cuprates revealed by high-magnetic fields*

The small reconstructed Fermi surface revealed by high-magnetic field quantum oscillation measurements in bilayer YBa₂Cu₃O_6+x opened a path towards identifying broken symmetry states in underdoped cuprate supercoductors. Recent quantum oscillation measurements on the structurally simpler HgBa₂CuO_4+d indicate that the Fermi surface comprises only a single quasi-two dimensional pocket. These results suggests Fermi-surface reconstruction attributable to the charge-density-wave observed with other spectroscopic methods. However, the relationship of this charge-density-wave to high-temperature superconductivity and quantum criticality remains a pressing open question. We will present new insights into the low temperature electronic structure of the cuprates probed with electrical transport in magnetic fields up to 90 tesla.