Electronic structure of high-T$_{\mathrm{c}}$ cuprates revealed by high-magnetic fields

The small reconstructed Fermi surface revealed by high-magnetic field quantum oscillation measurements in bilayer YBa$_{\mathrm{2}}$Cu$_{\mathrm{3}}$O$_{\mathrm{6+x}}$ opened a path towards identifying broken symmetry states in underdoped cuprate supercoductors. Recent quantum oscillations measurements on the structurally simpler HgBa$_{\mathrm{2}}$CuO$_{\mathrm{4+d}}$ 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 exact form of this charge-density-wave and its relationship to high-Tc superconductivity 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 90T.