From low-field Sondheimer oscillations to high-field very large and linear magnetoresistance in a SrTiO$_3$-based two-dimensional electron gas

Quantum materials harbor a cornucopia of exotic transport phenomena challenging our understanding of condensed matter. Among these, a giant, non-saturating linearmagnetoresistance (MR) has been reported in various systems, from Weyl semi-metals to topological insulators. Its origin is often ascribed to unusual band structure effects but it may also be caused by extrinsic sample disorder. Here, we report a very large linear MR in a SrTiO$_3$ two-dimensional electron gas and, by combining transport measurements with electron spectro-microscopy, show that it is caused by nanoscale inhomogeneities that are self-organized during sample growth. Our data also reveal semi-classical Sondheimer oscillations arising from interferences between helicoidal electron trajectories, from which we determine the 2DEG thickness. Our results bring insight into the origin of linear MR in quantum materials, expand the range of functionalities of oxide 2DEGs and suggest exciting routes to explore the interaction of linear MR with features like Rashba spin-orbit coupling.