De Haas–van Alphen oscillations for nonrelativistic fermions coupled to an emergentU(1)gauge field

Abstract

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 underdoped 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 $\mathcal{N}$ species of fermions. The $\mathcal{N}\ensuremath{\rightarrow}\ensuremath{\infty}$ 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 $1/\mathcal{N}$. Our main finding is the presence of qualitative and quantitative differences compared to standard Fermi-liquid theory.