Onset field for Fermi-surface reconstruction in the cuprate superconductor YBa$_{2}$Cu$_{3}$O$_{y}$

Discovery of quantum oscillations in underdoped cuprates [1] at low temperature and high magnetic field revealed the Fermi surface to contain a small closed electron pocket. It is thought to result from a reconstruction by charge order, but whether it is the order seen by NMR [2], and ultrasound [3] above a threshold field or the short-range modulations seen by X-ray diffraction in zero field is unclear [4]. Here we report measurements of the thermal Hall conductivity in YBa$_{2}$Cu$_{3}$O$_{y}$ to show that Fermi-surface reconstruction occurs only above a sharply defined onset field, equal to the transition field seen in ultrasound. This reveals that electrons do not experience long-range broken translational symmetry in the zero-field ground state. [1] Doiron-Leyraud et al., Nature 447,565 (2007) [2] Wu et al., Nature 477,191 (2011) [3] LeBoeuf et al., Nat. Phys. 9,79 (2013) [4] Ghiringhelli et al. Science 337, 821-825 (2012)