Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Quantum valley pseudospin controlled by strain

Maurício F. C. Martins Quintela1,2,3,*, Miguel Sá1,2,3, Alejandro J. Uría-Álvarez3, Mikhail Malakhov4, Giovanni Cistaro1,5, Jorge Quereda6, Juan J. Palacios2,3,7, and Antonio Picón1,2,6,†

  • *Contact author: mfcmquintela@gmail.com
  • †Contact author: antonio.picon@csic.es

Phys. Rev. Research 7, 043265 – Published 8 December, 2025

DOI: https://doi.org/10.1103/fpwv-vtvk

Abstract

Valleytronics, as an alternative to traditional electronics or spintronics, is based on the encoding of quantum information in pseudospin valley quantum numbers, rather than in charge or spin states. A key ingredient is the (optical) manipulation of valley states before loss of coherence, which can be as fast as 100 fs. Previous works have shown the possibility of valley state manipulation using external fields. Here, we propose uniaxial strain as a more flexible and robust scheme to manipulate the valley state through the breaking of the crystal symmetry and the concomitant lifting of the degeneracy of the 1s exciton energy. Our theory is corroborated by state-of-the-art numerical simulations in monolayer hBN and shows the possibility to control valley pseudospin at the attosecond timescale.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (71)

  1. L. Du, T. Hasan, A. Castellanos-Gomez, G.-B. Liu, Y. Yao, C. N. Lau, and Z. Sun, Engineering symmetry breaking in 2D layered materials, Nat. Rev. Phys. 3, 193 (2021).
  2. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012).
  3. S. A. Vitale, D. Nezich, J. O. Varghese, P. Kim, N. Gedik, P. Jarillo-Herrero, D. Xiao, and M. Rothschild, Valleytronics: Opportunities, challenges, and paths forward, Small 14, 1801483 (2018).
  4. J. Freudenstein, M. Borsch, M. Meierhofer, D. Afanasiev, C. P. Schmid, F. Sandner, M. Liebich, A. Girnghuber, M. Knorr, M. Kira, and R. Huber, Attosecond clocking of correlations between Bloch electrons, Nature (London) 610, 290 (2022).
  5. G. Wang, X. Marie, B. L. Liu, T. Amand, C. Robert, F. Cadiz, P. Renucci, and B. Urbaszek, Control of exciton valley coherence in transition metal dichalcogenide monolayers, Phys. Rev. Lett. 117, 187401 (2016).
  6. Z. Ye, D. Sun, and T. F. Heinz, Optical manipulation of valley pseudospin, Nat. Phys. 13, 26 (2017).
  7. E. J. Sie, C. H. Lui, Y.-H. Lee, L. Fu, J. Kong, and N. Gedik, Large, valley-exclusive Bloch-Siegert shift in monolayer WS2, Science 355, 1066 (2017).
  8. J. Li, R. Yang, R. Li, and C. P. Grigoropoulos, Exciton dynamics in 2D transition metal dichalcogenides, Adv. Opt. Mater. 13, 2403137 (2025).
  9. A. Kormányos, V. Zólyomi, N. D. Drummond, and G. Burkard, Spin-orbit coupling, quantum dots, and qubits in monolayer transition metal dichalcogenides, Phys. Rev. X 4, 011034 (2014).
  10. G Széchenyi, L. Chirolli, and A. Pályi, Impurity-assisted electric control of spin-valley qubits in monolayer MoS2, 2D Mater. 5, 035004 (2018).
  11. J. Pawłowski, D. Żebrowski, and S. Bednarek, Valley qubit in a gated MoS2 monolayer quantum dot, Phys. Rev. B 97, 155412 (2018).
  12. A. J. Uría-Álvarez, J. J. Esteve-Paredes, M. García-Blázquez, and J. J. Palacios, Efficient computation of optical excitations in two-dimensional materials with the xatu code, Comput. Phys. Commun. 295, 109001 (2024).
  13. D. Çakır, H. Sahin, and F. M. Peeters, Tuning of the electronic and optical properties of single-layer black phosphorus by strain, Phys. Rev. B 90, 205421 (2014).
  14. R. Roldán, A. Castellanos-Gomez, E. Cappelluti, and F. Guinea, Strain engineering in semiconducting two-dimensional crystals, J. Phys.: Condens. Matter 27, 313201 (2015).
  15. J. J. Esteve-Paredes, S. Pakdel, and J. J. Palacios, Quenching of exciton recombination in strained two-dimensional monochalcogenides, Phys. Rev. Lett. 123, 077402 (2019).
  16. S. Zhao, X. Li, B. Dong, H. Wang, H. Wang, Y. Zhang, Z. Han, and H. Zhang, Valley manipulation in monolayer transition metal dichalcogenides and their hybrid systems: Status and challenges, Rep. Prog. Phys. 84, 026401 (2021).
  17. H. Li, D.-Y. Lin, A. Di Renzo, S. Puebla, R. Frisenda, X. Gan, J. Quereda, Y. Xie, A. M. Al-Enizi, A. Nafady, and A. Castellanos-Gomez, Stretching ReS2 along different crystal directions: Anisotropic tuning of the vibrational and optical responses, Appl. Phys. Lett. 120, 063101 (2022).
  18. I. Niehues, E. D. S. Nysten, R. Schmidt, M. Weiß, and D. Wigger, Excitons in quantum technologies: The role of strain engineering, MRS Bull. 49, 958 (2024).
  19. G. Krizman, J. Bermejo-Ortiz, T. Zakusylo, M. Hajlaoui, T. Takashiro, M. Rosmus, N. Olszowska, J. J. Kołodziej, G. Bauer, Y. Guldner, G. Springholz, and L.-A. de Vaulchier, Valley-polarized quantum Hall phase in a strain-controlled Dirac system, Phys. Rev. Lett. 132, 166601 (2024).
  20. Z. An, P. Soubelet, Y. Zhumagulov, M. Zopf, A. Delhomme, C. Qian, P. E. Faria Junior, J. Fabian, X. Cao, J. Yang, A. V. Stier, F. Ding, and J. J. Finley, Strain control of exciton and trion spin-valley dynamics in monolayer transition metal dichalcogenides, Phys. Rev. B 108, L041404 (2023).
  21. M. A. Conway, S. K. Earl, J. B. Muir, T.-H.-Y. Vu, J. O. Tollerud, K. Watanabe, T. Taniguchi, M. S. Fuhrer, M. T. Edmonds, and J. A. Davis, Effects of Floquet engineering on the coherent exciton dynamics in monolayer WS2, ACS Nano 17, 14545 (2023).
  22. J.-Y. Li, A.-D. Fan, Y.-K. Wang, Y. Zhang, and S. Li, Strain-induced valley polarization, topological states, and piezomagnetism in two-dimensional altermagnetic V2Te2O, V2STeO, V2SSeO, and V2S2O, Appl. Phys. Lett. 125, 222404 (2024).
  23. M. M. Glazov, F. Dirnberger, V. M. Menon, T. Taniguchi, K. Watanabe, D. Bougeard, J. D. Ziegler, and A. Chernikov, Exciton fine structure splitting and linearly polarized emission in strained transition-metal dichalcogenide monolayers, Phys. Rev. B 106, 125303 (2022).
  24. A. M. Kumar, D. Yagodkin, R. Rosati, D. J. Bock, C. Schattauer, S. Tobisch, J. Hagel, B. Höfer, J. N. Kirchhof, P. Hernández López, K. Burfeindt, S. Heeg, C. Gahl, F. Libisch, E. Malic, and K. I. Bolotin, Strain fingerprinting of exciton valley character in 2D semiconductors, Nat. Commun. 15, 7546 (2024).
  25. R. Schmidt, A. Arora, G. Plechinger, P. Nagler, A. Granados del Águila, M. V. Ballottin, P. C. M. Christianen, S. Michaelis de Vasconcellos, C. Schüller, T. Korn, and R. Bratschitsch, Magnetic-field-induced rotation of polarized light emission from monolayer WS2, Phys. Rev. Lett. 117, 077402 (2016).
  26. F. Gucci, E. B. Molinero, M. Russo, P. San-Jose, F. V. A. Camargo, M. Maiuri, M. Ivanov, Á. Jiménez-Galán, R. E. F. Silva, S. D. Conte, and G. Cerullo, Ultrafast valleytronic logic operations, arXiv:2412.08318.
  27. G. Gupta, K. Watanabe, T. Taniguchi, and K. Majumdar, Observation of ∼100% valley-coherent excitons in monolayer MoS2 through giant enhancement of valley coherence time, Light Sci. Appl. 12, 173 (2023).
  28. K. Hao, G. Moody, F. Wu, C. K. Dass, L. Xu, C.-H. Chen, L. Sun, M.-Y. Li, L.-J. Li, A. H. MacDonald, and X. Li, Direct measurement of exciton valley coherence in monolayer WSe2, Nat. Phys. 12, 677 (2016).
  29. P. Herrmann, S. Klimmer, T. Lettau, T. Weickhardt, A. Papavasileiou, K. Mosina, Z. Sofer, I. Paradisanos, D. Kartashov, J. Wilhelm, and G. Soavi, Nonlinear valley selection rules and all-optical probe of broken time-reversal symmetry in monolayer WSe2, Nat. Photon. 19, 300 (2025).
  30. A. L’Huillier, Nobel lecture: The route to attosecond pulses, Rev. Mod. Phys. 96, 030503 (2024).
  31. A. Moulet, J. B. Bertrand, T. Klostermann, A. Guggenmos, N. Karpowicz, and E. Goulielmakis, Soft x-ray excitonics, Science 357, 1134 (2017).
  32. M. Lucchini, S. A. Sato, G. D. Lucarelli, B. Moio, G. Inzani, R. Borrego-Varillas, F. Frassetto, L. Poletto, H. Hübener, U. De Giovannini, A. Rubio, and M. Nisoli, Unravelling the intertwined atomic and bulk nature of localised excitons by attosecond spectroscopy, Nat. Commun. 12, 1021 (2021).
  33. G. Cistaro, L. Plaja, F. Martín, and A. Picón, Attosecond x-ray transient absorption spectroscopy in graphene, Phys. Rev. Res. 3, 013144 (2021).
  34. M. Malakhov, G. Cistaro, F. Martín, and A. Picón, Exciton migration in two-dimensional materials, Commun. Phys. 7, 196 (2024).
  35. J. F. P. Mosquera, G. Cistaro, M. Malakhov, E. Pisanty, A. Dauphin, L. Plaja, A. Chacón, M. Lewenstein, and A. Picón, Topological phase transitions via attosecond x-ray absorption spectroscopy, Rep. Prog. Phys. 87, 117901 (2024).
  36. G. Cistaro, M. Malakhov, J. J. Esteve-Paredes, A. J. Uría-Álvarez, R. E. F. Silva, F. Martín, J. J. Palacios, and A. Picón, Theoretical approach for electron dynamics and ultrafast spectroscopy (EDUS), J. Chem. Theory Comput. 19, 333 (2023).
  37. W. Yao, D. Xiao, and Q. Niu, Valley-dependent optoelectronics from inversion symmetry breaking, Phys. Rev. B 77, 235406 (2008).
  38. F. Zhang, C. S. Ong, J. W. Ruan, M. Wu, X. Q. Shi, Z. K. Tang, and S. G. Louie, Intervalley excitonic hybridization, optical selection rules, and imperfect circular dichroism in monolayer h−BN, Phys. Rev. Lett. 128, 047402 (2022).
  39. S. Ishii, N. Yokoshi, and H. Ishihara, Optical selection rule of monolayer transition metal dichalcogenide by an optical vortex, J. Phys.: Conf. Ser. 1220, 012056 (2019).
  40. M. S. Dresselhaus, G. Dresselhaus, and A. Jorio, Group Theory: Application to the Physics of Condensed Matter (Springer, Berlin, 2007), 2008 ed.
  41. J. Jasiński, A. Balgarkashi, V. Piazza, D. Dede, A. Surrente, M. Baranowski, D. K. Maude, M. Banerjee, R. Frisenda, A. Castellanos-Gomez, A. Fontcuberta i Morral, and P. Plochocka, Strain induced lifting of the charged exciton degeneracy in monolayer MoS2 on a GaAs nanomembrane, 2D Mater. 9, 045006 (2022).
  42. S. Hirata and M. Head-Gordon, Time-dependent density functional theory within the Tamm–Dancoff approximation, Chem. Phys. Lett. 314, 291 (1999).
  43. A. Dreuw and M. Head-Gordon, Single-reference ab initio methods for the calculation of excited states of large molecules, Chem. Rev. 105, 4009 (2005).
  44. I. Ozfidan, M. Korkusinski, A. D. Güçlü, J. A. McGuire, and P. Hawrylak, Microscopic theory of the optical properties of colloidal graphene quantum dots, Phys. Rev. B 89, 085310 (2014).
  45. Z. Peng, X. Chen, Y. Fan, D. J. Srolovitz, and D. Lei, Strain engineering of 2D semiconductors and graphene: From strain fields to band-structure tuning and photonic applications, Light Sci. Appl. 9, 190 (2020).
  46. J. Pawłowski, J. E. Tiessen, R. Dax, and J. Shi, Electrical manipulation of valley qubit and valley geometric phase in lateral monolayer heterostructures, Phys. Rev. B 109, 045411 (2024).
  47. A. Picón, L. Plaja, and J. Biegert, Attosecond x-ray transient absorption in condensed-matter: A core-state-resolved Bloch model, New J. Phys. 21, 043029 (2019).
  48. B. Buades, A. Picón, E. Berger, I. León, N. Di Palo, S. L. Cousin, C. Cocchi, E. Pellegrin, J. H. Martin, S. Mañas-Valero, E. Coronado, T. Danz, C. Draxl, M. Uemoto, K. Yabana, M. Schultze, S. Wall, M. Zürch, and J. Biegert, Attosecond state-resolved carrier motion in quantum materials probed by soft x-ray XANES, Appl. Phys. Rev. 8, 011408 (2021).
  49. Y.-K. Zhang, J.-D. Zheng, W.-Y. Tong, Y.-F. Zhao, Y.-F. Tan, Y.-H. Shen, Z. Guan, F.-Y. Yue, P.-H. Xiang, N. Zhong, J.-H. Chu, and C.-G. Duan, Ferroelastically controlled ferrovalley states in stacked bilayer systems with inversion symmetry, Phys. Rev. B 108, L241120 (2023).
  50. Mechanics of Fibrous Networks, Elsevier Series in Mechanics of Advanced Materials, edited by V. Silberschmidt (Elsevier Science Publishing, Philadelphia, PA, 2022).
  51. V. M. Pereira, A. H. Castro Neto, and N. M. R. Peres, Tight-binding approach to uniaxial strain in graphene, Phys. Rev. B 80, 045401 (2009).
  52. Q. Peng, W. Ji, and S. De, Mechanical properties of the hexagonal boron nitride monolayer: Ab initio study, Comput. Mater. Sci. 56, 11 (2012).
  53. T. Han, Y. Luo, and C. Wang, Effects of temperature and strain rate on the mechanical properties of hexagonal boron nitride nanosheets, J. Phys. D 47, 025303 (2014).
  54. A. Falin, Q. Cai, E. J. Santos, D. Scullion, D. Qian, R. Zhang, Z. Yang, S. Huang, K. Watanabe, T. Taniguchi, M. R. Barnett, Y. Chen, R. S. Ruoff, and L. H. Li, Mechanical properties of atomically thin boron nitride and the role of interlayer interactions, Nat. Commun. 8, 15815 (2017).
  55. A. H. Castro Neto and F. Guinea, Electron-phonon coupling and Raman spectroscopy in graphene, Phys. Rev. B 75, 045404 (2007).
  56. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009).
  57. B. Wunsch, F. Guinea, and F. Sols, Dirac-point engineering and topological phase transitions in honeycomb optical lattices, New J. Phys. 10, 103027 (2008).
  58. Y. Hasegawa, R. Konno, H. Nakano, and M. Kohmoto, Zero modes of tight-binding electrons on the honeycomb lattice, Phys. Rev. B 74, 033413 (2006).
  59. T. G. Pedersen, Intraband effects in excitonic second-harmonic generation, Phys. Rev. B 92, 235432 (2015).
  60. A. Taghizadeh and T. G. Pedersen, Nonlinear optical selection rules of excitons in monolayer transition metal dichalcogenides, Phys. Rev. B 99, 235433 (2019).
  61. M. F. C. M. Quintela and T. G. Pedersen, Anisotropic linear and nonlinear excitonic optical properties of buckled monolayer semiconductors, Phys. Rev. B 107, 235416 (2023).
  62. C. Aversa and J. E. Sipe, Nonlinear optical susceptibilities of semiconductors: Results with a length-gauge analysis, Phys. Rev. B 52, 14636 (1995).
  63. K. Nakagahara and K. Wakabayashi, Enhanced valley polarization of graphene on h-BN under circularly polarized light irradiation, Phys. Rev. B 106, 075403 (2022).
  64. R. de L. Kronig, On the theory of dispersion of X-rays, J. Opt. Soc. Am. 12, 547 (1926).
  65. H. A. M. Kramers, La diffusion de la lumiere par les atomes, in Atti del Congresso Internazionale dei Fisici, Settembre 1927 (N. Zanichelli, Bologna, Italy, 1928), pp. 545–557.
  66. G. Arfken, Mathematical Methods for Physicists (Academic Press, San Diego, CA, 1985), 3rd ed.
  67. B. Y. Hu, Kramers–Kronig in two lines, Am. J. Phys. 57, 821 (1989).
  68. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), 3rd ed.
  69. J. A. Bearden, X-ray wavelengths, Rev. Mod. Phys. 39, 78 (1967).
  70. A. Thompson, X-ray Data Booklet, Lawrence Berkeley National Laboratory (Lawrence Berkeley National Laboratory, University of California, Berkeley, CA, 2001), 3rd ed.
  71. C. Ott, A. Kaldun, P. Raith, K. Meyer, M. Laux, J. Evers, C. H. Keitel, C. H. Greene, and T. Pfeifer, Lorentz meets Fano in spectral line shapes: A universal phase and its laser control, Science 340, 716 (2013).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation