Probing electron-electron interaction along with superconducting fluctuations in disordered TiN thin films

Abstract

In two-dimensional (2D) disordered superconductors prior to superconducting (SC) transition, the appearance of a resistance peak in the temperature dependent resistance $R(T)$ measurements indicates the presence of weak localization (WL) and electron-electron interaction (EEI) in the diffusion channel and SC fluctuations in the Cooper channel. Here, we demonstrate an interplay between SC fluctuations and EEI by low-temperature magnetotransport measurements for a set of 2D disordered TiN thin films. While cooling the sample, a characteristic temperature ${T}^{*}$ is obtained from the $R(T)$ at which SC fluctuations start to appear. The upturn in $R(T)$ above ${T}^{*}$ corresponds to WL and/or EEI. By the temperature and field dependences of the observed resistance, we show that the upturn in $R(T)$ originates mainly from EEI with a negligible contribution from WL. Further, we have used the modified Larkin's electron-electron attraction strength $\ensuremath{\beta}(T/{T}_{\mathrm{c}})$, containing a field-induced pair-breaking parameter, in the Maki-Thompson SC fluctuation term. Here, the temperature dependence of $\ensuremath{\beta}(T/{T}_{\mathrm{c}})$ obtained from the magnetoresistance (MR) analysis shows a diverging behavior close to ${T}_{\mathrm{c}}$, and it remains almost constant at higher temperature within the limit of $\mathrm{ln}(T/{T}_{\mathrm{c}})<1$. Interestingly, the variation of $\ensuremath{\beta}(T/{T}_{\mathrm{c}})$ on the reduced temperature $(T/{T}_{\mathrm{c}})$ offers a common trend which has been closely followed by all the concerned samples presented in this paper. Finally, the temperature dependence of inverse phase scattering time (${\ensuremath{\tau}}_{\ensuremath{\phi}}^{\ensuremath{-}1}$), as obtained from the MR analysis, clearly shows two different regimes; the first one close to ${T}_{\mathrm{c}}$ follows the Ginzburg-Landau relaxation rate $({\ensuremath{\tau}}_{\mathrm{GL}}^{\ensuremath{-}1})$, whereas the second one at high temperature varies almost linearly with temperature, indicating the dominance of inelastic electron-electron scattering for the dephasing mechanism. These two regimes are followed in a generic way by all the samples despite being grown under different growth conditions.