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Valleytronics in bulk MoS2 with a topologic optical field

Nature volume 628, pages 746–751 (2024)Cite this article

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Abstract

The valley degree of freedom1,2,3,4 of electrons in materials promises routes towards energy-efficient information storage with enticing prospects for quantum information processing5,6,7. Current challenges in utilizing valley polarization are symmetry conditions that require monolayer structures8,9 or specific material engineering10,11,12,13, non-resonant optical control to avoid energy dissipation and the ability to switch valley polarization at optical speed. We demonstrate all-optical and non-resonant control over valley polarization using bulk MoS2, a centrosymmetric material without Berry curvature at the valleys. Our universal method utilizes spin angular momentum-shaped trefoil optical control pulses14,15 to switch the material’s electronic topology and induce valley polarization by transiently breaking time and space inversion symmetry16 through a simple phase rotation. We confirm valley polarization through the transient generation of the second harmonic of a non-collinear optical probe pulse, depending on the trefoil phase rotation. The investigation shows that direct optical control over the valley degree of freedom is not limited to monolayer structures. Indeed, such control is possible for systems with an arbitrary number of layers and for bulk materials. Non-resonant valley control is universal and, at optical speeds, unlocks the possibility of engineering efficient multimaterial valleytronic devices operating on quantum coherent timescales.

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Fig. 1: Valley polarization in bulk MoS2 with a strong trefoil field.
Fig. 2: Pump–probe setup for valley control in bulk MoS2.
Fig. 3: Time-dependent optical control in bulk MoS2 induced by the trefoil field.
Fig. 4: Probing valley polarization in bulk MoS2.

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Data availability

All data supporting the study are available as source data and with the responding data processing scripts on https://github.com/jbiegert/ICFO-AUO-Valleytronics. All parameters necessary to reproduce the calculations are given in Methods and Supplementary Information. This information and ref. 16 provide the necessary details for a researcher to run IWERIA, or to develop a similar code. Further details on request.

Code availability

Three numerical codes were used in this work: Quantum Espresso40, Wannier90 (ref. 41) and IWERIA16. The first two are open-source and can be found at https://www.quantum-espresso.org/ and https://wannier.org/, respectively. IWERIA is an in-house code and parts of it relevant to reproducing the results of this work can be made available from the corresponding author upon request. All scripts can be found under https://github.com/jbiegert/ICFO-AUO-Valleytronics.

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Acknowledgements

J.B. acknowledges financial support from the European Research Council for ERC Advanced Grant “TRANSFORMER” (788218), ERC Proof of Concept Grant “miniX” (840010), FET-OPEN “PETACom” (829153), FET-OPEN “OPTOlogic” (899794), FET-OPEN “TwistedNano” (101046424), Laserlab-Europe (871124), MINECO for Plan Nacional PID2020–112664GB-I00; AGAUR for SGR-2021-01449, MINECO for “Severo Ochoa” (CEX2019-000910-S), Fundació Cellex Barcelona, the CERCA Programme/Generalitat de Catalunya and the Alexander von Humboldt Foundation for the Friedrich Wilhelm Bessel Prize. I.T. and J.B. acknowledge support from Marie Skłodowska-Curie ITN “smart-X” (860553). A.J.-G. acknowledges support from the Comunidad de Madrid through the Talento Grant 2022-T1/IND-24102 and from the EU Marie Skłodowska-Curie Global Fellowship (101028938). R. S. acknowledges support from Grant No. PID2021-122769NB-I00 funded by MCIN/AEI and from the fellowship LCF/BQ/PR21/11840008 from “La Caixa” Foundation (ID 100010434). M.I. acknowledges support from FET-OPEN “OPTOlogic” (899794). M.I. also acknowledges the Limati SFB 1777 “Light–matter interaction at interfaces” project, award number 441234705. O.S. acknowledges funding from the European Union (ERC ULISSES, award number 101054696). We thank Ryo Mizuta Graphics for their 3D assets. We also thank U. Elu, M. Enders and L. Maidment for their assistance.

Author information

Authors and Affiliations

  1. ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Spain

    Igor Tyulnev, Julita Poborska, Lenard Vamos & Jens Biegert

  2. Instituto de Ciencia de Materiales de Madrid (ICMM), Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain

    Álvaro Jiménez-Galán & Rui E. F. Silva

  3. Max-Born-Institut, Berlin, Germany

    Álvaro Jiménez-Galán, Olga Smirnova & Misha Ivanov

  4. Max-Planck Institute for Science of Light, Erlangen, Germany

    Philip St. J. Russell & Francesco Tani

  5. Department of Physics, Friedrich-Alexander-Universität, Erlangen, Germany

    Philip St. J. Russell

  6. Technische Universität Berlin, Berlin, Germany

    Olga Smirnova

  7. Technion - Israel Institute of Technology, Haifa, Israel

    Olga Smirnova & Misha Ivanov

  8. Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany

    Misha Ivanov

  9. Department of Physics, Imperial College London, London, UK

    Misha Ivanov

  10. ICREA, Barcelona, Spain

    Jens Biegert

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  1. Igor Tyulnev
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Contributions

J.B. conceived the project. I.T., J.P. and L.V. performed the experiments with support from J.B. I.T. prepared the sample and analysed experimental data with support from J.B. and L.V. A.J.-G. performed the calculations with support from R.F.S., M.I. and O.S. A.J.-G., R.F.S., M.I. and O.S. analysed theory data. R.S. developed the numerical code. F.T. and P.St.J.R. supplied the ARR-PCF. J.B. wrote the manuscript with I.T. and input from all authors.

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Correspondence to Jens Biegert.

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Extended data figures and tables

Extended Data Fig. 1 Polarization scans for linear, circular and trefoil driving fields.

Harmonic spectra from GaSe are recorded as a function of the crystal rotation angle.

Extended Data Fig. 2 Trefoil selection rules from two-colour mixing of pump photons with opposite spin-angular momentum.

Right, simulated pump spectra for perfect and experimental ellipticity of the pump colours. Maximal suppression of 3 N harmonics is observed for perfectly circular 3.2 µm + 1.6 µm. Imperfect ellipticity leads to a detectable 3 N harmonic signal, meanwhile suppression reduces with harmonic orders approaching the cut-off.

Extended Data Fig. 3 Probe second harmonic signal’s dependency on the pump trefoil rotation, analysed through Fast Fourier Transform.

Clear modulation with 60° periodicity appears in the power spectral density (PSD) during strong field excitation (green) following the six-fold symmetry of the 2H-MoS2 sample.

Extended Data Fig. 4 DFT-calculated bilayer MoS2.

a, Crystal structure. b, First Brillouin zone. c, Band structure obtained by projecting onto the d orbitals of Mo and the p orbitals of S. Red (blue) dispersion curves indicate the ground state fully-filled (empty) valence (conduction) bands.

Supplementary information

Supplementary Information

Supplementary Notes 1–3, Figs 1–6 and References.

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Tyulnev, I., Jiménez-Galán, Á., Poborska, J. et al. Valleytronics in bulk MoS2 with a topologic optical field. Nature 628, 746–751 (2024). https://doi.org/10.1038/s41586-024-07156-y

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