Phase Separation on Bicontinuous Cubic Membranes: Symmetry Breaking, Re-entrant and Domain Facetting

We study the phase separation of binary lipid mixtures that form bicontinuous cubic phases. The competition between non-uniform Gaussian membrane curvature and line tension leads to a very rich phase diagram, where we observe symmetry breaking of the membrane morphologies and reentrant phenomena due to the formation of bridges between segregated domains. Upon increasing the line tension contribution, we also find facetting of lipid domains that we explain using a simple argument based on the symmetry of the underlying surface and topology.