External fields create topological states anywhere, not just at edges.

Topological insulatorsTopological insulatorsMaterials that conduct electricity only on their edges, not through their interior. are special materials that conduct energy or signals along their outer borders while blocking them on the inside. Usually, creating these pathways requires piecing together materials with strictly different internal symmetries. This restriction makes the materials hard to adjust or redesign. To fix this, researchers introduced a new method they call topological lithography. Instead of changing the material itself, they apply an external field to time-reversal-symmetric systems. This field alters a physical process called the Jackiw-Rebbi mechanismJackiw-Rebbi mechanismA theoretical explanation for how certain defects in a material create special states at the boundary., triggering a localized topological shift inside the material. As a result, protected pathways can now appear at geometric edges, deep inside the interior bulk, or even remotely. Because operators can precisely control the applied field, these pathways can be drawn, erased, reprogrammed, and shaped into custom patterns across electronic, mechanical, and acoustic systems.

Why it matters

Topological insulators are prized for their robust edge states, but until now they were limited to boundaries between different materials. This work shows that external fields can create these states anywhere, even inside a material, and change them on demand. That means engineers could design reconfigurable circuits or waveguides that adapt in real time.

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