Photonic axion insulator.

Axions, hypothetical elementary particles that remain undetectable in nature, can arise as quasiparticles in three-dimensional crystals known as axion insulators. Previous implementations of axion insulators have largely been limited to two-dimensional systems, leaving their topological properties in three dimensions unexplored in experiment. Here, we realize an axion insulator in a three-dimensional photonic crystal and probe its topological properties. Demonstrated features include half-quantized Chern numbers on each surface that resembles a fractional Chern insulator, unidirectional chiral hinge states forming topological transport in three dimensions, and arithmetic operations between fractional and integer Chern numbers. Our work experimentally establishes the axion insulator as a three-dimensional topological phase of matter and enables chiral states to form complex, unidirectional three-dimensional networks through braiding.