The 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 Letter, we develop a theory to study the effect of many-body interactions on these unconventional oscillations. We consider a weak interaction, focusing on the effect of renormalization of the quasiparticle spectrum on these oscillations. We find that the 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.

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• de Haas-van Alphen effect
• Narrow band gap systems
• Green's function methods
• Many-body techniques