  We show that inversion-asymmetric tethered membranes exhibit a new
double-spiral phase with long range orientational order not present in
symmetric membranes. We calculate the universal algebraic spiral shapes of
these membranes in this phase. Asymmetry can trigger the crumpling of these
membranes as well.
  In-vitro experiments on lipid, red blood cell membrane extracts, and on
graphene coated on one side, could test these predictions.
