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 (${\mathrm{△}}_0$), 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.