Hot Electrons and Electron-Phonon Coupling in a Cylindrical Nanoshell

We use a standard model for the low-temperature electron-phonon interaction in metals to calculate the rate of thermal energy transfer between electrons and acoustic phonons in suspended metallic nanoshells. The electrons are treated as three-dimensional and noninteracting, whereas the vibrational modes are that of an thin cylindrical elastic shell of radius R with a free surface and thickness h. Disorder is neglected. The temperature dependence of the thermal power is obtained analytically for this model, and a crossover from the T-3 dependence expected for one-dimensional phonons to a T-3/(1 - v(2)) + 9 gamma T*/(1 - v(2))(3/2)] dependence is obtained.