One of the leading challenges of condensed matter physics in the past few decades in an understanding of the high-temperature copper-oxide superconductors. While the d-wave character of the superconducting state is well understood, the normal state i
n the underdoped regime has eluded understanding. Here we review the past few years of quantum oscillation measurements performed in the underdoped cuprates that have culminated in an understanding of the normal ground state of these materials. A nodal electron pocket created by charge order is found to characterise the normal ground state in YBa2Cu3O6+x and is likely universal to a majority of the cuprate superconductors. An open question remains regarding the origin of the suppression of the antinodal density of states at the Fermi energy in the underdoped normal state, either from mainly charge correlations, or more likely, from mainly pairing and / or magnetic correlations that precede charge order.
Pulsed field measurements of the Hall resistivity and magnetoresistance of underdoped YBa2Cu4O8 are analyzed self-consistently using a simple model based on coexisting electron and hole carriers. The resultant mobilities and Hall numbers are found to
vary markedly with temperature. The conductivity of the hole carriers drops by one order of magnitude below 30 K, explaining the absence of quantum oscillations from these particular pockets. Meanwhile the Hall coefficient of the electron carriers becomes strongly negative below 50 K. The overall quality of the fits not only provides strong evidence for Fermi-surface reconstruction in Y-based cuprates, it also strongly constrains the type of reconstruction that might be occurring.
