Nonlinearity effects on thermal transport properties of a mass-spring chain

Using Green's function technique, we present a self-consistent formalism to study the phonon transport properties of an extended nonlinear mass-spring chain. We calculate the phonon transmission coefficient, thermal conductivity, and specific heat for some chains with different configurations of masses feeling the nonlinearity potential. The numerical results show that in a critical value of the nonlinearity coefficient, a sharp decrease in thermal conductivity will be observed. The same scenario happens in a critical temperature proportional to the inverse of the nonlinearity coefficient for the specific heat. Indeed, thermal conductor-insulator transition can occur in the system depending on the strength and distribution of nonlinearity. The model can aid our understanding of the effect of lattice nonlinearity on the thermal properties of one-dimensional materials to design the thermal switches.