Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Optical analogue of Dresselhaus spin–orbit interaction in photonic graphene

## Abstract

The concept of gauge fields plays a significant role in many areas of physics, from particle physics and cosmology to condensed-matter systems, where gauge potentials are a natural consequence of electromagnetic fields acting on charged particles and are of central importance in topological states of matter1. Here, we report on the experimental realization of a synthetic non-Abelian gauge field for photons2 in a honeycomb microcavity lattice3. We show that the effective magnetic field associated with transverse electric–transverse magnetic splitting has the symmetry of the Dresselhaus spin–orbit interaction around Dirac points in the dispersion, and can be regarded as an SU(2) gauge field4. The symmetry of the field is revealed in the optical spin Hall effect, where, under resonant excitation of the Dirac points, precession of the photon pseudospin around the field direction leads to the formation of two spin domains. Furthermore, we observe that the Dresselhaus-type field changes its sign in the same Dirac valley on switching from s to p bands, in good agreement with the tight-binding modelling. Our work demonstrating a non-Abelian gauge field for light on the microscale paves the way towards manipulation of photons via spin on a chip.

This is a preview of subscription content, access via your institution

## Relevant articles

• ### Circularly polarized electroluminescence from a single-crystal organic microcavity light-emitting diode based on photonic spin-orbit interactions

Nature Communications Open Access 03 January 2023

• ### Manipulating polariton condensates by Rashba-Dresselhaus coupling at room temperature

Nature Communications Open Access 01 July 2022

## Access options

\$39.95

Prices may be subject to local taxes which are calculated during checkout

## Data availability

The data that support the findings of this study are openly available from the University of Sheffield repository at https://doi.org/10.15131/shef.data.13060610.

## References

1. Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

2. Chen, Y. et al. Non-Abelian gauge field optics. Nat. Commun. 10, 3125 (2019).

3. Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).

4. Nalitov, A. V., Malpuech, G., Terças, H. & Solnyshkov, D. D. Spin–orbit coupling and the optical spin Hall effect in photonic graphene. Phys. Rev. Lett. 114, 026803 (2015).

5. Yang, C. N. & Mills, R. L. Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96, 191–195 (1954).

6. Wilczek, F. & Zee, A. Appearance of gauge structure in simple dynamical systems. Phys. Rev. Lett. 52, 2111–2114 (1984).

7. Fröhlich, J. & Studer, U. M. Gauge invariance and current algebra in nonrelativistic many-body theory. Rev. Mod. Phys. 65, 733–802 (1993).

8. Jin, P.-Q., Li, Y.-Q. & Zhang, F.-C. SU(2) × U(1) unified theory for charge, orbit and spin currents. J. Phys. A 39, 7115–7123 (2006).

9. Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1260 (2015).

10. Ohno, H., Stiles, M. D. & Dieny, B. Spintronics. Proc. IEEE. Inst. Electr. Electron. Eng. 104, 1782–1786 (2016).

11. Aidelsburger, M., Nascimbene, S. & Goldman, N. Artificial gauge fields in materials and engineered systems. Comptes Rendus Phys. 19, 394–432 (2018).

12. Shelykh, I. A., Kavokin, A. V. & Malpuech, G. in Spin Dynamics of Exciton Polaritons in Microcavities Ch. 9, 187–210 (Wiley, 2007).

13. Rechtsman, M. C. et al. Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures. Nat. Photon. 7, 153–158 (2013).

14. Liu, F., Xu, T., Wang, S., Hang, Z. H. & Li, J. Polarization beam splitting with gauge field metamaterials. Adv. Opt. Mater. 7, 1801582 (2019).

15. Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

16. Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).

17. Rechcińska, K. et al. Engineering spin–orbit synthetic Hamiltonians in liquid–crystal optical cavities. Science 366, 727–730 (2019).

18. Gianfrate, A. et al. Measurement of the quantum geometric tensor and of the anomalous Hall drift. Nature 578, 381–385 (2020).

19. Fieramosca, A. et al. Chromodynamics of photons in an artificial non-Abelian magnetic Yang–Mills field. Preprint at https://arxiv.org/abs/1912.09684 (2019).

20. Solnyshkov, D., Nalitov, A., Teklu, B., Franck, L. & Malpuech, G. Spin-dependent Klein tunneling in polariton graphene with photonic spin–orbit interaction. Phys. Rev. B 93, 085404 (2016).

21. Milićević, M. et al. Edge states in polariton honeycomb lattices. 2D Mater. 2, 034012 (2015).

22. Milićević, M. et al. Type-III and tilted Dirac cones emerging from flat bands in photonic orbital graphene. Phys. Rev. X 9, 031010 (2019).

23. Sala, V. G. et al. Spin–orbit coupling for photons and polaritons in microstructures. Phys. Rev. X 5, 011034 (2015).

24. Whittaker, C. E. et al. Exciton polaritons in a two-dimensional Lieb lattice with spin–orbit coupling. Phys. Rev. Lett. 120, 097401 (2018).

25. Yang, Y. et al. Synthesis and observation of non-Abelian gauge fields in real space. Science 365, 1021–1025 (2019).

26. Zhang, C., Wang, Y. & Zhang, W. Topological phase transition with p orbitals in the exciton–polariton honeycomb lattice. J. Phys. Condens. Matter 31, 335403 (2019).

27. Dresselhaus, G. Spin–orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955).

28. Kavokin, A., Malpuech, G. & Glazov, M. Optical spin Hall effect. Phys. Rev. Lett. 95, 136601 (2005).

29. Leyder, C. et al. Observation of the optical spin Hall effect. Nat. Phys. 3, 628–631 (2007).

30. Gulevich, D. R., Yudin, D., Iorsh, I. V. & Shelykh, I. A. Kagome lattice from an exciton–polariton perspective. Phys. Rev. B 94, 115437 (2016).

31. Nalitov, A. V., Solnyshkov, D. D. & Malpuech, G. Polariton $${\mathbb{Z}}$$ topological insulator. Phys. Rev. Lett. 114, 116401 (2015).

32. Klembt, S. et al. Exciton–polariton topological insulator. Nature 562, 552–556 (2018).

33. Bleu, O., Solnyshkov, D. D. & Malpuech, G. Interacting quantum fluid in a polariton Chern insulator. Phys. Rev. B 93, 085438 (2016).

34. Flayac, H., Solnyshkov, D. D., Shelykh, I. A. & Malpuech, G. Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect. Phys. Rev. Lett. 110, 016404 (2013).

35. Shapochkin, P. Y. et al. Polarization-resolved strong light-matter coupling in planar GaAs/AlGaAs waveguides. Opt. Lett. 43, 4526–4529 (2018).

36. Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2015).

37. Khanikaev, A. B. & Shvets, G. Two-dimensional topological photonics. Nat. Photon. 11, 763–773 (2017).

38. Whittaker, C. E. et al. Effect of photonic spin–orbit coupling on the topological edge modes of a Su–Schrieffer–Heeger chain. Phys. Rev. B 99, 081402 (2019).

39. Shelykh, I. A., Nalitov, A. V. & Iorsh, I. V. Optical analog of Rashba spin–orbit interaction in asymmetric polariton waveguides. Phys. Rev. B 98, 155428 (2018).

## Acknowledgements

The work was supported by UK EPSRC grants nos. EP/N031776/1 and EP/R04385X/1 and by the Russian Science Foundation (project no. 19-72-20120). I.A.S. acknowledges support from the Icelandic Science Foundation, project ‘Hybrid Polaritonics’. A.V.N. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 846353.

## Author information

Authors

### Contributions

C.E.W. and T.D. performed the experiments and analysed the data. E.C. grew the sample. B.R. performed post-growth fabrication. A.V.N. and I.A.S. provided theoretical input. C.E.W., A.V.N. and A.V.Y. performed theory calculations. C.E.W. and D.N.K. designed the experiment. C.E.W., A.V.N., I.A.S., M.S.S. and D.N.K. wrote the manuscript.

### Corresponding authors

Correspondence to C. E. Whittaker or D. N. Krizhanovskii.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature Photonics thanks Yi Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–9 and Sections 1–6.

## Rights and permissions

Reprints and Permissions

Whittaker, C.E., Dowling, T., Nalitov, A.V. et al. Optical analogue of Dresselhaus spin–orbit interaction in photonic graphene. Nat. Photonics 15, 193–196 (2021). https://doi.org/10.1038/s41566-020-00729-z

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41566-020-00729-z

• ### Circularly polarized electroluminescence from a single-crystal organic microcavity light-emitting diode based on photonic spin-orbit interactions

• Jichao Jia
• Xue Cao
• Hongbing Fu

Nature Communications (2023)

• ### Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature

• Renjie Tao
• Kai Peng
• Wei Bao

Nature Materials (2022)

• ### Manipulating polariton condensates by Rashba-Dresselhaus coupling at room temperature

• Yao Li
• Xuekai Ma
• Tingge Gao

Nature Communications (2022)

• ### Non-Abelian gauge fields in circuit systems

• Jiexiong Wu
• Zhu Wang
• Rui Yu

Nature Electronics (2022)