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

Abstract

Whether a quantum critical point (QCP) demarcates the end of the pseudogap (PG) regime in hole-doped cuprates at a singular doping level $p^{\ast }\approx 0.19$ remains an open question. A crucial part of this puzzle is how the carrier density predicted by electronic structure calculations is recovered for $p>p^{\ast }$. 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 $p^{\ast }$. 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 $p^{\ast }$. This result disfavors a conventional QCP scenario in which the PG endpoint corresponds to a reconstructed Fermi surface.