Real-space charge-density imaging with sub-ångström resolution by four-dimensional electron microscopy

The distribution of charge density in materials dictates their chemical bonding, electronic transport, and optical and mechanical properties. Indirectly measuring the charge density of bulk materials is possible through X-ray or electron diffraction techniques by fitting their structure factors^1-3, but only if the sample is perfectly homogeneous within the area illuminated by the beam. Meanwhile, scanning tunnelling microscopy and atomic force microscopy enable us to see chemical bonds, but only on the surface^4-6. It remains a challenge to resolve charge density in nanostructures and functional materials with imperfect crystalline structures-such as those with defects, interfaces or boundaries at which new physics emerges. Here we describe the development of a real-space imaging technique that can directly map the local charge density of crystalline materials with sub-ångström resolution, using scanning transmission electron microscopy alongside an angle-resolved pixellated fast-electron detector. Using this technique, we image the interfacial charge distribution and ferroelectric polarization in a SrTiO₃/BiFeO₃ heterojunction in four dimensions, and discover charge accumulation at the interface that is induced by the penetration of the polarization field of BiFeO₃. We validate this finding through side-by-side comparison with density functional theory calculations. Our charge-density imaging method advances electron microscopy from detecting atoms to imaging electron distributions, providing a new way of studying local bonding in crystalline solids.