Relaxation of incommensurate bi- and trilayer heterostructures and networks of domain walls

Paul Cazeaux
University of Kansas
Department of Mathematics

We discuss novel mathematical models for the analysis and computational prediction of mechanical relaxation of two-dimensional layered atomic crystals in the presence of large-scale moiré patterns.
The concept of configuration space or hull, previously introduced for the study of transport properties in aperiodic materials by Belissard et al., is shown to allow for a unified description of mechanical as well as electronic structure models for any materials in the truly incommensurate (aperiodic) regime.

We will present some preliminary analysis and numerical results in the case of graphene bi- and tri-layers in the small twist angle regime, showing the appearance of a sharp network of domain walls supporting a network of 1D edge modes for electronic transport.

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