Doping dependence of the low temperature planar carrier density in overdoped YBa$_2$Cu$_3$O$_{7-\delta}$

TL;DR

This study investigates how the planar carrier density in overdoped YBa$_2$Cu$_3$O$_{7-b4}$ evolves with doping, revealing a partial recovery of the Fermi volume at the pseudogap critical point, challenging traditional quantum critical point models.

Contribution

It provides new experimental insights into the doping dependence of carrier density and Fermi surface reconstruction in cuprates, using high magnetic fields and resistivity anisotropy measurements.

Findings

Planar carrier density $n_{pl}$ approximately equals doping level $p$ at optimal doping.

Sharp increase in Hall number $n_H$ is softened near $p^*$, indicating partial Fermi volume recovery.

Results challenge the conventional quantum critical point scenario for the pseudogap endpoint.

Abstract

Whether a quantum critical point (QCP) demarcates the end of the pseudogap (PG) regime in hole-doped cuprates at a singular doping level $p^* \approx 0.19$ remains an open question. A crucial part of this puzzle is how the carrier density predicted by electronic structure calculations is recovered for $p > p^*$. Here, we use magnetic fields up to 67 T to suppress superconductivity down to 50 K, allowing simultaneous measurement of the low-temperature Hall number $n_{\mathrm{H}}$ and the in-plane resistivity anisotropy $\rho_a/\rho_b$ in overdoped Y$_{1-x}$Ca$_x$Ba$_2$Cu$_3$O$_{7-\delta}$ single crystals. We confirm a previous finding [Badoux et al., Nature 531, 210 (2016)] that $n_{\mathrm{H}}$(50 K) exhibits a sharp increase below $p^*$. Using the measured resistivity anisotropy, we extract the planar carrier density $n_{\mathrm{pl}} = n_{\mathrm{H}} (\rho_a/\rho_b)^{-1}$. The doping dependence of $n_{\mathrm{pl}}$(50 K) reveals two key findings: (i) at optimal doping, $n_{\mathrm{pl}} \approx p$, and (ii) the sharp rise in $n_{\mathrm{H}}(p)$ is softened such that the full Fermi volume ($n_{\mathrm{pl}} = 1 + p$) is only partially recovered at $p^*$. This result disfavors a conventional QCP scenario in which the PG endpoint corresponds to a reconstructed Fermi surface.