Probing the local density of states of dilute electron systems in different dimensions

Scanning tunneling spectroscopy at T = 6 K is used to investigate the local density of states (LDOS) of electron systems belonging to the bulk conduction band of InAs. In particular, the three-dimensional electron system (3DES) of the n-doped material, an adsorbate-induced two-dimensional electron system (2DES) and the tip-induced quantum dot (ODES) are investigated at B = 0 T and B = 6 T. It is found that the 3DES at B = 0 T can be described by Bloch states weakly interacting with the potential disorder provided by ionized dopants. The 2DES at B = 0 T exhibits much stronger LDOS corrugations, stressing the tendency for weak localization in the potential disorder. In a magnetic field, 3DES and 2DES show drift states, which are expected in 2D, but are surprising in 3D, where they point to a new electron phase consisting of droplets of quasi-2D systems. The 0DES at B = 0 T reveals quantized states in accordance with Hartree calculations. At B = 6 T it exhibits Landau states with exchange enhanced spin splitting. These states are used to investigate the influence of potential disorder on the exchange enhancement, which visualizes the nonlocality of the exchange interaction.