Hot electrons in low-dimensional phonon systems

A simple bulk model of electron-phonon coupling in metals has been partially successful in explaining experiments on metal films that actually involve surfaceor other low-dimensional phonons. However, by an exact application of this standard model to a semi-infinite substrate with a free surface, making use of the actual vibrational modes of the substrate, we show that such agreement is fortuitous, and that the model actually predicts a low-temperature crossover from the familiar T5 temperature dependence to a stronger T6 log T scaling. Comparison with existing experiments suggests a widespread breakdown of the standard model of electron-phonon coupling in metals.