Quantcast

Photonic topological insulator with broken time-reversal symmetry

Research paper by Cheng He, Xiao-Chen Sun, Xiao-Ping Liu, Ming-Hui Lu, Yulin Chen, Liang Feng, Yan-Feng Chen

Indexed on: 19 Apr '16Published on: 18 Apr '16Published in: PNAS



Abstract

A topological insulator is a material with an insulating interior but time-reversal symmetry-protected conducting edge states. Since its prediction and discovery almost a decade ago, such a symmetry-protected topological phase has been explored beyond electronic systems in the realm of photonics. Electrons are spin-1/2 particles, whereas photons are spin-1 particles. The distinct spin difference between these two kinds of particles means that their corresponding symmetry is fundamentally different. It is well understood that an electronic topological insulator is protected by the electron’s spin-1/2 (fermionic) time-reversal symmetry <mml:math><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">T</mml:mi><mml:mi mathvariant="bold-italic">f</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>Tf2=−1. However, the same protection does not exist under normal circumstances for a photonic topological insulator, due to photon’s spin-1 (bosonic) time-reversal symmetry <mml:math><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">T</mml:mi><mml:mi mathvariant="bold-italic">b</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>Tb2=1. In this work, we report a design of photonic topological insulator using the Tellegen magnetoelectric coupling as the photonic pseudospin orbit interaction for left and right circularly polarized helical spin states. The Tellegen magnetoelectric coupling breaks bosonic time-reversal symmetry but instead gives rise to a conserved artificial fermionic-like-pseudo time-reversal symmetry, Tp (<mml:math><mml:mrow><mml:msubsup><mml:mi mathvariant="bold-italic">T</mml:mi><mml:mi mathvariant="bold-italic">p</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>Tp2=−1), due to the electromagnetic duality. Surprisingly, we find that, in this system, the helical edge states are, in fact, protected by this fermionic-like pseudo time-reversal symmetry Tp rather than by the bosonic time-reversal symmetry Tb. This remarkable finding is expected to pave a new path to understanding the symmetry protection mechanism for topological phases of other fundamental particles and to searching for novel implementations for topological insulators.