Atomic-like high-harmonic generation from two-dimensional materials

Science Advances 4, (2018)

Atomic-like high-harmonic generation from two-dimensional materials

Nicolas Tancogne-Dejean, Angel Rubio

The generation of high-order harmonics from atomic and molecular gases enables the production of high-energy photons and ultrashort isolated pulses. Obtaining efficiently similar photon energy from solid-state systems could lead, for instance, to more compact extreme ultraviolet and soft x-ray sources. We demonstrate from ab initio simulations that it is possible to generate high-order harmonics from free-standing monolayer materials, with an energy cutoff similar to that of atomic and molecular gases. In the limit in which electrons are driven by the pump laser perpendicularly to the monolayer, they behave qualitatively the same as the electrons responsible for highharmonic generation (HHG) in atoms, where their trajectories are described by the widely used semiclassical model,and exhibit real-space trajectories similar to those of the atomic case. Despite the similarities, the first and last steps of the well-established three-step model for atomic HHG are remarkably different in the two-dimensional materials from gases. Moreover, we show that the electron-electron interaction plays an important role in harmonic generation from monolayer materials because of strong local-field effects, which modify how the material is ionized. The recombination of the accelerated electron wave packet is also found to be modified because of the infinite extension of the material in the monolayer plane, thus leading to a more favorable wavelength scaling of the harmonic yield than in atomic HHG. Our results establish a novel and efficient way of generating high-order harmonics based on a solid-state device, with an energy cutoff and a more favorable wavelength scaling of the harmonic yield similar to those of atomic and molecular gases. Two-dimensional materials offer a unique platform where both bulk and atomic HHG can be investigated, depending on the angle of incidence. Devices based on two-dimensional materials can extend the limit of existing sources.

Additional Information

Preprint - 1.47 MB
We would like to acknowledge O. D. Mücke and M. Altarelli for very interesting and fruitful discussions. Funding: We acknowledge financial support from the European Research Council (ERC-2015-AdG-694097). Author contributions: N.T.-D. and A.R. conceived and designed the project. N.T.-D. carried out the code implementation and the numerical calculations. N.T.-D. and A.R. participated in the discussion of the results and contributed to the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. The data that support the findings of this study are available from the corresponding authors upon request and will be deposited on the NOMAD repository. The Octopus code is available from

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