A graphene sheet is 2D – but some thin materials may not fit neatly into that category ALFRED PASIEKA/SCIENCE PHOTO LIBRARY A new quantum state of matter behaves as if it doesn’t fully belong to a world with two or three dimensions of space, revealing a previously unobserved way for electrons to move. Physicists categorise states of matter based on how electrons move within a material. This motion depends on many factors, such as the arrangement of the material’s atoms. When a thin material is immersed in a magnetic field, its electrons trace tiny circles, and any stream of them is pushed to the material’s side. This is known as the Hall effect. For materials that are magnetic, electron choreographies become more complex, giving rise to different versions of this effect. Lei Wang at Nanjing University in China and his colleagues unexpectedly discovered a new version of this phenomenon, which they call the transdimensional anomalous Hall effect (TDAHE). The team was studying electrons in a thin material made from carbon atoms arranged in a pattern …