Effect of many-body interaction on de Haas-van Alphen oscillations in insulators

De Haas-van Alphen (dHvA) oscillations are oscillations in the magnetization as a function of the inverse magnetic field. These oscillations are usually considered to be a property of the Fermi surface and, hence, a metallic property. Recently, however, such oscillations have been shown to arise, both experimentally and theoretically, in certain insulators which have a narrow gap and an inverted band structure. In this work, we develop a theory to study the effect of many-body interaction on these unconventional oscillations. We consider weak interaction, focusing on the effect of renormalization of the quasiparticle spectrum on these oscillations. We find that interaction has an unusual effect: unlike in metals, in a certain regime the amplitude of oscillations may be enhanced substantially, both at zero and nonzero temperatures, even when the interaction is perturbatively weak.