Temperature dependence of resistivity and Hall coefficient in strongly disordered NbN thin films

We report the temperature dependence of resistivity $(\ensuremath{\rho})$ and Hall coefficient $({R}_{H})$ in the normal state of homogeneously disordered epitaxial NbN thin films with ${k}_{F}l\ensuremath{\sim}1.68\char21{}10.12$. The superconducting transition temperature $({T}_{c})$ of these films varies from 2.7 to 16.8 K. While our least disordered film displays usual metallic behavior, for all the films with ${k}_{F}l\ensuremath{\le}8.13$, both $\frac{d\ensuremath{\rho}}{dT}$ and $\frac{d{R}_{H}}{dT}$ are negative up to 285 K. We observe that${R}_{H}(T)$ varies linearly with $\ensuremath{\rho}(T)$ for all the films and $[\frac{{R}_{H}(T)\ensuremath{-}{R}_{H}(285\text{ }\text{K})}{{R}_{H}(285\text{ }\text{K})}]=\ensuremath{\gamma}[\frac{\ensuremath{\rho}(T)\ensuremath{-}\ensuremath{\rho}(285\text{ }\text{K})}{\ensuremath{\rho}(285\text{ }\text{K})}]$, where $\ensuremath{\gamma}=0.68\ifmmode\pm\else\textpm\fi{}0.11$. Measurements performed on a 2-nm-thick Be film show similar behavior with $\ensuremath{\gamma}=0.69$. This behavior is inconsistent with existing theories of localization and $e\text{\ensuremath{-}}e$ interactions in a disordered metal.