Upper critical field of electron-doped Pr$_{2-x}$Ce$_x$CuO$_{4-\delta}$ in parallel magnetic fields

We report a systematic study of the resistive superconducting transition in the electron-doped cuprates Pr$_{2-x}$Ce$_{x}$CuO$_{4-\delta}$ down to 1.5 K for magnetic field up to 58 T applied parallel to the conducting ab-planes. We find that the zero temperature parallel critical field (H$_{c2\parallel ab}$(0)) exceeds 58 T for the underdoped and optimally-doped films. For the overdoped films, 58 T is sufficient to suppress the superconductivity. We also find that the Zeeman energy $\mu_B$H$_{c2\parallel ab}$(0) reaches the superconducting gap ($\triangle_0$), i.e. $\mu_B$H$_{c2\parallel ab}(0)\simeq \triangle_0$, for all the dopings, strongly suggesting that the parallel critical field is determined by the Pauli paramagnetic limit in electron-doped cuprates.