Quantum oscillations and the Fermi surface of high-temperature cuprate superconductors

Over 20 years since the discovery of high temperature superconductivity in cuprates (Bednorz and Müller, 1986 [1]), the first convincing observation of quantum oscillations in underdoped YBa2Cu3O6.5 (Doiron-Leyraud et al., 2007 [2]) has deeply changed the theoretical landscape relevant to these materials. The Fermi surface is a basic concept of solid state physics, which underpins most physical properties (electrical, thermal, optical, etc.) of a metal. Even in the presence of interactions, this fundamental concept remains robust. While there was little doubt about the existence of a Fermi surface on the overdoped side of the phase diagram of the cuprates, the discovery of quantum oscillations in the underdoped regime was a surprise. The small pockets inferred from the measurements in underdoped YBa2Cu3Oy contrast with the large orbit found in overdoped Tl2Ba2CuO6 + δ. A central issue in understanding the phase diagram of high temperature superconductors is the origin of this difference at opposite sides of the superconducting dome. This review aims to shed light on this issue by bringing together recent results of quantum oscillation and transport measurements under high magnetic fields in hole-doped cuprates.