Disorder and Strong Correlations in Two-Dimensional Electron Liquids in SrTiO$_{\mathrm{3}}$

We report on angle-dependent measurements of the resistances and Hall coefficients of two-dimensional electron liquids in MBE-grown SmTiO$_{\mathrm{3}}$/SrTiO$_{\mathrm{3}}$/SmTiO$_{\mathrm{3}}$ quantum wells on DyScO$_{\mathrm{3\thinspace }}$(001) substrates, which were found to possess highly anisotropic planar defects. The defects lead to strong in-plane anisotropy in the transport properties, allowing for a systematic investigation of the interplay between disorder and the strong correlations that give rise to a number of unusual phenomena in this system. Disorder was found to increase the residuals in the resistance and Hall angle by up to a factor of 11, while the Hall scattering amplitude was unaffected. The Hall angles exhibited strong T$^{\mathrm{2}}$ temperature dependences along all directions, while the longitudinal resistances displayed very different direction-dependent behavior with temperature. This is indicative of carrier-lifetime separation between the longitudinal and Hall scattering rates. Remarkably, the degree of the carrier-lifetime separation was completely insensitive to disorder.