Electron-Phonon renormalization effects in high magnetic fields

Abstract

When a metal is placed in a sufficiently strong magnetic field, it is to be expected that the effective mass of the electrons due to electron phonon interactions will be modified. The condition that the field will be strong enough to have an effect is that the cyclotron frequency be comparable to phonon frequencies. It is expected that such effects may be observable with experimentally realizable fields in some special cases. We have calculated the amplitude dependence of the de Haas-van Alphen effect as a function of temperature and magnetic field. This amplitude can be interpreted as giving a field dependent effective mass. The amplitude has been calculated numerically for several cases of interest. It is found that the field effects are rather smooth and depend most directly on the electron self-energy function for pure imaginary values of the frequency.