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Two-Dimensional Topological Edge States in Periodic Space-Time Interfaces

Ohad Segal1, Yonatan Plotnik2, Eran Lustig3, Yonatan Sharabi1, Moshe-Ishay Cohen2, Alexander Dikopoltsev4, and Mordechai Segev1,2,*

  • 1Electrical and Computer Engineering Department, Technion, 32000 Haifa, Israel
  • 2Physics Department, Technion, 32000 Haifa, Israel
  • 3Ginzton Laboratory and Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA
  • 4Institute of Quantum Electronics, ETH Zürich, Zurich, Switzerland

  • *Contact author: msegev@technion.ac.il
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Phys. Rev. Lett. 135, 163801 – Published 14 October, 2025

DOI: https://doi.org/10.1103/5hf5-pg3t

Abstract

Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals, offer nonresonant amplification drawing energy from the modulation. Combining these concepts, we explore topological systems that vary periodically in both time and space, manifesting the best of both worlds. We present topological phases and topological edge states in photonic space-time crystals—materials in which the refractive index varies periodically in both space and time, displaying band gaps in both frequency and momentum. The topological nature of this system leads to topological invariants that govern the phase between refracted and reflected waves generated from both the spatial and the temporal interfaces. The 2D (1D space + 1D time) nature of this system leads to propagating edge states, and a unique edge state that grows exponentially in amplitude while following the space-time edge.

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Outline

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Phys. Rev. Lett. 135, 163801– Published 14 October, 2025
  • Received 10 June 2025
  • Revised 10 August 2025
  • Accepted 15 September 2025
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