The influence of many-body interactions on the de Haas van Alphen effect

The de Haas-van Alphen (dHvA) effect, or Landau quantum oscillatory magnetization of metals, has been widely used to explore the single-particle aspects of electrons in metals with the aim of determining their Fermi surfaces. Its role in studying many-body effects in metals is less familiar, even though the influence of such interactions is well known. We present a general field-theoretic approach to this problem which shows that the paradigm for understanding the influence of many-body interactions in the dHvA effect should be shifted from the intuitively reasonable but potentially misleading arguments based on the electron self-energy on the real energy axis to an analysis of the self-energy along the imaginary energy axis. When viewed in this way, the dHvA effect assumes the role of a many-body self-energy filter in which the real part of the self-energy renormalizes the dHvA frequency while the imaginary part renormalizes independently the dHvA amplitude. We obtain a general theory for the dHvA effect in an interacting system which preserves the structure of the original non-interacting theory of Lifshitz and Kosevich. We then apply this extended Lifshitz-Kosevich theory to the analysis of several problems of interest, including electron-electron and electron-phonon interactions, heavy fermions and type II superconductors.