Fermionic time-reversal symmetry in a photonic topological insulator


Much of the recent attention directed towards topological insulators is motivated by their hallmark feature of protected chiral edge states. In electronic (or fermionic) topological insulators, these states originate from time-reversal symmetry and allow carriers with opposite spin-polarization to propagate in opposite directions at the edge of an insulating bulk. By contrast, photonic (or bosonic) systems are generally assumed to be precluded from supporting edge states that are intrinsically protected by time-reversal symmetry. Here, we experimentally demonstrate counter-propagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is the design of a Floquet driving protocol that incorporates effective fermionic time-reversal symmetry, enabling the realization of the photonic version of an electronic topological insulator. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby offering alternative opportunities for photonics as well as acoustics, mechanical waves and cold atoms.

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Fig. 1: Conceptual idea.
Fig. 2: Schematic of the driving protocol.
Fig. 3: Experimental demonstration of TRS-protected counter-propagating edge modes.
Fig. 4: Experimental verification of fermionic TRS.

Data availability

The data represented in Figs. 3d,e,g,h and 4b are provided with the paper as source data. All other data that support results in this Article are available from the corresponding author upon reasonable request.

Code availability

The numerical codes that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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A.S. gratefully acknowledges financial support from the Deutsche Forschungsgemeinschaft (grants SZ 276/9-1, SZ 276/19-1, SZ 276/20-1, BL 574/13-1) and the Alfried Krupp von Bohlen und Halbach Foundation. We thank C. Otto for preparing the high-quality fused silica samples used in all experiments presented here.

Author information




The theory was established by B.H., A.A. and H.F. The sample design and lattice implementation were developed by L.M., M.H. and A.S. The characterization of the lattice structure was carried out by L.M., M.K. and T.B. The project was supervised by H.F. and A.S. All authors discussed the results and co-wrote the paper.

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Correspondence to Andreas Alvermann or Alexander Szameit.

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Supplementary information

Supplementary Information

Detailed experimental techniques, additional measurements, extended theory, stability checking

Source data

Source Data Fig. 3

Image data of Fig. 3

Source Data Fig. 4

Experimental data points of Fig. 4b

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Maczewsky, L.J., Höckendorf, B., Kremer, M. et al. Fermionic time-reversal symmetry in a photonic topological insulator. Nat. Mater. (2020). https://doi.org/10.1038/s41563-020-0641-8

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