Investigation of the Pauli paramagnetic effect in systematically tuned NbN thin films

Superconductivity and the normal-state properties of NbN films can be tuned in a wide range, supplying a suitable platform to investigate the systematical evolution of the superconducting performances. Herein, we report the upper critical field of NbN films in both the vertical ($B\perp$ film) and parallel ($B\parallel$ film) orientations over a wide temperature range. Eight samples with the superconducting critical temperature $T_c$ ranging from 2.5 K to 9.8 K are studied. Meanwhile, the normal-state resistivity is tuned by more than six times by changing the conditions of the film growth. It is found that the magnitudes of the upper critical field in both field directions ($B_{c2}^{\perp}$ and $B_{c2}^{\parallel}$) exceed the paramagnetic limiting field $B_p$. The temperature dependent $B_{c2}^{\perp}$ can be described by the extended Werthamer--Helfand--Hohenberg (WHH) model considering the Pauli spin paramagnetism. Meanwhile, the $B_{c2}^{\parallel}$-$T$ data shows the feature of two-dimensional superconductivity in the temperature range near $T_c$. The evolution of the obtained Maki parameter with other parameters, such as the slope of the upper critical field near $T_c$ and the normal-state resistivity, are discussed to reveal the characteristics of the Pauli paramagnetic effect in this system.