Quadratic temperature dependence of the electron-phonon scattering rate in disordered metals

We have measured the electron-phonon scattering rates 1/τₑₚ from a weak-localization study of a series of high-resistivity tin-doped Ti₇₃Al₂₇ alloys. The resistivities of these alloys are essentially the same and are so high that the electron elastic mean free path l approaches the interatomic spacing, resulting in a very small value of qₚₕl≈0.0056T (qₚₕ is the wave number of the thermal phonons, and T is the temperature). Based on as many as about 60 magnetoresistivity measurements between 2 and 22 K, we are able to determine the dependence of 1/τₑₚ on T to within a great degree of accuracy and find that 1/τₑₚ varies essentially with T² in the dirty limit (qₚₕl1). This observation is not understood in terms of the current theoretical concept of electron-phonon interaction in disordered metals.