Topological insulators are a new phase of matter unique for their insulating bulk and perfectly conducting edges. They have been at the forefront of condensed matter physics for the past decade, and more recently inspired the emergence of topological phases in many classical-wave systems, such as photonics and acoustics. To date, all studies of topological insulators have explored systems in integer dimensions (physically, 2-D or 3-D) with a well-defined bulk and edges. However, physical dimensions do not always define the dimensions in which a system evolves: Some structures have a noninteger (fractal) dimension, despite being in a 2-D or 3-D realm.
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Source: Phys.org