The disordered potential landscape in an InGaAs/InAlAs two-dimensional electron gas patterned into narrow wires is investigated by means of scanning gate microscopy. It is found that scanning a negatively charged tip above particular sites of the wir
es produces conductance oscillations that are periodic in the tip voltage. These oscillations take the shape of concentric circles whose number and diameter increase for more negative tip voltages until full depletion occurs in the probed region. These observations cannot be explained by charging events in material traps, but are consistent with Coulomb blockade in quantum dots forming when the potential fluctuations are raised locally at the Fermi level by the gating action of the tip. This interpretation is supported by simple electrostatic simulations in the case of a disorder potential induced by ionized dopants. This work represents a local investigation of the mechanisms responsible for the disorder-induced metal-to-insulator transition observed in macroscopic two-dimensional electron systems at low enough density.
In the Quantum Hall regime, near integer filling factors, electrons should only be transmitted through spatially-separated edge states. However, in mesoscopic systems, electronic transmission turns out to be more complex, giving rise to a large spect
rum of magnetoresistance oscillations. To explain these observations, recent models put forward that, as edge states come close to each other, electrons can hop between counterpropagating edge channels, or tunnel through Coulomb islands. Here, we use scanning gate microscopy to demonstrate the presence of quantum Hall Coulomb islands, and reveal the spatial structure of transport inside a quantum Hall interferometer. Electron islands locations are found by modulating the tunneling between edge states and confined electron orbits. Tuning the magnetic field, we unveil a continuous evolution of active electron islands. This allows to decrypt the complexity of high magnetic field magnetoresistance oscillations, and opens the way to further local scale manipulations of quantum Hall localized states.
This paper presents an overview of scanning-gate microscopy applied to the imaging of electron transport through buried semiconductor nanostructures. After a brief description of the technique and of its possible artifacts, we give a summary of some
of its most instructive achievements found in the literature and we present an updated review of our own research. It focuses on the imaging of GaInAs-based quantum rings both in the low magnetic field Aharonov-Bohm regime and in the high-field quantum Hall regime. In all of the given examples, we emphasize how a local-probe approach is able to shed new, or complementary, light on transport phenomena which are usually studied by means of macroscopic conductance measurements.
We study the relationship between the local density of states (LDOS) and the conductance variation $Delta G$ in scanning-gate-microscopy experiments on mesoscopic structures as a charged tip scans above the sample surface. We present an analytical mo
del showing that in the linear-response regime the conductance shift $Delta G$ is proportional to the Hilbert transform of the LDOS and hence a generalized Kramers-Kronig relation holds between LDOS and $Delta G$. We analyze the physical conditions for the validity of this relationship both for one-dimensional and two-dimensional systems when several channels contribute to the transport. We focus on realistic Aharonov-Bohm rings including a random distribution of impurities and analyze the LDOS-$Delta G$ correspondence by means of exact numerical simulations, when localized states or semi-classical orbits characterize the wavefunction of the system.
Combining Scanning Gate Microscopy (SGM) experiments and simulations, we demonstrate low temperature imaging of electron probability density $|Psi|^{2}(x,y)$ in embedded mesoscopic quantum rings (QRs). The tip-induced conductance modulations share th
e same temperature dependence as the Aharonov-Bohm effect, indicating that they originate from electron wavefunction interferences. Simulations of both $|Psi|^{2}(x,y)$ and SGM conductance maps reproduce the main experimental observations and link fringes in SGM images to $|Psi|^{2}(x,y)$.
