Oxidative deintercalation of single crystal Na$_{1-\delta}$FeAs upon Interaction with the environment

Due to high mobility of Na ions, NaFeAs superconductor exhibits pronounced reaction with the environment, leading to a bulk change change in stoichiometry. We study the doping evolution of the same single crystals as a function of time of the environmental exposure. In NaFeAs, a controlled reaction with air increases the superconducting transition temperature, $T_{c}$, from the initial value of 12 K to 27 K as probed by transport and magnetic measurements. Temperature dependent resistivity, $\rho_{a}$(T), shows a dramatic change with the exposure time. In freshly prepared samples, $\rho_{a}$(T) reveals clear features at the structural, $T_{s} \approx$ 60 K, and magnetic, $T_{m}$=45 K, transitions and superconductivity with onset $T_{c;ons} \approx$16 K and offset $T_{c;off} \approx$12 K. The exposed samples show $T-$linear variation of $\rho_{a}$(T) above $T_{c;ons} \approx$30 K ($T_{c;off} \approx$26 K). This suggests bulk doping and implies the existence of a quantum critical point at the optimal doping. The resistivity for different doping levels is affected below $\sim$ 200 K suggesting the existence of a characteristic energy scale that caps the $T-$linear regime, which could be identified with a pseudogap.