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Observation of the boson peak in a two-dimensional material

Nature Physics volume 19, pages 1910–1915 (2023)Cite this article

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Abstract

The boson peak is an excess in the phonon vibrational density of states relative to the Debye model. It has been observed in a wide range of amorphous materials, from inorganic glasses to polymers. Two-dimensional random matrix models and molecular dynamics simulations predict that the boson peak should also be present in amorphous two-dimensional materials, a notion that is of practical importance because it leads to an excess of heat capacity and influences transport properties. However, up until now, experimental observations in actual materials have not been possible due to the limited surface sensitivity of the methods usually applied to measure the boson peak. Here we present the experimental evidence of a boson peak in two-dimensional silica, through phonon spectra measured by means of inelastic helium-atom scattering. We identify the boson peak as a wavenumber-independent spectral maximum at a frequency similar to what has been observed in and predicted for bulk vitreous silica. Furthermore, we present a heterogeneous-elastic theory calculation in two dimensions, which shows how the vibrational coupling of the transversal and flexural shear vertical phonon modes produces the boson peak in two-dimensional materials at a frequency similar to that of the bulk, in agreement with our measurements.

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Fig. 1: Several examples of HAS TOF spectra, converted to energy transfer ΔE, for 2D silica supported on Ru(0001).
Fig. 2: Spectral function normalized to a linear increase in ω as a function of ΔE.
Fig. 3: Average negative ΔE part of the spectral function.
Fig. 4: Phonon dispersion curves showing energy transfer ΔE as a function of parallel momentum transfer ΔK.
Fig. 5: Σ″(ω)/ω versus ω/ωξ.

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Data availability

The experimental dataset is available via DataverseNO at https://doi.org/10.18710/CMKTQX (ref. 78).

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Acknowledgements

We want to specially thank H.-J. Freund and M. Heyde for making the 2D silica sample available for these experiments. We also thank W. Steurer for useful discussions and acknowledge the valuable contributions and stimulating discussions with G. Pacchioni. L.W. acknowledges funding from the Carl Zeiss Foundation through its breakthrough program. B.H. acknowledges funding from the Research Council of Norway (project nos. 213453 and 234159), both within the FRIPRO program. M.T. acknowledges funding from the Research Council of Norway (project no. 337339) (travel support).

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Author notes

  1. Christin Büchner

    Present address: Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Authors and Affiliations

  1. Department of Physics and Technology, University of Bergen, Bergen, Norway

    Martin Tømterud, Sabrina D. Eder & Bodil Holst

  2. Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany

    Christin Büchner

  3. Otto Schott Institute of Materials Research, University of Jena, Jena, Germany

    Lothar Wondraczek

  4. Department of Physics, NTNU–Norwegian University of Science and Technology, Trondheim, Norway

    Ingve Simonsen

  5. Institute of Physics, University of Mainz, Mainz, Germany

    Walter Schirmacher

  6. Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, Roma, Italy

    Walter Schirmacher

  7. Department of Physics and Astronomy, Clemson University, Clemson, SC, USA

    Joseph R. Manson

  8. Donostia International Physics Center (DIPC), Donostia-San Sebastián, Spain

    Joseph R. Manson

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Contributions

C.B. prepared the sample, S.D.E. performed the experiments and M.T. performed the data analysis. L.W. and W.S. provided the theoretical model. I.S. and J.R.M. supported the analysis. B.H. designed the experiments. M.T., J.R.M. and B.H. wrote the paper with contributions from all authors.

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Correspondence to Martin Tømterud or Bodil Holst.

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Tømterud, M., Eder, S.D., Büchner, C. et al. Observation of the boson peak in a two-dimensional material. Nat. Phys. 19, 1910–1915 (2023). https://doi.org/10.1038/s41567-023-02177-2

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