Abstract

When a metal is subjected to a strong magnetic field B, nearly all measurable quantities show oscillations periodic in 1/B. Such quantum oscillations represent a canonical probe of the defining aspect of a metal, its Fermi surface. Recent breakthrough experiments demonstrating the existence of unambiguous quantum oscillations in a cuprate superconductor, YBa₂Cu₃O_6.51, contradict the well-established result of many angle resolved photoemission studies, which consistently indicate 'Fermi arcs'—truncated segments of a Fermi surface—in the normal state of the cuprates. In this study, with the goal of reconciling the above disagreement, we introduce a mechanism for quantum oscillations that requires only finite segments of a Fermi surface. We show that oscillations periodic in 1/B can occur if the Fermi surface segments are terminated by a pairing gap and present arguments that these oscillations are in fact occurring in the cuprates.