Topology leads to robustly quantized physical properties. In solids, many topological phenomena appear in Bloch states of nearly free electrons moving in a periodic potential. Recently, periodic media composing metamaterials enable photons to carry modulated momenta. These systems have highly tunable band structures and their dynamics are generically described by non-Hermitian matrices when dissipation is considered. The level crossings between such photonic bands are known as exceptional points. In this presentation, I will demonstrate that exceptional points are carrying non–Abelian charges. This leads to non-commuting operations of moving them in the reciprocal space and violation of the famous fermion-doubling theorem, realised in recent experiments. Then I will introduce parity-time symmetric systems, where two very distinct regimes, symmetry-preserving regime and spontaneous-symmetry-breaking regime, exist. The two regimes have contrasting gauge structures and their coexistence renders the system beyond Cartan's symmetric spaces and Bott periodicity. This leads to some new ideas of preparing topological states via dissipation.

杨康, 本科毕业自北京大学, 后于巴黎高等师范学院和巴黎索邦大学取得硕士和博士学位。曾于斯德哥尔摩大学任博士后, 现为柏林自由大学博士后。研究方向包括量子霍尔效应、陈绝缘体、耗散光学能带系统以及数学物理。