Many novel 2D structures that can exist in free-standing form have been discovered during the past two decades. Excitement in this general area was initially sparked by the discovery of free-standing graphene sheets which are one-atom thick and have extraordinary electronic behavior due to linear dispersion near the Fermi level. Experimental methods for interleaving layers of 2D materials have since been developed with endless possibilities for creating stable structures with any combination of desired electronic, optical, magnetic, and thermal properties when guided by mathematical models and computational methods. More recently, the discovery of superconductivity and other correlated phases in twisted moiré systems with flat bands has motivated effort to investigate new moiré superlattice systems of interest and to derive and simulate models that accurately describe their electronic properties.
To study the effect of mechanical relaxation of the 2D heterostructures, we generalize the transformations and duality found in incommensurate 2D systems between real space, configuration space, momentum space, and reciprocal space to study electronic observables of incommensurate bilayers in the tight-binding framework using a wide class of applicable Hamiltonians. We then apply this generalization to obtain the effects of mechanical relaxation on nearly aligned materials in momentum space, which produce in-plane incommensurate scattering. The relaxation scattering is long ranged in this case, which likewise changes the momentum space numerical scheme convergence rate. We study this convergence theoretically and perform a numerical study on twisted bilayer graphene at small angles with mechanical relaxation. Joint Work with Daniel Massatt and Stephen Carr.
Copyright. All Rights Reserved.