de Haas-van Alphen oscillations for nonrelativistic fermions coupled to an emergent U(1) gauge field

In this paper we investigate magneto-oscillations in the specific heat and the magnetization of nonrelativistic fermions coupled to a fluctuating U(1) gauge field. This model obtains as an effective model for the under-doped cuprates realizing a so-called algebraic charge liquid, which is a true non-Fermi-liquid state. Our study is driven by very recent observations of quantum oscillations in the underdoped cuprates. We calculate corrections to the standard Lifshitz-Kosevich expression due to the internal gauge degree of freedom for the oscillation amplitude. We perform this calculation in the dirty limit in a model with N species of fermions. The N ->infinity result corresponds to the well-known Fermi-liquid result reproducing the Lifshitz-Kosevich result. We capture the effect of the gauge field on the oscillation amplitude to Gaussian accuracy controlled in the small parameter 1/N. Our main finding is the presence of qualitative and quantitative differences compared to standard Fermi-liquid theory.