Low temperature near-field fingerprint spectroscopy of 2D electron systems in oxide heterostructures and beyond

Confined electron systems, such as 2D electron gases (2DEGs), 2D materials, or topological insulators, show great technological promise but their susceptibility to defects often results in nanoscale inhomogeneities with unclear origins. Scattering-type scanning near-field optical microscopy (s-SNOM) is useful to investigate buried confined electron systems non-destructively with nanoscale resolution, however, a clear separation of carrier concentration and mobility was so far impossible in s-SNOM. Here, we predict a previously inaccessible characteristic "fingerprint" response of the prototypical LaAlO₃/SrTiO₃ 2DEG, and verify it using a state-of-the-art tunable narrow-band laser in mid-infrared cryo-s-SNOM at 8 K. Our modeling allows us to separate the influence of carrier concentration and mobility on fingerprint spectra and to characterize 2DEG inhomogeneities on the nanoscale. Finally, we model the surface accumulation layer in doped InAs, to show that our fingerprint spectra are a universal feature and generally applicable to confined electron systems, like topological insulators or stacked van-der-Waals materials.