Spatial localization and thermal rectification in inhomogeneously deformed lattices

We reveal that inhomogeneous deformations (stretching, compression, twisting, or bending) of anharmonic lattices can lead to a local change of the coupling coefficients and induce the energy localization of high-frequency phonon modes. We consider a linear chain of particles interacting via the Lennard-Jones potentials under the action of a constant external force, and demonstrate that high-frequency oscillations can be localized at the edge of the inhomogeneously deformed chain. We also show stable propagation of an acoustic soliton in such chains that only changes its velocity due to the deformations. Additionally, we demonstrate that this mechanism is responsible for the formation of spatially localized phonon states in twisted graphene nanoribbons and the topological M\"obius-like graphene structures through stretching of the valent bonds between carbon atoms. We argue that these anharmonic effects can be employed for rectification and control of heat flows in stretched lattices at the nanoscale.