Towards multiscale modeling of incommensurate 2D van der Waals heterostructures

Two-dimensional materials have generated a lot of interest in the past decade as a new toolbox for electron- ics [1]. This family includes insulators (boron nitride), semiconductors (transition metal dichalcogenides), and conductors (graphene). Vertical stacks of a few layers of such materials, interacting through van der Waals forces, create a venue to explore and tune desired mechanical and electronic properties. Numerical computations will be essential to explore the possibilites of such assemblies, such as tuning properties through the relative twist angle between layers, chemical doping, elastic stresses, etc. However, the generically incommensurate character of these systems represents a significant hurdle. Due to the lack of periodicity, many problems remain open in this field [2]. In this talk, we present some progress towards multi-scale calculations aimed at predicting macroscopic prop- erties of heterostructures. First, we recall the electronic properties of monolayer 2D materials and the geometry of mono- as well as few-layers assemblies. Tight-binding models can be parameterized from ab-initio, micro-scale DFT calculations [3]. These models can then be used as reduced models for meso-scale numerical calculations. We present a perturbation approach which allows the computation of observables such as the density matrix in an incommensurate bilayer stacking. We also present some prospects for the calculation of transport properties in incommensurate stockings. These results have been obtained in the framework of a collaboration with the groups of M. Luskin (Math, UofM), Efthimios Kaxiras (Physics, Harvard) and Eric Cancès (Ecole des Ponts). References [1] A.K.GEIMANDI.V.GRIGORIEVA,VanderWaalsheterostructures.Nature,Vol.499,419–425,2013 [2] G.A. TRITSARIS, S.N. SHIRODKAR, E. KAXIRAS, P. CAZEAUX, M. LUSKIN, P. PLECHÁCˇ AND E. CANCÈS, Perturbation theory for weakly coupled two-dimensional layers. Journal of Materials Research, Vol. 31(7), 959–966, 2016 [3] S.FANGANDE.KAXIRASElectronicStructureTheoryofWeaklyInteractingBilayers.arXivpreprint,arXiv:1604.05371,2016Non UBCUnreviewedAuthor affiliation: University of MinnesotaPostdoctora