rubio, Optimized effective potential for quantum electrodynamical time-dependent density functional theory, Phys. Rev. Lett. 115, 093001 (2015).
  67. J. Flick, C. Schäfer, M. Ruggenthaler, H. Appel, and A. Rubio, Ab initio optimized effective potentials for real molecules in optical cavities: Photon contributions to the molecular ground state, ACS Photonics 5, 992 (2018).
  68. M. K. Svendsen, M. Ruggenthaler, H. Hübener, C. Schäfer, M. Eckstein, A. Rubio, and S. Latini, Effective equilibrium theory of quantum light-matter interaction in cavities for extended systems and the long wavelength approximation, Commun. Phys. 8, 425 (2025).
  69. A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys. 75, 473 (2003).
  70. The electron mass used here is the physical mass. In typical cavity geometries only a very small subset of the photonic continuum is modified, whereas the vast majority of free-space modes remain unchanged. The self-energy contribution from these unmodified modes is already included in the physical mass of the electron, and only the cavity-induced deviation from free space is described explicitly through the effective photonic modes in the model.
  71. J. Flick, H. Appel, M. Ruggenthaler, and A. Rubio, Cavity Born–Oppenheimer approximation for correlated electron–nuclear-photon systems, J. Chem. Theory Comput. 13, 1616 (2017).
  72. J. Feist, J. Galego, and F. J. Garcia-Vidal, Polaritonic chemistry with organic molecules, ACS Photonics 5, 205 (2018).
  73. C. Schäfer, M. Ruggenthaler, and A. Rubio, Ab initio nonrelativistic quantum electrodynamics: Bridging quantum chemistry and quantum optics from weak to strong coupling, Phys. Rev. A 98, 043801 (2018).
  74. R. M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2020).
  75. We note that the Ckj and Dkj terms become larger when the photon frequency becomes smaller. Therefore, below a certain photon frequency, we might not be able to neglect those terms, which we leave for the future investigation.
  76. C. F. Craig, W. R. Duncan, and O. V. Prezhdo, Trajectory surface hopping in the time-dependent Kohn-Sham approach for electron-nuclear dynamics, Phys. Rev. Lett. 95, 163001 (2005).
  77. Q. Zheng, W. Chu, C. Zhao, L. Zhang, H. Guo, Y. Wang, X. Jiang, and J. Zhao, Ab initio nonadiabatic molecular dynamics investigations on the excited carriers in condensed matter systems, WIREs Comput Mol Sci 9, e1411 (2019).
  78. M. Guan, D. Chen, S. Hu, H. Zhao, P. You, and S. Meng, Theoretical insights into ultrafast dynamics in quantum materials, Ultrafast Sci. 2022, 9767251 (2022).
  79. G. D. Mahan, Many-Particle Physics (Springer Science & Business Media, New York, 2013).
  80. In the SI unit, λα is proportional to ℏΩαε0 where ℏ and ε0 are the reduced Planck constant and the vacuum permittivity, respectively.
  81. M. K. Svendsen, K. S. Thygesen, A. Rubio, and J. Flick, Ab initio calculations of quantum light–matter interactions in general electromagnetic environments, J. Chem. Theory Comput. 20, 926 (2024).
  82. L.-Y. Hsu, Chemistry meets plasmon polaritons and cavity photons: A perspective from macroscopic quantum electrodynamics, J. Phys. Chem. Lett. 16, 1604 (2025).
  83. C. M. Bustamante, F. P. Bonafé, M. Sukharev, M. Ruggenthaler, A. Nitzan, and A. Rubio, Molecular polariton dynamics in realistic cavities, J. Chem. Theory Comput. 21, 9823 (2025).
  84. F. H. M. Faisal, Theory of Multiphoton Processes (Springer Science & Business Media, New York, 2013).
  85. N. Tancogne-Dejean, M. J. Oliveira, X. Andrade, H. Appel, C. H. Borca, G. Le Breton, F. Buchholz, A. Castro, S. Corni, A. A. Correa, et al., Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems, J. Chem. Phys. 152, 124119 (2020).
  86. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, et al., Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
  87. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  88. I. Ahmadabadi, I.-T. Lu, L. A. Cunha, M. Ruggenthaler, J. Flick, and A. Rubio, Testing electron-photon exchange-correlation functional performance for many-electron systems under weak and strong light-matter coupling, arXiv:2512.14655.
  89. J. Flick, Simple exchange-correlation energy functionals for strongly coupled light-matter systems based on the fluctuation-dissipation theorem, Phys. Rev. Lett. 129, 143201 (2022).
  90. D. Novokreschenov, A. Kudlis, I. Iorsh, and I. V. Tokatly, Quantum electrodynamical density functional theory for generalized Dicke model, Phys. Rev. B 108, 235424 (2023).
  91. C. Tasci, L. A. Cunha, and J. Flick, Photon many-body dispersion: Exchange-correlation functional for strongly coupled light-matter systems, Phys. Rev. Lett. 134, 073002 (2025).
  92. M.-L. M. Tchenkoue, M. Penz, I. Theophilou, M. Ruggenthaler, and A. Rubio, Force balance approach for advanced approximations in density functional theories, J. Chem. Phys. 151, 154107 (2019).
  93. N. Tancogne-Dejean, M. Penz, A. Laestadius, M. A. Csirik, M. Ruggenthaler, and A. Rubio, Exchange energies with forces in density-functional theory, J. Chem. Phys. 160, 024103 (2024).
  94. S. Baroni, S. De Gironcoli, A. Dal Corso, and P. Giannozzi, Phonons and related crystal properties from density-functional perturbation theory, Rev. Mod. Phys. 73, 515 (2001).
  95. X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet, J.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet, et al., The ABINIT project: Impact, environment and recent developments, Comput. Phys. Commun. 248, 107042 (2020).
  96. S. Poncé, D. Jena, and F. Giustino, Hole mobility of strained GaN from first principles, Phys. Rev. B 100, 085204 (2019).
  97. I. V. Tokatly, Time-dependent density functional theory for many-electron systems interacting with cavity photons, Phys. Rev. Lett. 110, 233001 (2013).
  98. H. Herzig Sheinfux, L. Orsini, M. Jung, I. Torre, M. Ceccanti, S. Marconi, R. Maniyara, D. Barcons Ruiz, A. Hötger, R. Bertini, et al., High-quality nanocavities through multimodal confinement of hyperbolic polaritons in hexagonal boron nitride, Nat. Mater. 23, 499 (2024).
  99. V. Yu. Davydov, Y. E. Kitaev, I. N. Goncharuk, A. N. Smirnov, J. Graul, O. Semchinova, D. Uffmann, M. B. Smirnov, A. P. Mirgorodsky, and R. A. Evarestov, Phonon dispersion and Raman scattering in hexagonal GaN and AlN, Phys. Rev. B 58, 12899 (1998).
  100. T. Ruf, J. Serrano, M. Cardona, P. Pavone, M. Pabst, M. Krisch, M. D'astuto, T. Suski, I. Grzegory, and M. Leszczynski, Phonon dispersion curves in wurtzite-structure GaN determined by inelastic X-ray scattering, Phys. Rev. Lett. 86, 906 (2001).
  101. K. Parlinski and Y. Kawazoe, Ab initio study of phonons in hexagonal GaN, Phys. Rev. B 60, 15511 (1999).
  102. X. Gonze and C. Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55, 10355 (1997).
  103. A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
  104. A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
  105. C. E. Dreyer, A. Janotti, C. G. Van de Walle, and D. Vanderbilt, Correct implementation of polarization constants in wurtzite materials and impact on III-nitrides, Phys. Rev. X 6, 021038 (2016).
  106. T. Yasui, K. Kawamoto, Y.-D. Hsieh, Y. Sakaguchi, M. Jewariya, H. Inaba, K. Minoshima, F. Hindle, and T. Araki, Enhancement of spectral resolution and accuracy in asynchronous-optical-sampling terahertz time-domain spectroscopy for low-pressure gas-phase analysis, Opt. Express 20, 15071 (2012).
  107. D. Shin, I.-T. Lu, B. Fan, E. V. Boström, H. Liu, M. K. Svendsen, S. Latini, P. Tang, and A. Rubio, Multiple photon field-induced topological states in bulk HgTe, Sci. Adv. 12, eaea5823 (2026).
  108. M. J. Van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rignanese, The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018).
  109. D. Vanderbilt, Berry Phases in Electronic Structure Theory: Electric Polarization, Orbital Magnetization and Topological Insulators (Cambridge University Press, Cambridge, 2018).
  110. S. J. Byrnes, Multilayer optical calculations, arXiv:1603.02720.

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Phys. Rev. B 114, 105111– Published 10 August, 2026
  • Received 21 February 2026
  • Revised 15 June 2026
  • Accepted 16 July 2026
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