Angular deficits in flat space: remotely controllable apertures in nematic solid sheets

Recent attention has been given to the realization of angular deficits and surpluses in the local ground-state geometry of thin sheets of nematic solids as out-of-plane deformations. Such systems exhibit conical or anti-conical curvature sites, or possibly arrays of such polyhedral corners, in order to satisfy the material's spontaneous strain-generated metric requirements. Here, we turn the angular deficit requirement on its head, and show theoretically and experimentally that by appropriately altering the topology of the initially flat sheet-for example, by cutting it in carefully chosen regions-the same angular deficits and surpluses may manifest simply in-plane by changing the geometry of the cut region. Such amechanism offers a route to apertures or arrays of apertures that may be reversibly opened and closed by applying spontaneous strain with heat, light or chemical potential.