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Electron-electron scatttering in Sn-doped indium oxide thick films

We have measured the low-field magnetoresistances (MRs) of a series of Sn-doped indium oxide thick films in the temperature $T$ range 4--35 K. The electron dephasing rate $1/τ_φ$ as a function of $T$ for each film was extracted by comparing the MR data with the three-dimensional (3D) weak-localization theoretical predictions. We found that the extracted $1/τ_φ$ varies linearly with $T^{3/2}$. Furthermore, at a given $T$, $1/τ_φ$ varies linearly with $k_F^{-5/2}l^{-3/2}$, where $k_{F}$ is the Fermi wavenumber, and $l$ is the electron elastic mean free path. These features are well explained in terms of the small-energy-transfer electron-electron scattering time in 3D disordered conductors. This electron dephasing mechanism dominates over the electron-phonon ($e$-ph) scattering process because the carrier concentrations in our films are $\sim$ 3 orders of magnitude lower than those in typical metals, which resulted in a greatly suppressed $e$-ph relaxation rate.