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Lightwave valleytronics in a monolayer of tungsten diselenide


As conventional electronics approaches its limits1, nanoscience has urgently sought methods of fast control of electrons at the fundamental quantum level2. Lightwave electronics3—the foundation of attosecond science4—uses the oscillating carrier wave of intense light pulses to control the translational motion of the electron’s charge faster than a single cycle of light5,6,7,8,9,10,11,12,13,14,15. Despite being particularly promising information carriers, the internal quantum attributes of spin16 and valley pseudospin17,18,21 have not been switchable on the subcycle scale. Here we demonstrate lightwave-driven changes of the valley pseudospin and introduce distinct signatures in the optical readout. Photogenerated electron–hole pairs in a monolayer of tungsten diselenide are accelerated and collided by a strong lightwave. The emergence of high-odd-order sidebands and anomalous changes in their polarization direction directly attest to the ultrafast pseudospin dynamics. Quantitative computations combining density functional theory with a non-perturbative quantum many-body approach assign the polarization of the sidebands to a lightwave-induced change of the valley pseudospin and confirm that the process is coherent and adiabatic. Our work opens the door to systematic valleytronic logic at optical clock rates.

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Fig. 1: High-odd-order sideband generation in monolayer WSe2.
Fig. 2: Electronic structure of WSe2 and quantum theory of high-order sideband generation.
Fig. 3: High-order sideband polarization for different crystal orientations.
Fig. 4: Intervalley mixing and lightwave valleytronics.


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The work in Regensburg was supported by the European Research Council through grant number 305003 (QUANTUMsubCYCLE) as well as by the Deutsche Forschungsgemeinschaft (through grant number HU 1598/2-1, SFB 1277, projects A05, B05 and B06, and GRK 1570) and the work in Marburg and Michigan by the Deutsche Forschungsgemeinschaft (through SFB 1083 and grant numbers KI 917/3-1 and KI 917/2-2).

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Nature thanks J. Wang and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Authors and Affiliations



F.L., P.G.H., C.P.S., S.S., S.W.K., M.K. and R.H. conceived the study. F.L., C.P.S., S.S. and R.H. carried out the experiment and analysed the data. P.N., C.S. and T.K. provided, processed and characterized the samples. M.G. and J.F. performed the DFT calculations and P.G.H., J.T.S., U.H., S.W.K. and M.K. developed the quantum-mechanical model, carried out the computations and analysed the data. All authors discussed the results and contributed to the writing of the manuscript.

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Correspondence to M. Kira.

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Extended data figures and tables

Extended Data Fig. 1 Sample orientation.

a, Azimuthal scan of the second-harmonic intensity polarized parallel to the excitation pulse, ISHG,|| (blue curve), revealing the armchair direction at a crystal angle of φ = 30°. The dashed line marks the expected scaling proportional to sin2(3φ). Around the polar diagram, the hexagonal Brillouin zone of WSe2 is depicted with the high-symmetry points. b, Optical microscope image of the exfoliated monolayer on the visco-elastic gel film used for exfoliation. Areas appearing in lighter grey are few-layer tungsten diselenide. c, Monolayer sample after transfer to a diamond substrate. The contrast of this image has been enhanced to improve the visibility of the atomically thin WSe2 film. The red arrows mark the same edge in b and c, which has been identified as the zigzag direction using the SHG scan.

Extended Data Fig. 2 Polarization of subcycle sideband emission.

Circularly polarized 10-fs near-infrared (NIR) pulses (polarization-resolved intensity depicted as black spheres) excite valley-polarized electron–hole pairs in a monolayer of tungsten diselenide. Simultaneously, an atomically strong terahertz wave is applied in the zigzag direction and may transfer electrons and holes to the non-excited K′ valley. The high-order sideband emission resulting from coherent electron–hole collisions driven by the most intense half-cycle is measured to have an elliptical polarization (blue spheres), and contains contributions from the opposite valley. Our quantum theory reproduces this polarization state (red curve) and reveals a transfer yield of 66% to the initially unexcited K′ valley.

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Langer, F., Schmid, C.P., Schlauderer, S. et al. Lightwave valleytronics in a monolayer of tungsten diselenide. Nature 557, 76–80 (2018).

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