# Ultrafast coherent nonlinear nanooptics and nanoimaging of graphene

## Abstract

With its linear energy dispersion and large transition dipole matrix element, graphene is an attractive material for nonlinear optoelectronic applications. However, the mechanistic origin of its strong nonlinear response, the ultrafast coherent dynamics and the associated nanoscale phenomena have remained elusive due to a lack of suitable experimental techniques. Here, using adiabatic nanofocusing and imaging, we study the broadband four-wave mixing (FWM) response of graphene with nanometre and femtosecond spatio-temporal resolution. We detect a nonlinear signal enhancement at the edges and dependence on the number of layers from excitation areas as small as 104 carbon atoms. Femtosecond FWM nanoimaging and concomitant frequency-domain measurements reveal dephasing on T2 ≈ 6 ± 1 fs timescales, which we attribute to a strong electron–electron interaction. We also identify an unusual non-local FWM response on ~100–400 nm length scales, which we assign to a Doppler effect controlling the nonlinear interaction between the tip near-field momenta and the graphene electrons with high Fermi velocity. These results illustrate the distinct nonlinear nanooptical properties of graphene, expected also in related classes of two-dimensional materials, that could form the basis for improved nonlinear and ultrafast nanophotonic devices.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

T.J., V.K. and M.B.R. acknowledge funding from the US Department of Energy, Office of Basic Sciences, Division of Material Sciences and Engineering, under award no. DE-SC0008807. A.B. and M.B.R. acknowledge additional support from the Air Force Office for Scientific Research through grants nos. FA9550-17-1-0341 and FA9550-14-1-0376. V.K. acknowledges support from ITMO Fellowship. M.T. acknowledges support from the Ministry of Science and Higher Education of the Russian Federation under contract no. 14.W03.31.0032. The authors thank R. Ernstorfer for valuable discussions and Y. Cai, J. Yan, G. C. Geschwind and M. May for experimental support.

## Author information

V.K., T.J. and M.B.R. conceived and designed the experiments. T.J. and V.K. conducted the measurements. M.T. and A.B. provided the theory. All authors discussed and interpreted the results. T.J. wrote the manuscript with the help of all authors.

Correspondence to Alexey Belyanin or Markus B. Raschke.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information: Nature Nanotechnology thanks Andrea Giugni, Themistoklis Sidiropoulos and other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Notes 1–15, Supplementary Figs. 1–13 and Supplementary refs. 1–18.

### Supplementary Movie 1

Supplementary video of Fig. 5.

### Supplementary Movie 2

Supplementary video of Fig. 6.

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