Response of thermalized ribbons to pulling and bending

Motivated by recent free-standing graphene experiments, we show how thermal fluctuations affect the mechanical properties of microscopically thin solid ribbons, which can be many thousand times wider than their atomic thickness. A renormalization group analysis of flexural phonons reveals that elongated ribbons behave like highly anisotropic polymers, where the two dimensional nature of ribbons is reflected in nontrivial power law scalings of the persistence length and effective bending and twisting rigidities with the ribbon width. With a coarse-grained transfer matrix approach, we then examine the nonlinear response of thermalized ribbons to pulling and bending forces over a wide spectrum of temperatures, forces, and ribbon lengths.