Heat-flow properties of systems with alternate masses or alternate on-site potentials

We address a central issue of phononics: the search of properties or mechanisms to manage the heat flow in reliable materials. We analytically study standard and simple systems modeling the heat flow in solids, namely, the harmonic, self-consistent harmonic and also anharmonic chains of oscillators, and we show an interesting insulating effect: While in the homogeneous models the heat flow decays as the inverse of the particle mass, in the chain with alternate masses it decays as the inverse of the square of the mass difference, that is, it decays essentially as the mass ratio (between the smaller and the larger one) for a large mass difference. A similar effect holds if we alternate on-site potentials instead of particle masses. The existence of such behavior in these different systems, including anharmonic models, indicates that it is a ubiquitous phenomenon with applications in the heat flow control.