Smectic order in double-twist cylinders

I propose a double-twist texture with local smectic order, which may have been seen in recent experiments [1]. As in the Renn-Lubensky TGB phase, the smectic order is broken only through a lattice of screw dislocations. A melted lattice of screw dislocations can produce a double-twist texture as can an unmelted lattice. In the latter case I show that geometry only allows for certain angles between smectic regions. I discuss the possibility of connecting these double-twist tubes together to form a smectic blue phase.