Electron-phonon relaxation in a model of a granular film

TL;DR

This paper investigates electron-phonon relaxation in a granular metal film model, analyzing how grain boundary transparency affects relaxation rates and cooling power at low temperatures.

Contribution

It introduces a model considering both standard and boundary-mediated electron-phonon interactions, highlighting the impact of grain boundary transparency on relaxation.

Findings

Relaxation rate follows a power-law temperature dependence similar to clean systems.

Cooling power's prefactor increases as grain boundary transparency decreases.

Both interaction mechanisms significantly influence electron-phonon relaxation in granular films.

Abstract

We study the electron-phonon relaxation in the model of a granular metal film, where the grains are formed by regularly arranged potential barriers of arbitrary transparency. The relaxation rate of Debye acoustic phonons is calculated, taking into account two mechanisms of electron-phonon scattering: the standard Fr\"ohlich interaction of the lattice deformation with the electron density and the interaction mediated by the displacement of grain boundaries dragged by the lattice vibration. At the lowest temperatures, the electron-phonon cooling power follows the power-law temperature dependence typical for clean systems but with the prefactor growing as the transparency of the grain boundaries decreases.