Rippling instabilities in suspended nanoribbons

Morphology mediates the interplay between the structure and electronic transport in atomically thin nanoribbons such as graphene as the relaxation of edge stresses occurs preferentially via out-of-plane deflections. In the case of end-supported suspended nanoribbons that we study here, past experiments and computations have identified a range of equilibrium morphologies, in particular, for graphene flakes, yet a unified understanding of their relative stability remains elusive. Here, we employ atomic-scale simulations and a composite framework based on isotropic elastic plate theory to chart out the morphological stability space of suspended nanoribbons with respect to intrinsic (ribbon elasticity) and engineered (ribbon geometry) parameters, and the combination of edge and body actuation. The computations highlight a rich morphological shape space that can be naturally classified into two competing shapes, bendinglike and twistlike, depending on the distribution of ripples across the interacting edges. The linearized elastic framework yields exact solutions for these rippled shapes. For compressive edge stresses, the body strain emerges as a key variable that controls their relative stability and in extreme cases stabilizes coexisting transverse ripples. Tensile edge stresses lead to dimples within the ribbon core that decay into the edges, a feature of obvious significance for stretchable nanoelectronics. The interplay between geometry and mechanics that we report should serve as a key input for quantifying the transport along these ribbons.