Spatial Engineering of Topological Quantum Matter with Structured Light

Structured light provides a powerful means of controlling matter while itself exhibiting nontrivial spatial topology. Here, we show that these spatial structures can be harnessed to locally engineer the topological properties of matter. In a paradigmatic example of a topological insulator with Dirac surface states driven by an optical skyrmion beam, we show that structured light spatially tailors the effective Hamiltonian, yielding position-dependent topological gaps and Dirac velocities. The resulting gap modulation can create topological and trivial regions separated by optically defined interfaces, without introducing material boundaries or chemical modifications. We further show that the geometry of these interfaces can be controlled through the spatial structure of the light, in particular its orbital angular momentum. Our results establish structured light as a route to dynamically pattern topological phases and open a broader perspective on the interplay between topology in light and matter, including the possibility of transferring topological characteristics between the two.