# Absence of Weak Localization Effects in Strontium Ferromolybdate
## 1 Introduction
Assuming only one dephasing process and accounting for the fact that \(l_{\phi}(0)\) is in the order of 50 nm to several micrometers, that is, usually \(l_{\phi}(0)>>l_{\phi}(T)\)[14; 15; 18; 19; 20], a simplified approximation formula is given by [19]:  
\[\frac{1}{l_{\phi}^{2}(T)}\approx A^{\prime}T^{p_{1}}, \tag{7}\]  
where \(p_{1}=1\) represents quasielastic electron-electron scattering, in agreement with experimental results reported in Bi\({}_{2}\)Te\({}_{3}\) thin films [21], 50 nm-thick Cd\({}_{3}\)As\({}_{2}\) films [19], Bi\({}_{2}\)Te\({}_{3}\) single crystals [15] and Mo\({}_{x}\)W\({}_{1.x}\)Te\({}_{2+\delta}\) ultrathin films [22]. As a result, for quasielastic electron-electron scattering, we obtain:  
\[l_{\phi}^{2}=l_{\phi}^{2}(T_{0})\cdot\frac{T_{0}}{T}, \tag{8}\]  
Consequently, Equation (5) transforms to  
\[ \begin{array}{c}\Delta\sigma_{2D,WL}=-\frac{e^{2}}{\pi h}\ln\left(\frac{l_{ \phi}^{2}(T_{0})}{l_{e}^{2}}\cdot\frac{T_{0}}{T}\right)=\frac{e^{2}}{\pi h} \ln\left(\frac{l_{\phi}^{2}}{l_{\phi}^{2}(T_{0})}\cdot\frac{T}{T_{0}}\right) \\ =\frac{e^{2}}{\pi h}\left[\ln\left(\frac{l_{\phi}^{2}}{l_{\phi}^{2}(T_{0})} \right)+\ln\left(\frac{T}{T_{0}}\right)\right]\\ \delta\sigma_{3D,WL}=-\frac{e^{2}}{\pi}\left(\frac{1}{l_{e}}-\frac{1}{l_{\phi }}\right)=-\frac{e^{2}}{\pi l_{\phi}(T_{0})}\left(\frac{T}{T_{0}}\right)^{1/2} \end{array}  \tag{9}\]  
Finally, the total bulk conductivity consisting also two-dimensional contributions under high magnetic fields is written as:  
\[\sigma(T)=\sigma_{0}+A\cdot\ln\left(\frac{T}{T_{0}}\right)+B\cdot\left(\frac{T }{T_{0}}\right)^{1/2}, \tag{10}\]where  
\[\sigma_{0}=\sigma_{D}-\frac{e^{2}}{\pi\hbar b}\cdot\ln\left(\frac{l_{\phi}^{2}(T_{ 0})}{l_{e}^{2}}\right)-\frac{e^{2}}{\pi\hbar\cdot l_{e}}, \tag{11}\]  
and the coefficients:  
\[A=\frac{e^{2}}{\pi\hbar b},\ B=\frac{e^{2}}{\pi\hbar\cdot l_{\phi}(T_{0})}, \tag{12}\]  
where \(b\) is the effective thickness of the 2D layer introduced to convert a 2D conductivity to a 3D conductivity. A minimum of conductivity appears only when the second right-side term in Equation (10) changes sign, i.e.,  
\[B=-\frac{2A}{\left(T_{\max}/T_{0}\right)^{1/2}}\underset{T_{0}=T_{\max}}{=}-2A, \tag{13}\]  
with regard to Equation (10), quantum correction to residual conductivity may be written as [23]:  
\[\Delta\sigma(T)=A\prime\cdot\ln T+B\prime\cdot T^{1/2}, \tag{14}\]  
Assuming that Matthiessen's rule holds and representing resistivity as a sum of elastic and inelastic contributions, where the latter increase with increasing temperature due to a power law (e.g., a term such as \(CT^{m}\)), the resistivity data can be fitted to [24; 25]:  
\[\rho(T)=\frac{1}{\sigma_{0}+A\prime\cdot\ln T+B\prime\cdot T^{1/2}}+C_{n}T^{n}, \tag{15}\]  
where \(n\) is equal to 3/2, 2, 3, depending on the dominant scattering mechanism [26]. Separate conductivity quantum correction terms in the form of \(A^{\prime}\)ln\(T\) and \(B^{\prime}T^{1/2}\) were introduced by [PERSON] et al. for La\({}_{0.7}\)Ca\({}_{0.3}\)MnO\({}_{3}\)[27]. The first term (\(A^{\prime}\)ln\(T\)) was also attributed also to the Kondo effect [28]. In order to account for higher-order scattering mechanisms and to extend the analytical description to higher temperatures, an additional term (\(CT^{n}\)) was included.