Direct Comparison between Potential Landscape and Local Density of States in a Disordered Two-Dimensional Electron System

The local density of states (LDOS) of the adsorbate-induced two-dimensional electron system (2DES) on $n\mathrm{\text{−}}\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}(110)$ is studied by scanning tunneling spectroscopy. In contrast to a similar 3DES, the 2DES LDOS exhibits 20 times stronger corrugations and rather irregular structures. Both results are interpreted as consequences of weak localization. Fourier transforms of the LDOS reveal that the $k$ values of the unperturbed 2DES still dominate the 2DES, but additional lower $k$ values contribute. To clarify the origin of the LDOS patterns, we measure the potential landscape of the 2DES area. We use it to calculate the expected LDOS and find reasonable agreement between calculation and experiment.