Evidence for weak antilocalization-weak localization crossover and metal-insulator transition in CaCu${}_3$Ru${}_4$O${}_{12}$ thin films

Artificial confinement of electrons by tailoring the layer thickness has turned out to be a powerful tool to harness control over competing phases in nano-layers of complex oxides. We investigate the effect of dimensionality on transport properties of $d$-electron based heavy-fermion metal CaCu${}_3$Ru${}_4$O${}_{12}$. Transport behavior evolves from metallic to localized regime upon reducing thickness and a metal insulator transition is observed below 3 nm film thickness for which sheet resistance crosses $h/e^{2} \sim 25~$k$\Omega$, the quantum resistance in 2D. Magnetotransport study reveals a strong interplay between inelastic and spin-orbit scattering lengths upon reducing thickness, which results in weak antilocalization (WAL) to weak localization (WL) crossover in magnetoconductance.