Modification of the Lifshitz-Kosevich formula for anomalous de Haas–van Alphen oscillations in inverted insulators

Traditionally, quantum oscillations were interpreted as the hallmark of a Fermi surface. Recently, it was understood that in order to have well defined de Haas–van Alphen oscillations the presence of a Fermi surface is not required. Following the Luttinger approach, we investigate the oscillations of an inverted insulator. Clear quantum oscillations are found and we provide a formula for the Lifshitz-Kosevich amplitude both in the clean as well as weakly disordered regime. We find that the LK formula is strongly modified compared to systems with a Fermi surface.