Science_-_6_March_2020

occur at frequencies lying within the allowed
bands of the host. The recognition of reso-
nant modes was delayed by their peculiar
characteristics, where the vibrational ampli-
tudedoesnotvanishfarfromthedefect,ex-
tending instead over the entire crystal ( 28 ).
Furthermore, experimental observations of
these effects have, thus far, been limited to
indirect fingerprints, often at the macroscopic
scale. Volgmannet al.( 13 ) used scanning probe
microscope (SPM)–IETS to detect a local energy-
dependent increase in phonon DOS on a Ag (100)
surface, which they attributed to a substitu-
tional Cu atom. However, the surface nature
of these experiments and the lack of more
direct visualization means precluded an un-
ambiguous interpretation.
In contrast, the ability demonstrated in this
work to directly measure, at the atomic scale,
the localized component of the vibrational
signature of a single impurity atom within a
solid, and to match the observed spectral fine
structure to theoretically predicted modes,
realizes the potential of phonon spectroscopy
intheSTEM.TheSTEM-EELStechnique,char-
acterized by single-atom defect sensitivity com-
bined with isotope selectivity ( 17 ) and the ability
to operate at cryogenic temperatures ( 29 ), now
enables potential experiments where a single
functionalizing isotope is fingerprinted at the
atomic scale through its vibrational signature.
The approach should be applicable to three-

dimensional structures, although challenges

will arise from the complexity of the compu-

tational work necessary to inform these ex-

periments. Nevertheless, this opens up a path

to further applications in solid-state science,

where the electron beam of the STEM can be

used to assemble functional devices atom by

atom ( 30 ) and to spectroscopically probe the

resulting lattice dynamics and their coupling

with other quasiparticles.

REFERENCES AND NOTES

1. W. R. Hamilton,Philos. Trans. R. Soc. 124 , 247–308 (1834).


2. J. W. Strutt,The Theory of Sound(Cambridge Univ. Press,
   1887).


3. I. M. Lifšic,Nuovo Cim. 3 , 716–734 (1956).


4. A. S. Barker, A. J. Sievers,Rev. Mod. Phys. 47 ,S1–S179 (1975).


5. D. J. Voneshenet al.,Nat. Mater. 12 , 1028–1032 (2013).


6. C. Brunet al.,Nat. Phys. 10 , 444–450 (2014).


7. M. Shaoet al.,Nat. Commun. 5 , 3180 (2014).


8. R. F. Wallis, Ed.,Localized Excitations in Solids(Springer, 1968).


9. O. L. Krivaneket al.,Nature 514 , 209–212 (2014).


10. T. Miyataet al.,Microscopy 63 , 377–382 (2014).


11. P. Z. El-Khouryet al.,Adv. Phys. X. 1 ,35–54 (2016).


12. H. Gawronski, M. Mehlhorn, K. Morgenstern,Science 319 ,
    930 – 933 (2008).


13. K. Volgmannet al.,Nat. Commun. 5 , 5089 (2014).


14. J. C. Idroboet al.,Phys. Rev. Lett. 120 , 095901 (2018).


15. M. J. Lagos, A. Trügler, U. Hohenester, P. E. Batson,Nature
    543 , 529–532 (2017).


16. F. S. Hageet al.,Sci. Adv. 4 , eaar7495 (2018).
    17.J. A. Hachtelet al.,Science 363 , 525–528 (2019).


17. K. Suenaga, M. Koshino,Nature 468 , 1088–1090 (2010).


18. W. Zhouet al.,Nature Nanotech. 7 , 161–165 (2012).


19. F. S. Hageet al.,ACS Nano 12 , 1837–1848 (2018).


20. T. C. Lovejoyet al.,Appl. Phys. Lett. 100 , 154101 (2012).


21. F. S. Hage, D. M. Kepaptsoglou, Q. M. Ramasse, L. J. Allen,
    Phys. Rev. Lett. 122 , 016103 (2019).
    23. C. Dwyeret al.,Phys. Rev. Lett. 117 , 256101 (2016).
    24. R. Sengaet al.,Nature 573 , 247–250 (2019).
    25. Q. M. Ramasseet al.,Nano Lett. 13 , 4989–4995 (2013).
    26. P. Giannozziet al.,J. Phys. Condens. Matter 21 , 395502
    (2009).
    27. E. W. Montroll, R. B. Potts,Phys. Rev. 100 , 525– 543
    (1955).
    28. R. Brout, W. Visscher,Phys. Rev. Lett. 9 ,54–55 (1962).
    29. M. T. Hotzet al.,Microsc. Microanal. 24 , 1132–1133 (2018).
    30. T. Susiet al.,2D Mater. 4 , 042004 (2017).

ACKNOWLEDGMENTS

The authors gratefully acknowledge R. Brydson, M. Bugnet, and

E. Prestat for useful discussions.Funding:SuperSTEM is the UK

National Research Facility for Advanced Electron Microscopy,

supported by the Engineering and Physical Sciences Research

Council (EPSRC). This work was granted access to the

High-Performance Computing resources of the Institut du

Développement et des Ressources en Informatique Scientifique

(IDRIS) under allocation 2019-A0060910820, attributed by the

Grand Equipement National de Calcul Intensif (GENCI).Author

contributions:Q.M.R. conceived the project. F.S.H., Q.M.R., and

D.M.K. designed and carried out the experiments and interpreted

the data. G.R. and M.L. carried out and interpreted the theoretical

calculations. All authors contributed to the preparation of the

manuscript.Competing interests:The authors declare no

competing interests.Data and materials availability:All data

necessary for evaluating the conclusions of the paper are included

in the main text and/or the supplementary materials. Data related

to those presented here are available from the authors upon

reasonable request.

SUPPLEMENTARY MATERIALS

science.sciencemag.org/content/367/6482/1124/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S12

References ( 31 – 43 )

7 November 2019; accepted 3 February 2020

10.1126/science.aba1136

Hageet al.,Science 367 , 1124–1127 (2020) 6 March 2020 4of4

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