Fracton-elasticity duality in twisted moir\'e superlattices

Understand

We formulate a fracton-elasticity duality for twisted moir\'e superlattices, taking into account that they are incommensurate crystals with dissipative phason dynamics.

• From a dual tensor-gauge formulation, as compared to standard crystals, we identify twice the number of conserved charges that describe topological lattice defects, namely, disclinations and a new type of defect that we dub discompressions.
• The key implication of these conservation laws is that both glide and climb motions of lattice dislocations are suppressed, indicating that dislocation networks may become exceptionally stable.
• Our results also apply to other planar incommensurate crystals and quasicrystals.