1. Département de physique and RQMP, Université de Sherbrooke, Sherbrooke J1K 2R1, Canada
   
2. Laboratoire National des Champs Magnétiques Pulsés (LNCMP), UMR CNRS-UPS-INSA 5147, Toulouse 31400, France
   
3. H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK
   
4. National High Magnetic Field Laboratory (NHMFL), Florida State University, Tallahassee, Florida 32306, USA
   
5. Department of Physics and Astronomy, University of British Columbia, Vancouver V6T 1Z4, Canada
   
6. Canadian Institute for Advanced Research, Toronto M5G 1Z8, Canada
   
7. Superconductivity Research Laboratory, International Superconductivity Technology Center, Shinonome 1-10-13, Koto-ku, Tokyo 135-0062, Japan

Correspondence to: Cyril Proust²Louis Taillefer^1,6 Correspondence and requests for materials should be addressed to C.P. (Email: proust@lncmp.org) or L.T. (Email: louis.taillefer@physique.usherbrooke.ca).

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry¹. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa₂Cu₃O_y and YBa₂Cu₄O₈ was recently shown to include small pockets^{2, 3, 4}, in contrast with the large cylinder that characterizes the overdoped regime⁵, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa₂Cu₃O_y and YBa₂Cu₄O₈, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order^{6, 7}. Comparison with materials of the La₂CuO₄ family that exhibit spin/charge density-wave order^{8, 9, 10, 11} suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T _c) superconductors.