Thermal conductance of metallic atomic-size contacts: Phonon transport and Wiedemann-Franz law

Motivated by recent experiments [Science 355, 1192 (2017); Nat. Nanotechnol. 12, 430 (2017)], we present here an extensive theoretical analysis of the thermal conductance of atomic-size contacts made of three different metals, namely gold (Au), platinum (Pt), and aluminum (Al). The main goal of this work is to elucidate the role of phonons in the thermal transport through these atomic contacts as well as to study the validity of the Wiedemann-Franz law, which relates the electrical and the thermal conductance. For this purpose, we have employed two different custom-developed theoretical approaches. The first one is a transport method based on density functional theory (DFT) that allows one to accurately compute the contributions of both electrons and phonons to the thermal transport in few-atom-thick contacts. The second technique is based on a combination of classical molecular dynamics (MD) simulations and a tight-binding model that enables the efficient calculation of the electronic contribution to the thermal conductance of atomic contacts of larger size. Our DFT-based calculations show that the thermal conductance of few-atom contacts of Au and Pt is dominated by electrons, with phonons giving a contribution typically below 10% of the total thermal conductance, depending on the contact geometry. For these two metals we find that the small deviations from the Wiedemann-Franz law, reported experimentally, largely stem from phonons. In the case of Al contacts we predict that the phononic contribution can be considerably larger with up to 40% of the total thermal conductance. We show that these differences in the phononic contribution acrossmetals originate mainly from their distinct Debye energies. On the other hand, our MD-based calculations demonstrate that the electronic contribution to the thermal conductance follows very closely the Wiedemann-Franz law, irrespective of the material and the contact size. Finally, the ensemble of our results consistently shows that the reported observation of quantized thermal transport at room temperature is restricted to few-atom contacts of Au, a monovalent metal in which the transport is dominated by the s valence orbitals. In the case of multivalent metals like Pt and Al this quantization is statistically absent due to the fact that additional orbitals contribute to the transport with conduction channels that have intermediate transmissions between 0 and 1, even in the case of single-atom contacts.