Glassy dynamics of SrTiO$_3$-based two-dimensional electron gas

Electron glasses offer a convenient laboratory platform to study glassy dynamics, traditionally attributed to the interplay of long-range Coulomb interactions and disorder. Existing experimental studies on electron glass have focused on doped semiconductors, strongly correlated systems, granular systems, etc., which are far from the well-delocalized limit. Here, we demonstrate that the ferroelastic twin walls of well-known quantum paraelectric SrTiO$_3$ can induce glassy electron dynamics even in a metallic phase. We show that the emergent two-dimensional electron gas at the $γ$-Al$_2$O$_3$/SrTiO$_3$ interface exhibits long-lasting resistance relaxations and memory effects at low temperatures, hallmarks of glassiness. Moreover, the glass-like relaxations can be tuned by the application of an electric field, implying that the observed glassy dynamics relate to the development of polarity near the structural twin walls of SrTiO3 and the complex interactions among them. The observation of this glassy metal phase also contributes to the growing understanding of the fascinating and diverse emergent phenomena near the quantum critical point.