Theory of quantum oscillations in the vortex-liquid state of high-Tc superconductors

The observation of quantum oscillations in underdoped cuprates has generated intense debate about the nature of the field-induced resistive state and its implications for the 'normal state' of high-T-c superconductors. Quantum oscillations suggest an underlying Fermi liquid at high magnetic fields H and low temperatures, in contrast with the pseudogap seen in zero-field, high-temperature spectroscopic experiments. Recent specific heat measurements show quantum oscillations in addition to a large field-dependent suppression of the electronic density of states. Here we present a theoretical analysis that reconciles these seemingly contradictory observations. We model the resistive state as a vortex liquid with short-range d-wave pairing correlations. We show that this state exhibits quantum oscillations, with a period determined by a Fermi surface reconstructed by a competing order parameter, in addition to a large suppression of the density of states that goes like root H pH at low fields.