Rolled Up or Crumpled: Phases of Asymmetric Tethered Membranes.

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 membranes, red blood cell membrane extracts, and on graphene coated on one side, could test these predictions.

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