Limits of Coherency and Strain Transfer in Flexible 2D van der Waals Heterostructures: Formation of Strain Solitons and Interlayer Debonding

In flexible 2D-devices, strain transfer between different van-der Waals stacked layers is expected to play an important role in determining their optoelectronic performances and mechanical stability. Using a 2D non-linear shear-lag model, we demonstrate that only 1-2% strain can be transferred between adjacent layers of different 2d-materials, depending on the strength of the interlayer vdW interaction and the elastic modulus of the individual layers. Beyond this critical strain, layers begin to slip with respect to each other. We further show that due to the symmetry of the periodic interlayer shear potential, stacked structures form strain solitons with alternating AB/BA or AB/AB stacking which are separated by incommensurate domain walls. The extent and the separation distance of these commensurate domains are found to be determined by the degree of the applied strain, and their magnitudes are calculated for several 2D heterostructures and bilayers including MoS(2)/WS(2), MoSe(2)/WSe(2), Graphene/Graphene and MoS2/MoS2 using a multiscale method. As bilayer structures have been shown to exhibit stacking-dependent electronic bandgap and quantum transport properties, the predictions of our study will not only be crucial in determining the mechanical stability of flexible 2D devices but will also help to better understand optoelectronic response of flexible devices.