Fracton-elasticity duality in twisted moir\'e superlattices

TL;DR

This paper develops a duality framework linking fracton physics and elasticity in twisted moiré superlattices, revealing new defect types and stability properties of dislocation networks in incommensurate crystals.

Contribution

It introduces a fracton-elasticity duality for incommensurate twisted moiré superlattices, identifying new topological defects and conservation laws affecting dislocation dynamics.

Findings

Disclinations and a new defect called discompressions are conserved.

Both glide and climb motions of dislocations are suppressed.

Dislocation networks may be exceptionally stable in these systems.

Abstract

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.