Ultra-high critical current densities of superconducting YBa$_2$Cu$_3$O$_{7-\delta}$ thin films in the overdoped state

Doping is one of the most relevant paths to tune the functionality of cuprates, it determines carrier density and the overall physical properties of these impressive superconducting materials. We present an oxygen doping study of YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) thin films from underdoped to overdoped state, correlating the measured charge carrier density, $n_\textrm{H}$, the hole doping, $p$, and the critical current density, $J_\textrm{c}$. Our results show a continuous increase of $J_\textrm{c}$ with charge carrier density, reaching 90 MA/cm$^2$ at 5 K for $p$-doping at the Quantum Critical Point (QCP), linked to an increase of the superconducting condensation energy. The ultra-high $J_\textrm{c}$ achived corresponds to a third of the depairing current, i.e. a value 60 % higher than ever reported in YBCO films. The overdoped regime is characterized by a sudden increase of $n_\textrm{H}$, associated to the reconstruction of the Fermi-surface at the QCP. Overdoping YBCO opens a promising route to extend the current carrying capabilities of REBCO coated conductors for applications.