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

We investigate magento-oscillations in the specific heat of non-relativistic fermions with a Fermi surface minimally coupled to a fluctuating U(1) gauge field. Our study is motivated by the recent observation of quantum oscillations in the underdoped cuprates, and by theoretical models of pocket Fermi surfaces realizing a non-Fermi liquid `algebraic charge liquid’. Our main result is the computation of the order 1/N correction to the Lifshitz-Kosevich expression for the oscillation amplitude in the dirty limit in a model with N species of fermions.