Spin properties of 2D semiconductors probed by scanning tunneling   microscopy
  The interrelation between spin and charge in semiconductors leads to interesting effects, e.g., the Rashba-type spin-orbit splitting or the exchange enhancement. These properties are proposed to be used in applications such as spin transistors or spin qubits. Probing them on the local scale with the ultimate spatial resolution of the scanning tunneling microscope addresses their susceptibility to disorder directly. Here we review the results obtained on two-dimensional semiconductor systems (2DES). We describe the preparation and characterization of an adequate 2DES which can be probed by scanning tunneling microscopy. It is shown how the electron density and the disorder within the 2DES can be tuned and measured. The observed local density of states of weakly and strongly disordered systems is discussed in detail. It is shown that the weakly disordered 2DES exhibits quantum Hall effect in magnetic field. The corresponding local density of states across a quantum Hall transition is mapped showing the development from localized states to extended states and back to localized states in real space. Decoupling the 2DES from screening electrons of the bulk of the III-V semiconductor leads to a measurable exchange enhancement of up to 0.7 meV which depends on the local spin polarization of the 2DES. At stronger confinement potential, i.e. larger doping, the Rashba spin splitting with $\alpha$ as large as $7\cdot 10^{-11}$eVm is observed as a beating in the density of states in magnetic field. The Rashba spin splitting varies with position by about $\pm 50$% being largest at potential hills. 
M. Morgenstern, A. Georgi, C. Stra{\ss}er, C. R. Ast, S. Becker, and   M. Liebmann
cond-mat.mes-hall cond-mat.other