Fluctuation contributions to quantum oscillations in excitonic insulators

The measurement of the de Haas-van Alphen effect in insulating systems kicked off a flurry of theoretical work to explain how quantum oscillation phenomenon, once thought intrinsic to metals, can manifest in gapped systems. For insulating systems with rigid gaps or interaction-generated gaps described by mean field theory, quantum oscillations are found to be exponentially suppressed for weak magnetic fields by a "Dingle damping" factor arising from the presence of the gap itself. Here we consider how collective fluctuations beyond the mean field description of these systems contribute to quantum oscillations. In a model excitonic insulator we examine the phase and amplitude (i.e. Higgs) fluctuations of the gap and find that they provide the dominant contributions to the oscillatory part of the free energy in this model for certain parameter regimes, and thus dominate quantum oscillations of the magnetization.