D. A. Ritchie

Imaging fractal conductance fluctuations and scarred wave functions in a quantum billiard.

We present scanning-probe images and magnetic-field plots which reveal fractal conductance fluctuations in a quantum billiard. The quantum billiard is drawn and tuned using erasable electrostatic lithography, where the scanning probe draws patterns of surface charge in the same environment used for measurements. A periodicity in magnetic field, which is observed in both the images and plots, suggests the presence of classical orbits. Subsequent high-pass filtered high-resolution images resemble the predicted probability density of scarred wave functions, which describe the classical orbits.

One-dimensional probability density observed using scanned gate microscopy

Using scanned gate microscopy, we observed transconductance structure relating to the transverse electron probability density of a quasi-one-dimensional electron system (Q1DES). The scanned gate created a movable scatterer to modify the transmission probability of the highest transmitted one-dimensional (1D) subband. Structure was seen for the first three 1D subbands, in addition to transconductance oscillations indicative of 1D ballistic transport. The Q1DES was electrostatically defined from a subsurface two-dimensional electron system created at a GaAs/AlGaAs heterojunction. The Q1DES confining potential was modelled as flat in the middle with parabolic walls, and Schrodingers equation solved numerically using a finite-difference method. Using this model, the experimental Q1DES width and 1D subband energy spacings were deduced.

Imaging diffraction-limited electronic collimation from a non-equilibrium one-dimensional ballistic constriction

We report on the use of a low-temperature scanning probe microscope to investigate non-equilibrium electronic transport through a one-dimensional ballistic constriction. Transconductance images of electrons backscattered in the adjoining two-dimensional reservoirs show a weak acceptance cone consistent with semiclassical collimation. The images also show a strong highly collimated beam of quasi-particles injected into each reservoir with a divergence consistent with quantum mechanical diffraction. In the lower-chemical-potential reservoir these quasi-particles are interpreted as hot electrons while in the higher-chemical-potential reservoir they are interpreted as conduction-band holes.

Imaging electrostatic microconstrictions in long 1D wires

Abstract We present scanned gate microscopy (SGM) images of a 4 μm long one-dimensional (1D) wire. The wire was defined by split-gate surface electrodes over a GaAs/AlGaAs heterostructure incorporating a subsurface 2D electron system. To generate SGM images, a charged tip scans a rectangular region over the wire. The wire conductance is recorded to determine the image contrast. A chain of circular features are seen along the length of the wire, caused by electrostatic microconstrictions. The microconstrictions were studied by changing either the tip voltage or the wire lateral position.

Imaging random telegraph signal sites near a quasi 1D electron system

Conductance of a quasi 1D electron system (Q1DES) is a sensitive detector of the local electric potential. Electrons hopping between defect states can generate a random telegraph signal in conductance measurements made against time. Such a detector, defined in a GaAs/AlGaAs heterostructure, was used to generate images of the electric potential of a scanning charged tip and structure seen in the Q1DES conductance images is consistent with an electron hopping between two defect states separated by slightly more than the Bohr orbit. The occupation probability being mediated by the position of the scanning tip over the defect near the Q1DES. Images suggest that a puddle of mobile charge in the donor layer can screen the tip from the defect system.