Fracton-elasticity duality in twisted moiré superlattices

Jonas Gaa, Grgur Palle, Rafael M. Fernandes, Jörg Schmalian

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Abstract

We formulate a fracton-elasticity duality for twisted moiré 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 another type of defects 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. We also generalize our results to other planar incommensurate crystals and quasicrystals.

Original languageEnglish (US)
Article number064109
JournalPhysical Review B
Volume104
Issue number6
DOIs
StatePublished - Aug 1 2021

Bibliographical note

Funding Information:
We thank H. Ochoa for fruitful discussions. J.G. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project No. SCHM 1031/12-1. G.P. and J.S. were supported by the DFG - TRR 288 - 422213477 Elasto-Q-Mat (Project No. A07). R.M.F. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0020045. R.M.F. also acknowledges a Mercator Fellowship (TRR 288 - 422213477) from the German Research Foundation (DFG).

Publisher Copyright:
© 2021 American Physical Society.

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