Visualising emergent phenomena at oxide interfaces
Knowledge of atomic-level details of structure, chemistry, and electronic states is paramount for a comprehensive understanding of emergent properties at oxide interfaces. We utilise a novel methodology based on atomic-scale electron energy loss spectroscopy (EELS) to spatially map the electronic states tied to the formation of a two-dimensional electron gas (2DEG) at the prototypical non-polar/polar $TiO_2$/$LaAlO_3$ interface. Combined with differential phase contrast analysis we directly visualise the microscopic locations of ions and charge and find that 2DEG states and $Ti^{3+}$ defect states exhibit different spatial distributions. Supported by density functional theory (DFT) and inelastic scattering simulations we examine the role of oxygen vacancies in 2DEG formation. Our work presents a general pathway to directly image emergent phenomena at interfaces using this unique combination of arising microscopy techniques with machine learning assisted data analysis procedures.