Reconstruction of electron-phonon interaction function from temperature dependence of electrical resistivity for metals

The determination of the electron-phonon interaction function (EPIF) from the temperature dependence of the electrical resistivity (TDER) for metals within a selected moderate temperature range is numerically demonstrated based on the general theory of the amplitude-phase-retrieval problem and an iterative algorithm. From the model calculation, the convergent solution can be obtained; however, the profile of the recovered EPIF depends on the initial frequency distribution used in the algorithm since this inversion problem is inherently ill-posed. In order to get reasonable result, it is necessary to introduce additional information about the feature of the EPIF for guiding the choice of the initial distribution. The algorithm can also furnish a robust reconstruction of EPIF from TDER contaminated with random noise. It means that this algorithm is relatively stable and insensitive to external perturbation; therefore in a sense, the presented algorithm overcomes the ill-posedness of the inversion problem.