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 a mechanism 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.