Imaging Coulomb Islands in a Quantum Hall Interferometer

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 spectrum 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.

Imaging Electron Wave Functions Inside Open Quantum Rings

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 the 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 $|Psi|^{2}(x,y)$.