Energetics and Structure of Domain Wall Networks in Minimally Twisted Bilayer Graphene under Strain

Abstract

The parameters of the triangular domain wall network in bilayer graphene with a simultaneously twisted and biaxially stretched bottom layer are studied using the two-chain Frenkel-Kontorova model. It is demonstrated that if the graphene layers are free to rotate, they prefer to stay co-aligned upon stretching the bottom layer and the regular triangular network of tensile domain walls is formed upon the commensurate-incommensurate phase transition. If the angle between the layers is fixed, the regular triangular network of shear domain walls is observed at zero elongation of the bottom layer. Upon stretching the bottom layer, however, the domain walls transform into the tensile ones and the size of the commensurate domains decreases. We also show that the parameters of the isosceles triangular domain wall network in twisted bilayer graphene under shear strain can be determined through purely geometrical considerations. Experimental analysis of the orientation of domain walls and period of the triangular network would, on the one hand, contribute to understanding of the interlayer interaction of graphene layers, and, on the other hand, serve for detection of relative strains and rotation between the layers. Vice versa external strains can be used to control the parameters of the triangular domain wall network and, therefore, electronic properties of twisted bilayer graphene.