Electron-phonon interaction in disordered conductors: Static and vibrating scattering potentials

Abstract

Employing the Keldysh diagram technique, we calculate the electron-phonon energy relaxation rate in a conductor with the vibrating and static ␦-correlated random electron-scattering potentials. If the scattering potential is completely dragged by phonons, this model yields the Schmid's result for the inelastic electronscattering rate e-ph Ϫ1. At low temperatures the effective interaction decreases due to disorder, and e-ph Ϫ1 ϰT 4 l ͑l is the electron mean-free path͒. In the presense of the static potential, quantum interference of numerous scattering processes drastically changes the effective electron-phonon interaction. In particular, at low temperatures the interaction increases, and e-ph Ϫ1 ϰT 2 /l. Along with an enhancement of the interaction, which is observed in disordered metallic films and semiconducting structures at low temperatures, the suggested model allows us to explain the strong sensitivity of the electron relaxation rate to the microscopic quality of a particular film.

Rise time of voltage pulses in NbN superconducting single photon detectors

“…(1) and (2) n ( In dirty metals, the electron-phonon interaction is modified through the presence of impurities, which provides the modification of the electron-phonon relaxation rate. We consider the case when 1/e-ph~Te 2 [9], which is close to the temperature dependence 1/e-ph~Te 1.6 experimentally observed in NbN [10]. Theoretically, a 1/e-ph~Te 2 -dependence stems from the energy-dependent electron-phonon coupling constant (which is inversely proportional to the energy in this case, which leads to a modification to the Eliashberg function [11]) in the electron-phonon collision integral.…”

Influence of Temperature Gradients on Tunnel Junction Thermometry below 1 K: Cooling and Electron–Phonon Coupling

“…5,6 The strength of e-p coupling depends significantly on several factors: the material in question; the level of disorder in the metal, parametrized by the electron mean free path l; 7,8 and the type of scattering potential. 9 In general, the electron-phonon scattering rate has a form…”

“…9 However, if the scattering rates for transverse and longitudinal phonons are are of the same magnitude, m can vary continuously between m = 2 − 3, so that n = 4 − 5 and Σ ∝ l −1 − l 0 . 9 In disordered metals, where ql < 1, electrons scatter strongly from impurities, defects and boundaries, and the situation is more complicated to model because of the interference processes between pure electron-phonon and electron-impurity scattering events. However, there is a theory that includes electron-impurity scattering by vibrating and static disorder.…”

Inhomogeneous state in nonequilibrium superconductor/normal-metal tunnel structures: A Larkin-Ovchinnikov-Fulde-Ferrell-like phase for nonmagnetic systems

“…However the approximation of the effective temperature allows one to solve the problem in an analytical form. In the limit of high impurity concentration (l < s/T ), the inelastic electron-phonon scattering rate τ −1 e−ph depends on energy even stronger [29,37,38,39], that is, the window between τ −1 e−e and τ −1 e−ph becomes larger and the situation is even more favorable for applicability of our approach. If the frequency ǫ 0 / is less than τ −1 e−ph , then the heat absorbed by quasiparticles in the superconductor is released mainly to the lattice, but not to the normal electrodes, and our approach is not applicable.…”