Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths

We use a generalised Langevin equation scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B 93, 174303 (2016)]. We consider model Al systems, i.e., one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length N and the temperature difference $ΔT$ between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures (⁠$T≳500$ K) and temperature differences (⁠$ΔT≳500$ K), the chains, with $N>18$ atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures (⁠$T≲500$ K) and temperature differences (⁠$ΔT≲400$ K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains (⁠$N≤15$⁠). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.