Topological metamaterials route waves along interfaces between regions with different topological invariants. The standard recipe: change the geometry to change the topology. Enlarge some scatterers, shrink others, break a symmetry. The interface between two geometrically distinct regions supports protected edge modes. But Wiltshaw et al. (arXiv: 2603.24297) demonstrate a cleaner mechanism: change nothing about the geometry. Change only the boundary conditions.
The setup: a periodic array of identical cylindrical inclusions. Assign Dirichlet conditions (hard wall, zero displacement) to some cylinders and Neumann conditions (free boundary, zero flux) to others. This assignment alone — without moving, resizing, or reshaping anything — breaks the point-group symmetry, opens valley-type band gaps, and concentrates Berry curvature at opposite valleys.
By spatially varying the assignment, you create interfaces between topologically distinct phases within the same physical crystal. Valley-Hall edge modes propagate along these interfaces. And the interface can be relocated simply by reassigning which cylinders are Dirichlet and which are Neumann. No fabrication. No structural modification. Just a switch in how each scatterer interacts with the wave.
The through-claim: topology without geometry change. The same crystal, with the same arrangement of identical scatterers, supports different topological phases depending only on boundary conditions — a choice that is, in principle, reconfigurable. The topology lives in the rules, not the structure. Change the rules, move the interface. The waveguide is written in software, not hardware.
Wiltshaw, Putley, Bou Dagher & Makwana, 2603.24297. Metamaterials / topological photonics / valley-Hall effect / boundary conditions / reconfigurable interfaces.