Local electron and ionic heating effects on the conductance of nanostructures

Heat production and dissipation induced by current flow in nanostructures is of primary importance to understand the stability of these systems. These effects have contributions from both electron-phonon and electron-electron interactions. Here, we consider the effect of the local electron and ionic heating on the conductance of nanoscale systems. Specifically we show that the non-linear dependence of the conductance on the external bias may be used to infer information about the local heating of both electrons and ions. We compare our results with available experimental data on transport in $\mathrm{D}_2$ and $\mathrm{H}_2$ molecules. The comparison between experiment and theory is reasonably good close to the lowest phonon mode of the molecule, especially for the $\mathrm{D}_2$ molecule. At higher biases we cannot rule out the presence of other effects like, e.g., current-induced forces that make the scenario more complex.