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# Observation of a roton collective mode in a two-dimensional Fermi liquid

## Abstract

Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, 4He (bosons) and 3He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon–roton mode in liquid 4He by neutron scattering, verifying Landau’s prediction1 and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as ‘zero-sound’ in 3He, and ‘plasmons’ in charged systems) and incoherent particle–hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau’s theory of Fermi liquids2,3. At higher wavevectors, the collective mode enters the particle–hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid 3He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau’s theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory4.

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## Acknowledgements

We are grateful to the Austrian–French programme Amadeus for providing initial support; to the Austrian Fonds zur Förderung der wissenschaftlichen Forschung (FWF grant P21264) , the French Agence Nationale de la Recherche (project ANR-2010-INTB-403-) and the EU FRP7 low-temperature infrastructure grant Microkelvin (project number 228464) for funding this research; and to the Institut Laue-Langevin for use of the facility.

## Author information

Authors

### Contributions

H.G., M.M., H.-J.L., A.S. and M.P. performed the neutron experiments; H.M.B., E.K. and M.P. developed the theory. All authors analysed the results and contributed to the work.

### Corresponding author

Correspondence to Henri Godfrin.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

This file contains Supplementary Text and Data, which includes Supplementary Figure 1 and additional references. (PDF 543 kb)

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Godfrin, H., Meschke, M., Lauter, HJ. et al. Observation of a roton collective mode in a two-dimensional Fermi liquid. Nature 483, 576–579 (2012). https://doi.org/10.1038/nature10919

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• DOI: https://doi.org/10.1038/nature10919

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