Mapping an electron wave function by a local electron scattering probe

A technique is developed which allows for the detailed mapping of the electronic wave function in two-dimensional electron gases with low-temperature mobilities up to $15\times {10}^{6}\;{\mathrm{cm}}^{2}\;{{\rm{V}}}^{-1}\;{{\rm{s}}}^{-1}$. Thin ('delta') layers of aluminium are placed into the regions where the electrons reside. This causes electron scattering which depends very locally on the amplitude of the electron wave function at the position of the Al δ-layer. By changing the distance of this layer from the interface we map the shape of the wave function perpendicular to the interface. Despite having a profound effect on the electron mobiliy, the δ-layers do not cause a widening of …