Multitip scanning gate microscopy for ballistic transport studies in systems with two-dimensional electron gas

We consider conductance mapping of systems based on the two-dimensional electron gas with scanning gate microscopy using two and more tips of the atomic force microscope. The paper contains results of numerical simulations for a model tip potential with a proposal of a few procedures for extraction and manipulation the ballistic transport properties. In particular, we demonstrate that the multi-tip techniques can be used for readout of the Fermi wavelength, detection of potential defects, filtering specific transverse modes, tuning the system into resonant conditions under which a stable map of a local density of states can be extracted from conductance maps using a third tip.Comment: 9 pages, 12 figure

Conductance measurement of spin-orbit coupling in the two-dimensional electron systems with in-plane magnetic field

We consider determination of spin-orbit (SO) coupling constants for the two-dimensional electron gas from measurements of electric properties in rotated in-plane magnetic field. %Due to the interplay Due to the SO coupling the electron backscattering is accompanied by spin precession and spin mixing of the incident and reflected electron waves. The competition of the external and SO-related magnetic fields produces a characteristic conductance dependence on the in-plane magnetic field value and orientation which, in turn, allows for determination of the absolute value of the effective spin-orbit coupling constant as well as the ratio of the Rashba and Dresselhaus SO contributions.Comment: 4 pages + supplementary material

Interference features in scanning gate conductance maps of quantum point contacts with disorder

We consider quantum point contacts (QPCs) defined within disordered two-dimensional electron gases as studied by scanning gate microscopy. We evaluate the conductance maps in the Landauer approach and wave function picture of electron transport for samples with both low and high electron mobility at finite temperatures. We discuss the spatial distribution of the impurities in the context of the branched electron flow. We reproduce the surprising temperature stability of the experimental interference fringes far from the QPC. Next, we discuss -- previously undescribed -- funnel-shaped features that accompany splitting of the branches visible in previous experiments. Finally, we study elliptical interference fringes formed by an interplay of scattering by the point-like impurities and by the scanning probe. We discuss the details of the elliptical features as functions of the tip voltage and the temperature, showing that the first interference fringe is very robust against the thermal widening of the Fermi level. We present a simple analytical model that allows for extraction of the impurity positions and the electron gas depletion radius induced by the negatively charged tip of the atomic force microscope, and apply this model on experimental scanning gate images showing such elliptical fringes