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Advances in momentum-resolved EELS of phonons, excitons and plasmons in 2D materials and their heterostructures

Cana Elgvin, Fredrik S. Hage, and Øystein Prytz

Khairi Elyas and Katja Höflich

Christoph T. Koch and Hannah C. Nerl*

  • *Contact author: hcnerl@physik.hu-berlin.de
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Phys. Rev. Materials 10, 020201 – Published 4 February, 2026

DOI: https://doi.org/10.1103/8wwb-lxk2

Abstract

Functional nanomaterials, including two-dimensional (2D) materials and their heterostructures, are expected to impact fields ranging from catalysis and optoelectronics to nanophotonics. To realize their potential, experimental approaches need to be developed to characterize the combined materials and their components. Techniques using fast electrons, such as electron energy-loss spectroscopy (EELS), probe phenomena over an unrivaled energy range with high resolution. In addition, momentum-resolved EELS simultaneously records energy and momentum transfer to the sample and thus generates 2D datasets for each beam position. This allows excitations that occur at large momentum transfer to be resolved, including those outside of the light cone and beyond the first Brillouin zone, all while retaining nanometer-sized spatial selectivity. Such capabilities are particularly important when probing phonons, plasmons, excitons, and their coupling in 2D materials and their heterostructures.

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New Insights into Functional Materials through Advanced Electron Microscopy

The Editors of Physical Review Materials are pleased to present the Collection on New Insights into Functional Materials through Advanced Electron Microscopy, highlighting cutting-edge microscopy techniques and the extraordinary advances in materials science and engineering that they enable. The Collection is being guest-edited by Joanne Etheridge from Monash University (Australia) and Yimei Zhu from Brookhaven National Laboratory (USA). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.

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References (216)

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306, 666 (2004).
  2. H. Kroemer, Nobel lecture: Quasielectric fields and band offsets: Teaching electrons new tricks, Rev. Mod. Phys. 73, 783 (2001).
  3. P. V. Pham, S. C. Bodepudi, K. Shehzad, Y. Liu, Y. Xu, B. Yu, and X. Duan, 2D heterostructures for ubiquitous electronics and optoelectronics: Principles, opportunities, and challenges, Chem. Rev. 122, 6514 (2022).
  4. F. J. García de Abajo, Optical excitations in electron microscopy, Rev. Mod. Phys. 82, 209 (2010).
  5. F. J. Garcia de Abajo and V. Di Giulio, Optical excitations with electron beams: Challenges and opportunities, ACS Photonics 8, 945 (2021).
  6. B. Reed and M. Sarikaya, Background subtraction for low-loss transmission electron energy-loss spectroscopy, Ultramicroscopy 93, 25 (2002).
  7. D. Johnson and J. C. H Spence, Determination of the single-scattering probability distribution from plural-scattering data, J. Phys. D 7, 771 (1974).
  8. R. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope (Springer US, Boston, 2011).
  9. D. A. Leon, C. Elgvin, P. D. Nguyen, O. Prytz, F. S. Hage, and K. Berland, Unraveling many-body effects in ZnO: Combined study using momentum-resolved electron energy-loss spectroscopy and first-principles calculations, Phys. Rev. B 109, 115153 (2024).
  10. R. B. Pettit, J. Silcox, and R. Vincent, Measurement of surface-plasmon dispersion in oxidized aluminum films, Phys. Rev. B 11, 3116 (1975).
  11. A. C. Ferrari and D. M. Basko, Raman spectroscopy as a versatile tool for studying the properties of graphene, Nat. Nanotechnol. 8, 235 (2013).
  12. X. Cong, X.-L. Liu, M.-L. Lin, and P.-H. Tan, Application of Raman spectroscopy to probe fundamental properties of two-dimensional materials, npj 2D Mater. Appl. 4, 13 (2020).
  13. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS2: A new direct-gap semiconductor, Phys. Rev. Lett. 105, 136805 (2010).
  14. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli, and F. Wang, Emerging photoluminescence in monolayer MoS2, Nano Lett. 10, 1271 (2010).
  15. Z. Dang, Y. Chen, and Z. Fang, Cathodoluminescence nanoscopy: State of the art and beyond, ACS Nano 17, 24431 (2023).
  16. M. Tebyetekerwa, J. Zhang, Z. Xu, T. N. Truong, Z. Yin, Y. Lu, S. Ramakrishna, D. Macdonald, and H. T. Nguyen, Mechanisms and applications of steady-state photoluminescence spectroscopy in two-dimensional transition-metal dichalcogenides, ACS Nano 14, 14579 (2020).
  17. F. Fossard, L. Sponza, L. Schué, C. Attaccalite, F. Ducastelle, J. Barjon, and A. Loiseau, Angle-resolved electron energy loss spectroscopy in hexagonal boron nitride, Phys. Rev. B 96, 115304 (2017).
  18. R. J. Nicholls, F. S. Hage, D. G. McCulloch, Q. M. Ramasse, K. Refson, and J. R. Yates, Theory of momentum-resolved phonon spectroscopy in the electron microscope, Phys. Rev. B 99, 094105 (2019).
  19. See https://www.ill.eu/for-ill-users/instruments/instruments-list/in12/characteristics.
  20. Y. Q. Cai, D. S. Coburn, A. Cunsolo, J. W. Keister, M. G. Honnicke, X. R. Huang, C. N. Kodituwakku, Y. Stetsko, A. Suvorov, N. Hiraoka, et al., The ultrahigh resolution IXS beamline of NSLS-II: Recent advances and scientific opportunities, J. Phys.: Conf. Ser. 425, 202001 (2013).
  21. S.-X. Wang and L.-F. Zhu, Non-resonant inelastic x-ray scattering spectroscopy: A momentum probe to detect the electronic structures of atoms and molecules, Matter Radiat. Extremes 5, 054201 (2020).
  22. A. Furrer, J. Mesot, and T. Strässle, Neutron Scattering in Condensed Matter Physics (World Scientific, Singapore, 2009).
  23. M. E. Zhitomirsky and A. L. Chernyshev, Colloquium: Spontaneous magnon decays, Rev. Mod. Phys. 85, 219 (2013).
  24. L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, Resonant inelastic x-ray scattering studies of elementary excitations, Rev. Mod. Phys. 83, 705 (2011).
  25. B. Fultz and J. Howe, Neutron scattering, in Transmission Electron Microscopy and Diffractometry of Materials, Graduate Texts in Physics, edited by B. Fultz and J. Howe (Springer, Berlin, 2013), pp. 117–144.
  26. H. Ibach and D. L. Mills, Electron Energy Loss Spectroscopy and Surface Vibrations (Academic Press, New York, 1982).
  27. H. Ibach, Electron energy loss spectroscopy: The vibration spectroscopy of surfaces, Surf. Sci. 299–300, 116 (1994).
  28. J. Eisinger and J. T. Law, Adsorption of oxygen on silicon, J. Chem. Phys. 30, 410 (1959).
  29. T. Aizawa, R. Souda, Y. Ishizawa, H. Hirano, T. Yamada, K.-i. Tanaka, and C. Oshima, Phonon dispersion in monolayer graphite formed on Ni(111) and Ni(001), Surf. Sci. 237, 194 (1990).
  30. D. Kepaptsoglou, J. Á. Castellanos-Reyes, A. Kerrigan, J. Alves do Nascimento, P. M. Zeiger, K. El Hajraoui, J. C. Idrobo, B. G. Mendis, A. Bergman, V. K. Lazarov, et al., Magnon spectroscopy in the electron microscope, Nature (London) 644, 83 (2025).
  31. F. S. Hage, G. Radtke, D. M. Kepaptsoglou, M. Lazzeri, and Q. M. Ramasse, Single-atom vibrational spectroscopy in the scanning transmission electron microscope, Science 367, 1124 (2020).
  32. M. Wu, R. Shi, R. Qi, Y. Li, J. Du, and P. Gao, Four-dimensional electron energy-loss spectroscopy., Ultramicroscopy 253, 113818 (2023).
  33. R. Egerton, Limits to the spatial, energy and momentum resolution of electron energy-loss spectroscopy, Ultramicroscopy 107, 575 (2007).
  34. D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, 2nd ed. (Springer, New York, 2008).
  35. Scanning Transmission Electron Microscopy, edited by S. J. Pennycook and P. D. Nellist (Springer, New York, 2011).
  36. F. S. Hage, R. J. Nicholls, J. R. Yates, D. G. McCulloch, T. C. Lovejoy, N. Dellby, O. L. Krivanek, K. Refson, and Q. M. Ramasse, Nanoscale momentum-resolved vibrational spectroscopy, Sci. Adv. 4, eaar7495 (2018).
  37. R. Senga, K. Suenaga, P. Barone, S. Morishita, F. Mauri, and T. Pichler, Position and momentum mapping of vibrations in graphene nanostructures, Nature (London) 573, 247 (2019).
  38. R. Qi, N. Li, J. Du, R. Shi, Y. Huang, X. Yang, L. Liu, Z. Xu, Q. Dai, D. Yu, et al., Four-dimensional vibrational spectroscopy for nanoscale mapping of phonon dispersion in BN nanotubes, Nat. Commun. 12, 1179 (2021).
  39. P. Midgley, A simple new method to obtain high angular resolution ω−q patterns, Ultramicroscopy 76, 91 (1999).
  40. H. T. Do, M. Zhao, P. Li, Y. W. Soh, J. Rangaraj, B. Liu, T. Jiang, X. Zhang, J. Lu, P. Song, et al., Slow and highly confined plasmons observed in atomically thin TaS2, Nat. Commun. 16, 5801 (2025).
  41. A. Guandalini, R. Senga, Y.-C. Lin, K. Suenaga, A. Ferretti, D. Varsano, A. Recchia, P. Barone, F. Mauri, T. Pichler, et al., Excitonic effects in energy-loss spectra of freestanding graphene, Nano Lett. 23, 11835 (2023).
  42. P. Wang, A. J. D’Alfonso, S. D. Findlay, L. J. Allen, and A. L. Bleloch, Contrast reversal in atomic-resolution chemical mapping, Phys. Rev. Lett. 101, 236102 (2008).
  43. F. S. Hage, Q. M. Ramasse, and L. J. Allen, Contrast reversal in atomic-scale phonon spectroscopic imaging, Phys. Rev. B 102, 214111 (2020).
  44. N. Bohr, On the constitution of atoms and molecules, London, Edinburgh, Dublin Philos. Mag. J. Sci. 26, 1 (1913).
  45. D. Muller and J. Silcox, Delocalization in inelastic scattering, Ultramicroscopy 59, 195 (1995).
  46. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).
  47. R. Egerton, Scattering delocalization and radiation damage in stem-eels, Ultramicroscopy 180, 115 (2017).
  48. C. Dwyer, T. Aoki, P. Rez, S. L. Y. Chang, T. C. Lovejoy, and O. L. Krivanek, Electron-beam mapping of vibrational modes with nanometer spatial resolution, Phys. Rev. Lett. 117, 256101 (2016).
  49. F. S. Hage, D. M. Kepaptsoglou, Q. M. Ramasse, and L. J. Allen, Phonon spectroscopy at atomic resolution, Phys. Rev. Lett. 122, 016103 (2019).
  50. Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2, Phys. Rev. B 90, 205422 (2014).
  51. R. Erni and N. D. Browning, The impact of surface and retardation losses on valence electron energy-loss spectroscopy, Ultramicroscopy 108, 84 (2008).
  52. L. Gu, V. Srot, W. Sigle, C. Koch, P. van Aken, F. Scholz, S. B. Thapa, C. Kirchner, M. Jetter, and M. Rühle, Band-gap measurements of direct and indirect semiconductors using monochromated electrons, Phys. Rev. B 75, 195214 (2007).
  53. C. Festenberg, Energieverlustmessungen an III–V-Verbindungen, Z. Phys. 227, 453 (1969).
  54. F. J. García de Abajo, A. Rivacoba, N. Zabala, and N. Yamamoto, Boundary effects in Cherenkov radiation, Phys. Rev. B 69, 155420 (2004).
  55. F. Chahshouri, M. Taleb, F. K. Diekmann, K. Rossnagel, and N. Talebi, Interaction of excitons with Cherenkov radiation in WSe2 beyond the non-recoil approximation, J. Phys. D 55, 145101 (2022).
  56. E. Kröger, Berechnung der Energieverluste schneller Elektronen in dünnen Schichten mit Retardierung, Z. Phys. 216, 115 (1968).
  57. A. Eljarrat and C. T. Koch, Design and application of a relativistic Kramers-Kronig analysis algorithm, Ultramicroscopy 206, 112825 (2019).
  58. R. H. Ritchie, Plasma losses by fast electrons in thin films, Phys. Rev. 106, 874 (1957).
  59. C. J. Powell and J. B. Swan, Origin of the characteristic electron energy losses in aluminum, Phys. Rev. 115, 869 (1959).
  60. M. Kociak, O. Stéphan, L. Henrard, V. Charbois, A. Rothschild, R. Tenne, and C. Colliex, Experimental evidence of surface-plasmon coupling in anisotropic hollow nanoparticles, Phys. Rev. Lett. 87, 075501 (2001).
  61. J. Nelayah, M. Kociak, O. Stéphan, F. J. Garcia de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, Mapping surface plasmons on a single metallic nanoparticle, Nat. Phys. 3, 348 (2007).
  62. S. C. Liou, M.-W. Chu, R. Sankar, F.-T. Huang, G. J. Shu, F. C. Chou, and C. H. Chen, Plasmons dispersion and nonvertical interband transitions in single crystal Bi2Se3 investigated by electron energy-loss spectroscopy, Phys. Rev. B 87, 085126 (2013).
  63. Z. L. Miškovic and M. Moshayedi, Plasmon wake in anisotropic two-dimensional materials, Phys. Rev. Res. 5, 033133 (2023).
  64. H. C. Nerl, K. T. Winther, F. S. Hage, K. S. Thygesen, L. Houben, C. Backes, J. N. Coleman, Q. M. Ramasse, and V. Nicolosi, Probing the local nature of excitons and plasmons in few-layer MoS2, npj 2D Mater. Appl. 1, 2 (2017).
  65. H. C. Nerl, J. P. Guerrero-Felipe, A. M. Valencia, K. F. Elyas, K. Höflich, C. T. Koch, and C. Cocchi, Mapping the energy-momentum dispersion of hBN excitons and hybrid plasmons in hBN-WSe2 heterostructures, npj 2D Mater Appl. 8, 68 (2024).
  66. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
  67. H. Watanabe, Experimental evidence for the collective nature of the characteristic energy loss of electrons in solids—Studies on the dispersion relation of plasma frequency, J. Phys. Soc. Jpn. 11, 112 (1956).
  68. D. Pines and D. Bohm, A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions, Phys. Rev. 85, 338 (1952).
  69. D. Pines, Collective energy losses in solids, Rev. Mod. Phys. 28, 184 (1956).
  70. K. S. Thygesen, Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures, 2D Mater. 4, 022004 (2017).
  71. J. Lindhard, On the Properties of a Gas of Charged Particles, Matematisk-Fysiske Meddelelser No. 8 (Kongelige Danske Videnskabernes Selskab, Copenhagen, 1954).
  72. J. Lu, K. P. Loh, H. Huang, W. Chen, and A. T. S. Wee, Plasmon dispersion on epitaxial graphene studied using high-resolution electron energy-loss spectroscopy, Phys. Rev. B 80, 113410 (2009).
  73. F. J. Nelson, J.-C. Idrobo, J. D. Fite, Z. L. Mišković, S. J. Pennycook, S. T. Pantelides, J. U. Lee, and A. C. Diebold, Electronic excitations in graphene in the 1–50 eV range: The ϕ and ϕ+σ peaks are not plasmons, Nano Lett. 14, 3827 (2014).
  74. S. C. Liou, C.-S. Shie, C. H. Chen, R. Breitwieser, W. W. Pai, G. Y. Guo, and M.-W. Chu, π-plasmon dispersion in free-standing graphene by momentum-resolved electron energy-loss spectroscopy, Phys. Rev. B 91, 045418 (2015).
  75. D. Novko, V. Despoja, and M. Šunjić, Changing character of electronic transitions in graphene: From single-particle excitations to plasmons, Phys. Rev. B 91, 195407 (2015).
  76. V. U. Nazarov, Electronic excitations in quasi-2D crystals: What theoretical quantities are relevant to experiment? New J. Phys. 17, 073018 (2015).
  77. P. Wachsmuth, R. Hambach, G. Benner, and U. Kaiser, Plasmon bands in multilayer graphene, Phys. Rev. B 90, 235434 (2014).
  78. C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, et al., Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene, Phys. Rev. Lett. 100, 196803 (2008).
  79. T. Pichler, M. Knupfer, M. S. Golden, J. Fink, A. Rinzler, and R. E. Smalley, Localized and delocalized electronic states in single-wall carbon nanotubes, Phys. Rev. Lett. 80, 4729 (1998).
  80. F. S. Hage, T. P. Hardcastle, A. J. Scott, R. Brydson, and Q. M. Ramasse, Momentum-and space-resolved high-resolution electron energy loss spectroscopy of individual single-wall carbon nanotubes, Phys. Rev. B 95, 195411 (2017).
  81. F. S. Hage, Q. M. Ramasse, D. M. Kepaptsoglou, Ø. Prytz, A. E. Gunnaes, G. Helgesen, and R. Brydson, Topologically induced confinement of collective modes in multilayer graphene nanocones measured by momentum-resolved STEM-VEELS, Phys. Rev. B 88, 155408 (2013).
  82. J. Köster, A. Storm, T. E. Gorelik, M. J. Mohn, F. Port, M. R. Gonçalves, and U. Kaiser, Evaluation of tem methods for their signature of the number of layers in mono- and few-layer TMDs as exemplified by MoS2 and MoTe2, Micron 160, 103303 (2022).
  83. J. Hong, M. K. Svendsen, M. Koshino, T. Pichler, H. Xu, K. Suenaga, and K. S. Thygesen, Momentum-dependent oscillator strength crossover of excitons and plasmons in two-dimensional PtSe2, ACS Nano 16, 12328 (2022).
  84. V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, Negative index of refraction in optical metamaterials, Opt. Lett. 30, 3356 (2005).
  85. R. Schuster, R. Kraus, M. Knupfer, H. Berger, and B. Büchner, Negative plasmon dispersion in the transition-metal dichalcogenide 2H-TaSe2, Phys. Rev. B 79, 045134 (2009).
  86. J. van Wezel, R. Schuster, A. König, M. Knupfer, J. van den Brink, H. Berger, and B. Büchner, Effect of charge order on the plasmon dispersion in transition-metal dichalcogenides, Phys. Rev. Lett. 107, 176404 (2011).
  87. P. Cudazzo, M. Gatti, and A. Rubio, Plasmon dispersion in layered transition-metal dichalcogenides, Phys. Rev. B 86, 075121 (2012).
  88. M. N. Gjerding, M. Pandey, and K. S. Thygesen, Band structure engineered layered metals for low-loss plasmonics, Nat. Commun. 8, 15133 (2017).
  89. B. Yue, F. Hong, K.-D. Tsuei, N. Hiraoka, Y.-H. Wu, V. M. Silkin, B. Chen, and H.-k. Mao, High-energy electronic excitations in a bulk MoS2 single crystal, Phys. Rev. B 96, 125118 (2017).
  90. S. Galambosi, L. Wirtz, J. A. Soininen, J. Serrano, A. Marini, K. Watanabe, T. Taniguchi, S. Huotari, A. Rubio, and K. Hämäläinen, Anisotropic excitonic effects in the energy loss function of hexagonal boron nitride, Phys. Rev. B 83, 081413(R) (2011).
  91. B. Zhu, X. Chen, and X. Cui, Exciton binding energy of monolayer WS2, Sci. Rep. 5, 9218 (2015).
  92. G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomically thin transition metal dichalcogenides, Rev. Mod. Phys. 90, 021001 (2018).
  93. M. Palummo, M. Bernardi, and J. C. Grossman, Exciton radiative lifetimes in two-dimensional transition metal dichalcogenides, Nano Lett. 15, 2794 (2015).
  94. J. A. Wilson and A. Yoffe, The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties, Adv. Phys. 18, 193 (1969).
  95. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol 7, 699 (2012).
  96. M. M. Ugeda, A. J. Bradley, S.-F. Shi, F. H. Da Jornada, Y. Zhang, D. Y. Qiu, W. Ruan, S.-K. Mo, Z. Hussain, Z.-X. Shen, et al., Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor, Nat. Mater. 13, 1091 (2014).
  97. J. L. O’Brien, A. Furusawa, and J. Vučković, Photonic quantum technologies, Nat. Photon. 3, 687 (2009).
  98. T. Mueller and E. Malic, Exciton physics and device application of two-dimensional transition metal dichalcogenide semiconductors, npj 2D Mater Appl. 2, 29 (2018).
  99. A. Blais, S. M. Girvin, and W. D. Oliver, Quantum information processing and quantum optics with circuit quantum electrodynamics, Nat. Phys. 16, 247 (2020).
  100. G. Fugallo, M. Aramini, J. Koskelo, K. Watanabe, T. Taniguchi, M. Hakala, S. Huotari, M. Gatti, and F. Sottile, Exciton energy-momentum map of hexagonal boron nitride, Phys. Rev. B 92, 165122 (2015).
  101. S. Y. Woo, A. Zobelli, R. Schneider, A. Arora, J. A. Preuß, B. J. Carey, S. M. de Vasconcellos, M. Palummo, R. Bratschitsch, and L. H. G. Tizei, Excitonic absorption signatures of twisted bilayer WSe2 by electron energy-loss spectroscopy, Phys. Rev. B 107, 155429 (2023).
  102. L. H. G. Tizei, Y.-C. Lin, M. Mukai, H. Sawada, A.-Y. Lu, L.-J. Li, K. Kimoto, and K. Suenaga, Exciton mapping at subwavelength scales in two-dimensional materials, Phys. Rev. Lett. 114, 107601 (2015).
  103. L. H. Tizei, Y.-C. Lin, A.-Y. Lu, L.-J. Li, and K. Suenaga, Electron energy loss spectroscopy of excitons in two-dimensional-semiconductors as a function of temperature, Appl. Phys. Lett. 108, 163107 (2016).
  104. N. Bonnet, H. Y. Lee, F. Shao, S. Y. Woo, J.-D. Blazit, K. Watanabe, T. Taniguchi, A. Zobelli, O. Stéphan, M. Kociak, et al., Nanoscale modification of WS2 trion emission by its local electromagnetic environment, Nanoscale 21, 10178 (2021).
  105. P. K. Gogoi, Y.-C. Lin, R. Senga, H.-P. Komsa, S. L. Wong, D. Chi, A. V. Krasheninnikov, L.-J. Li, M. B. Breese, S. J. Pennycook, et al., Layer rotation-angle-dependent excitonic absorption in van der Waals heterostructures revealed by electron energy loss spectroscopy, ACS Nano 13, 9541 (2019).
  106. F. Shao, S. Y. Woo, N. Wu, R. Schneider, A. J. Mayne, S. M. de Vasconcellos, A. Arora, B. J. Carey, J. A. Preuß, N. Bonnet, et al., Substrate influence on transition metal dichalcogenide monolayer exciton absorption linewidth broadening, Phys. Rev. Mater. 6, 074005 (2022).
  107. S. Y. Woo, F. Shao, A. Arora, R. Schneider, N. Wu, A. J. Mayne, C.-H. Ho, M. Och, C. Mattevi, A. Reserbat-Plantey, et al., Engineering 2D material exciton line shape with graphene/h-BN encapsulation, Nano Lett. 24, 3678 (2024).
  108. T. Deilmann and K. S. Thygesen, Finite-momentum exciton landscape in mono- and bilayer transition metal dichalcogenides, 2D Mater. 6, 035003 (2019).
  109. J. Hong, M. Koshino, R. Senga, T. Pichler, H. Xu, and K. Suenaga, Deciphering the intense postgap absorptions of monolayer transition metal dichalcogenides, ACS Nano 15, 7783 (2021).
  110. A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2, Phys. Rev. Lett. 113, 076802 (2014).
  111. H. C. Nerl, K. Elyas, Z. Kochovski, N. Talebi, C. T. Koch, and K. Höflich, Flat dispersion at large momentum transfer at the onset of exciton polariton formation, Commun. Phys. 7, 388 (2024).
  112. B. Plotkin-Swing, G. J. Corbin, S. De Carlo, N. Dellby, C. Hoermann, M. V. Hoffman, T. C. Lovejoy, C. E. Meyer, A. Mittelberger, R. Pantelic, et al., Hybrid pixel direct detector for electron energy loss spectroscopy, Ultramicroscopy 217, 113067 (2020).
  113. C. Habenicht, R. Schuster, M. Knupfer, and B. Büchner, Investigation of indirect excitons in bulk 2H-MoS2 using transmission electron energy-loss spectroscopy, J. Phys.: Condens. Matter 30, 205502 (2018).
  114. A. Koitzsch, A. Pawlik, C. Habenicht, T. Klaproth, R. Schuster, B. Büchner, and M. Knupfer, Nonlocal dielectric function and nested dark excitons in MoS2, npj 2D Mater Appl. 3, 41 (2019).
  115. J. Hong, R. Senga, T. Pichler, and K. Suenaga, Probing exciton dispersions of freestanding monolayer WSe2 by momentum-resolved electron energy-loss spectroscopy, Phys. Rev. Lett. 124, 087401 (2020).
  116. E. Malic, M. Selig, M. Feierabend, S. Brem, D. Christiansen, F. Wendler, A. Knorr, and G. Berghäuser, Dark excitons in transition metal dichalcogenides, Phys. Rev. Mater. 2, 014002 (2018).
  117. S. Dong, M. Puppin, T. Pincelli, S. Beaulieu, D. Christiansen, H. Hübener, C. W. Nicholson, R. P. Xian, M. Dendzik, Y. Deng, et al., Direct measurement of key exciton properties: Energy, dynamics, and spatial distribution of the wave function, Nat. Sci. 1, e10010 (2021).
  118. D. Basov, M. Fogler, and F. García de Abajo, Polaritons in van der Waals materials, Science 354, aag1992 (2016).
  119. O. Penrose and L. Onsager, Bose-Einstein condensation and liquid helium, Phys. Rev. 104, 576 (1956).
  120. J. M. Blatt, K. W. Böer, and W. Brandt, Bose-Einstein condensation of excitons, Phys. Rev. 126, 1691 (1962).
  121. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, et al., Bose-Einstein condensation of exciton polaritons, Nature (London) 443, 409 (2006).
  122. H. Deng, H. Haug, and Y. Yamamoto, Exciton-polariton Bose-Einstein condensation, Rev. Mod. Phys. 82, 1489 (2010).
  123. T. Byrnes, N. Y. Kim, and Y. Yamamoto, Exciton-polariton condensates, Nat. Phys. 10, 803 (2014).
  124. J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, Room-temperature Bose-Einstein condensation of cavity exciton-polaritons in a polymer, Nat. Mater. 13, 247 (2014).
  125. J. B. Khurgin, Two-dimensional exciton-polariton—Light guiding by transition metal dichalcogenide monolayers, Optica 2, 740 (2015).
  126. B. Munkhbat, D. G. Baranov, M. Stuhrenberg, M. Wersall, A. Bisht, and T. Shegai, Self-hybridized exciton-polaritons in multilayers of transition metal dichalcogenides for efficient light absorption, ACS Photonics 6, 139 (2019).
  127. M. Taleb, F. Davoodi, F. K. Diekmann, K. Rossnagel, and N. Talebi, Charting the exciton-polariton landscape of WSe2 thin flakes by cathodoluminescence spectroscopy, Adv. Photonics Res. 3, 2100124 (2022).
  128. A. Thilagam, Excitonic polarons in low-dimensional transition metal dichalcogenides, Phys. B: Condens. Matter 464, 44 (2015).
  129. J. Kikkawa and K. Kimoto, Optical and acoustic phonon temperature measurements using electron nanoprobe and electron energy loss spectroscopy, Phys. Rev. B 106, 195431 (2022).
  130. P. S. Minson, F. Rivera, and R. Vanfleet, Quantitative STEM: A method for measuring temperature and thickness effects on thermal diffuse scattering using STEM/EELS, and for testing electron scattering models, Ultramicroscopy 246, 113684 (2023).
  131. J. Huang, T. B. Hoang, and M. H. Mikkelsen, Probing the origin of excitonic states in monolayer WSe2, Sci. Rep. 6, 22414 (2016).
  132. T. Devakul, V. Crépel, Y. Zhang, and L. Fu, Magic in twisted transition metal dichalcogenide bilayers, Nat. Commun. 12, 6730 (2021).
  133. P. Rivera, J. R. Schaibley, A. M. Jones, J. S. Ross, S. Wu, G. Aivazian, P. Klement, K. L. Seyler, G. Clark, N. J. Ghimire, et al., Valley-polarized exciton dynamics in a 2D semiconductor heterostructure, Science 351, 688 (2016).
  134. A. Ciarrocchi, D. Unuchek, A. Avsar, K. Watanabe, T. Taniguchi, and A. Kis, Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures, Nat. Photon. 13, 131 (2019).
  135. C. Jin, E. C. Regan, A. Yan, M. I. B. Utama, D. Wang, S. Zhao, Y. Qin, S. Yang, Z. Zheng, S. Shi, et al., Observation of moiré excitons in WSe2/WS2 heterostructure superlattices, Nature (London) 567, 76 (2019).
  136. P. Rivera, K. L. Seyler, H. Yu, J. R. Schaibley, J. Yan, D. G. Mandrus, W. Yao, and X. Xu, Interlayer valley excitons in heterobilayers of transition metal dichalcogenides, Nat. Nanotechnol. 13, 1004 (2018).
  137. S. Susarla, M. H. Naik, D. D. Blach, J. Zipfel, T. Taniguchi, K. Watanabe, L. Huang, R. Ramesh, F. H. da Jornada, S. G. Louie, et al., Hyperspectral imaging of exciton confinement within a moiré unit cell with a subnanometer electron probe, Science 378, 1235 (2022).
  138. S. Susarla, L. M. Sassi, A. Zobelli, S. Y. Woo, L. H. Tizei, O. Stéphan, and P. M. Ajayan, Mapping modified electronic levels in the moiré patterns in MoS2/WSe2 using low-loss EELS, Nano Lett. 21, 4071 (2021).
  139. J. D. Caldwell, I. Aharonovich, G. Cassabois, J. H. Edgar, B. Gil, and D. Basov, Photonics with hexagonal boron nitride, Nat. Rev. Mater. 4, 552 (2019).
  140. G. Cassabois, P. Valvin, and B. Gil, Hexagonal boron nitride is an indirect bandgap semiconductor, Nat. Photon. 10, 262 (2016).
  141. B. Arnaud, S. Lebègue, P. Rabiller, and M. Alouani, Huge excitonic effects in layered hexagonal boron nitride, Phys. Rev. Lett. 96, 026402 (2006).
  142. L. Wirtz, A. Marini, and A. Rubio, Excitons in boron nitride nanotubes: Dimensionality effects, Phys. Rev. Lett. 96, 126104 (2006).
  143. W. Aggoune, C. Cocchi, D. Nabok, K. Rezouali, M. A. Belkhir, and C. Draxl, Dimensionality of excitons in stacked van der Waals materials: The example of hexagonal boron nitride, Phys. Rev. B 97, 241114(R) (2018).
  144. R. Schuster, C. Habenicht, M. Ahmad, M. Knupfer, and B. Büchner, Direct observation of the lowest indirect exciton state in the bulk of hexagonal boron nitride, Phys. Rev. B 97, 041201(R) (2018).
  145. G. J. Snyder and E. S. Toberer, Complex thermoelectric materials, Nat. Mater. 7, 105 (2008).
  146. G. Pernot, M. Stoffel, I. Savic, F. Pezzoli, P. Chen, G. Savelli, A. Jacquot, J. Schumann, U. Denker, I. Mönch, et al., Precise control of thermal conductivity at the nanoscale through individual phonon-scattering barriers, Nat. Mater. 9, 491 (2010).
  147. K. Biswas, J. He, I. D. Blum, C.-I. Wu, T. P. Hogan, D. N. Seidman, V. P. Dravid, and M. G. Kanatzidis, High-performance bulk thermoelectrics with all-scale hierarchical architectures, Nature (London) 489, 414 (2012).
  148. M. Maldovan, Sound and heat revolutions in phononics, Nature (London) 503, 209 (2013).
  149. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  150. S. Xie, H. Zhu, X. Zhang, and H. Wang, A brief review on the recent development of phonon engineering and manipulation at nanoscales, Int. J. Extrem. Manuf. 6, 012007 (2024).
  151. B. Haas, T. M. Boland, C. Elsässer, A. K. Singh, K. March, J. Barthel, C. T. Koch, and P. Rez, Atomic-resolution mapping of localized phonon modes at grain boundaries, Nano Lett. 23, 5975 (2023).
  152. X. Yan, C. Liu, C. A. Gadre, L. Gu, T. Aoki, T. C. Lovejoy, N. Dellby, O. L. Krivanek, D. G. Schlom, R. Wu, et al., Single-defect phonons imaged by electron microscopy, Nature (London) 589, 65 (2021).
  153. J. Yan, R. Shi, J. Wei, Y. Li, R. Qi, M. Wu, X. Li, B. Feng, P. Gao, N. Shibata, et al., Nanoscale localized phonons at Al2O3 grain boundaries, Nano Lett. 24, 3323 (2024).
  154. C. Dwyer, Localization of high-energy electron scattering from atomic vibrations, Phys. Rev. B 89, 054103 (2014).
  155. P. R. Griffiths, Fourier transform infrared spectrometry, Science 222, 297 (1983).
  156. P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry, 2nd ed. (John Wiley & Sons, Hoboken, 2007).
  157. M. Cardona and G. Güntherodt, Light Scattering in Solids II: Basic Concepts and Instrumentation (Springer, Berlin, 1982).
  158. R. Loudon, The Raman effect in crystals, Adv. Phys. 13, 423 (1964).
  159. O. L. Krivanek, T. C. Lovejoy, N. Dellby, T. Aoki, R. W. Carpenter, P. Rez, E. Soignard, J. Zhu, P. E. Batson, M. J. Lagos, et al., Vibrational spectroscopy in the electron microscope, Nature (London) 514, 209 (2014).
  160. T. Miyata, M. Fukuyama, A. Hibara, E. Okunishi, M. Mukai, and T. Mizoguchi, Measurement of vibrational spectrum of liquid using monochromated scanning transmission electron microscopy–electron energy loss spectroscopy, Microscopy 63, 377 (2014).
  161. M. J. Lagos, I. C. Bicket, S. S. Mousavi M., and G. A. Botton, Advances in ultrahigh-energy resolution EELS: Phonons, infrared plasmons and strongly coupled modes, Microscopy 71, i174 (2022).
  162. R. Senga, Y.-C. Lin, S. Morishita, R. Kato, T. Yamada, M. Hasegawa, and K. Suenaga, Imaging of isotope diffusion using atomic-scale vibrational spectroscopy, Nature (London) 603, 68 (2022).
  163. P. Rez, T. Aoki, K. March, D. Gur, O. L. Krivanek, N. Dellby, T. C. Lovejoy, S. G. Wolf, and H. Cohen, Damage-free vibrational spectroscopy of biological materials in the electron microscope, Nat. Commun. 7, 10945 (2016).
  164. H. Boersch, J. Geiger, and W. Stickel, Interaction of 25-keV electrons with lattice vibrations in LiF. Experimental evidence for surface modes of lattice vibration, Phys. Rev. Lett. 17, 379 (1966).
  165. M. J. Lagos and P. E. Batson, Thermometry with subnanometer resolution in the electron microscope using the principle of detailed balancing, Nano Lett. 18, 4556 (2018).
  166. J. C. Idrobo, A. R. Lupini, T. Feng, R. R. Unocic, F. S. Walden, D. S. Gardiner, T. C. Lovejoy, N. Dellby, S. T. Pantelides, and O. L. Krivanek, Temperature measurement by a nanoscale electron probe using energy gain and loss spectroscopy, Phys. Rev. Lett. 120, 095901 (2018).
  167. H. Ibach and D. Mills, Electron Energy Loss Spectroscopy and Surface Vibrations (Academic Press, New York, 1982).
  168. K. Venkatraman, B. D. A. Levin, K. March, P. Rez, and P. A. Crozier, Vibrational spectroscopy at atomic resolution with electron impact scattering, Nat. Phys. 15, 1237 (2019).
  169. M. Xu, D.-L. Bao, A. Li, M. Gao, D. Meng, A. Li, S. Du, G. Su, S. J. Pennycook, S. T. Pantelides, et al., Single-atom vibrational spectroscopy with chemical-bonding sensitivity, Nat. Mater. 22, 612 (2023).
  170. E. R. Hoglund, D.-L. Bao, A. O’Hara, T. W. Pfeifer, M. S. B. Hoque, S. Makarem, J. M. Howe, S. T. Pantelides, P. E. Hopkins, and J. A. Hachtel, Direct visualization of localized vibrations at complex grain boundaries, Adv. Mater. 35, 2208920 (2023).
  171. R. Shi, Q. Li, X. Xu, B. Han, R. Zhu, F. Liu, R. Qi, X. Zhang, J. Du, J. Chen, et al., Atomic-scale observation of localized phonons at FeSe/SrTiO3 interface, Nat. Commun. 15, 3418 (2024).
  172. R. Qi, R. Shi, Y. Li, Y. Sun, M. Wu, N. Li, J. Du, K. Liu, C. Chen, J. Chen, et al., Measuring phonon dispersion at an interface, Nature (London) 599, 399 (2021).
  173. B. Haas, C. T. Koch, and P. Rez, Perspective on atomic-resolution vibrational electron energy-loss spectroscopy, Appl. Phys. Lett. 125, 150502 (2024).
  174. H. Fröhlich, Electrons in lattice fields, Adv. Phys. 3, 325 (1954).
  175. A. Bleloch, N. Bacon, G. Corbin, N. Dellby, M. Hoffman, M. Hotz, P. Hrncirik, N. Johnson, T. Lovejoy, C. Meyer, et al., Advances in STEM and EELS: New operation modes, detectors and software, Microsc. Microanal. 25, 512 (2019).
  176. A. Li, P. M. Zeiger, Z. He, M. Xu, S. J. Pennycook, J. Rusz, and W. Zhou, Systematic absences of optical phonon modes in phonon dispersion measured by electron microscopy, Phys. Rev. Lett. 133, 046101 (2024).
  177. X. G. Xu, B. G. Ghamsari, J.-H. Jiang, L. Gilburd, G. O. Andreev, C. Zhi, Y. Bando, D. Golberg, P. Berini, and G. C. Walker, One-dimensional surface phonon polaritons in boron nitride nanotubes, Nat. Commun. 5, 4782 (2014).
  178. P. E. Batson and M. J. Lagos, Characterization of misfit dislocations in Si quantum well structures enabled by STEM based aberration correction, Ultramicroscopy 180, 34 (2017).
  179. N. Li, X. Guo, X. Yang, R. Qi, T. Qiao, Y. Li, R. Shi, Y. Li, K. Liu, Z. Xu, et al., Direct observation of highly confined phonon polaritons in suspended monolayer hexagonal boron nitride, Nat. Mater. 20, 43 (2021).
  180. Z. Jacob, Hyperbolic phonon-polaritons, Nat. Mater. 13, 1081 (2014).
  181. A. A. Govyadinov, A. Konečná, A. Chuvilin, S. Vélez, I. Dolado, A. Y. Nikitin, S. Lopatin, F. Casanova, L. E. Hueso, J. Aizpurua, et al., Probing low-energy hyperbolic polaritons in van der Waals crystals with an electron microscope, Nat. Commun. 8, 95 (2017).
  182. J. Li, L. Wang, Y. Wang, Z. Tao, W. Zhong, Z. Su, S. Xue, G. Miao, W. Wang, H. Peng, et al., Observation of the nonanalytic behavior of optical phonons in monolayer hexagonal boron nitride, Nat. Commun. 15, 1938 (2024).
  183. C. A. Gadre, X. Yan, Q. Song, J. Li, L. Gu, H. Huyan, T. Aoki, S.-W. Lee, G. Chen, R. Wu, et al., Nanoscale imaging of phonon dynamics by electron microscopy, Nature (London) 606, 292 (2022).
  184. X. Wu, Z. Liu, and T. Luo, Magnon and phonon dispersion, lifetime, and thermal conductivity of iron from spin-lattice dynamics simulations, J. Appl. Phys. 123, 085109 (2018).
  185. K. Lyon, A. Bergman, P. Zeiger, D. Kepaptsoglou, Q. M. Ramasse, J. C. Idrobo, and J. Rusz, Theory of magnon diffuse scattering in scanning transmission electron microscopy, Phys. Rev. B 104, 214418 (2021).
  186. J. Á. Castellanos-Reyes, P. Zeiger, A. Bergman, D. Kepaptsoglou, Q. M. Ramasse, J. C. Idrobo, and J. Rusz, Unveiling the impact of temperature on magnon diffuse scattering detection in the transmission electron microscope, Phys. Rev. B 108, 134435 (2023).
  187. J. Á. Castellanos-Reyes, P. M. Zeiger, and J. Rusz, Dynamical theory of angle-resolved electron energy loss and gain spectroscopies of phonons and magnons in transmission electron microscopy including multiple scattering effects, Phys. Rev. Lett. 134, 036402 (2025).
  188. Y. Cai, J. Lan, G. Zhang, and Y.-W. Zhang, Lattice vibrational modes and phonon thermal conductivity of monolayer MoS2, Phys. Rev. B 89, 035438 (2014).
  189. J. Barthel and L. J. Allen, Interpretation of phonon spectroscopic data at atomic resolution in scanning transmission electron microscopy, Phys. Rev. B 110, 094105 (2024).
  190. T. W. Pfeifer, H. A. Walker, H. T. Aller, S. Graham, S. Pantelides, J. A. Hachtel, P. E. Hopkins, and E. R. Hoglund, Understanding phonon selection and interference in momentum-resolved electron energy loss spectroscopy, arXiv:2503.09792.
  191. J. Mun, D. Potemkin, H. Jang, S. Park, S. Mick, C. Petrovic, S. W. Cheong, M. G. Han, and Y. Zhu, Atomic resolution scanning transmission electron microscopy at liquid helium temperatures for quantum materials, Ultramicroscopy 267, 114039 (2024).
  192. C. Johnson, Q. M. Ramasse, R. Nicholls, and L. J. Allen, Ultra-high energy resolution EELS beyond room temperature, Microsc. Microanal. 30, 677 (2024).
  193. P. A. Midgley and R. E. Dunin-Borkowski, Electron tomography and holography in materials science, Nat. Mater. 8, 271 (2009).
  194. K. L. Seyler, P. Rivera, H. Yu, N. P. Wilson, E. L. Ray, D. G. Mandrus, J. Yan, W. Yao, and X. Xu, Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers, Nature (London) 567, 66 (2019).
  195. K. S. Burch, D. Mandrus, and J.-G. Park, Magnetism in two-dimensional van der Waals materials, Nature (London) 563, 47 (2018).
  196. S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, 2D transition metal dichalcogenides, Nat. Rev. Mater. 2, 17033 (2017).
  197. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  198. X. Qian, J. Liu, L. Fu, and J. Li, Quantum spin Hall effect in two-dimensional transition metal dichalcogenides, Science 346, 1344 (2014).
  199. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, et al., Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals, Nature (London) 546, 265 (2017).
  200. F. Barantani, R. Claude, F. Iyikanat, I. Madan, A. A. Sapozhnik, M. Puppin, B. Weaver, T. LaGrange, F. J. G. de Abajo, and F. Carbone, Ultrafast momentum‐resolved visualization of the interplay between phonon‐mediated scattering and plasmons in graphite, Sci. Adv. 11 1001 (2025).
  201. A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-Gonzalez, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, et al., Highly confined low-loss plasmons in graphene–boron nitride heterostructures, Nat. Mater. 14, 421 (2015).
  202. A. Q. R. Baron, High-resolution inelastic x-ray scattering I: Context, spectrometers, samples, and superconductors, in Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science, edited by E. Jaeschke, S. Khan, J. R. Schneider, and J. B. Hastings (Springer International Publishing, Cham, 2016), pp. 1643–1719.
  203. P. Cudazzo, I. V. Tokatly, and A. Rubio, Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane, Phys. Rev. B 84, 085406 (2011).
  204. F. Caruso, H. Lambert, and F. Giustino, Band structures of plasmonic polarons, Phys. Rev. Lett. 114, 146404 (2015).
  205. V. Despoja, D. Novko, K. Dekanić, M. Sunjić, and L. Marušić, Two-dimensional and ϕ plasmon spectra in pristine and doped graphene, Phys. Rev. B 87, 075447 (2013).
  206. M. L. Trolle, T. G. Pedersen, and V. Véniard, Model dielectric function for 2D semiconductors including substrate screening, Sci. Rep. 7, 39844 (2017).
  207. D. Y. Qiu, F. H. da Jornada, and S. G. Louie, Optical spectrum of MoS2: Many-body effects and diversity of exciton states, Phys. Rev. Lett. 111, 216805 (2013).
  208. C. Cocchi and C. Draxl, Optical spectra from molecules to crystals: Insight from many-body perturbation theory, Phys. Rev. B 92, 205126 (2015).
  209. M. Botifoll, I. Pinto-Huguet, and J. Arbiol, Machine learning in electron microscopy for advanced nanocharacterization: Current developments, available tools and future outlook, Nanoscale Horizons 7, 1427 (2022).
  210. P. C. M. Pate, L. Hart, and S. K. Taheri, RapidEELS: Machine learning for denoising high-frame-rate EELS spectra, Sci. Rep. 11, 19515 (2021).
  211. J. Blanco-Portals, F. Peiró, and S. Estradé, Strategies for EELS data analysis: Introducing UMAP and HDBSCAN for dimensionality reduction and clustering, Microsc. Microanal. 28, 109 (2022).
  212. D. del-Pozo-Bueno, D. Kepaptsoglou, Q. M. Ramasse, F. Peiró, and S. Estradé, Support vector machines and artificial neural networks for classification of oxidation states in EELS white-line features, Ultramicroscopy 253, 113828 (2023).
  213. S. Sultanov, R. A. W. Ayyubi, J. P. Buban, and R. F. Klie, Robust spectral anomaly detection in EELS spectral images via 3D convolutional variational autoencoders, Small 21, 2503019 (2025).
  214. V. Deinhart, L.-M. Kern, J. N. Kirchhof, S. Juergensen, J. Sturm, E. Krauss, T. Feichtner, S. Kovalchuk, M. Schneider, D. Engel, et al., The patterning toolbox FIB-o-mat: Exploiting the full potential of focused helium ions for nanofabrication, Beilstein J. Nanotechnol. 12, 304 (2021).
  215. https://www.fit4nano.eu.
  216. Raw EELS data and momentum-resolved maps are available in Zenodo at https://doi.org/10.5281/zenodo.18016957.

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Phys. Rev. Materials 10, 020201– Published 4 February, 2026
  • Received 31 March 2025
  • Accepted 3 December 2025
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