Imaging magnetic focusing in a two-dimensional electron gas

The most direct way to understand how electrons move through semiconductor heterostructures is to spatially image their motion. The two-dimensional electron gas has proved its interest for both device applications and studies of fundamental physics, and offers many more opportunities as we better understand these systems. We wished to examine electron motion in magnetic fields, both to study fundamental physics (e.g. quantum Hall and spin-orbit coupling) and to design future devices (e.g. for spintronics and quantum information processing), and we successfully imaged the magnetic focusing of electron waves. To this end, much of my time at Harvard was spent building the He-3 cooled scanning probe microscope (SPM), which reaches 470 mK and can apply up to a 7 Tesla magnetic field perpendicular to the electron motion, or 3 Tesla parallel to the electron motion.; Prior to my work on this microscope, we created a V-shaped imaging interferometer that uses a backscattering technique to map out electron flow and interference. A negative charge is placed on the SPM tip, fully depleting the electrons below. Some electrons will backscatter and return to the QPC along the path they came, changing the conductance of the QPC. By scanning the tip above the surface and associating a change in conductance with each point, we image electron flow. We used this backscattering technique to look at flow from a QPC in a perpendicular magnetic field, and observed the decay of the measurable change in conductance with tip position. A perpendicular field breaks time reversal symmetry such that the electron may not have a path to return to the QPC after being scattered.; To image the magnetic focusing of electron waves, we developed a new technique that can image electrons transmitted from one QPC to another, taking advantage of the adjustable strength of our tip voltage induced scatterer. We source current through one QPC and measure the transmission through a second. We bring the tip close to the surface of the heterostructure and place a voltage on the tip, creating an area of reduced (or increased) density of electrons beneath. This area deflects the electrons away from their initial trajectories, changing the transmission between the QPCs. By scanning the tip with a small voltage applied and measuring the change in transmission at each tip location, we can image the originally transmitted trajectories. We see clear images of the skipping orbits of magnetic focusing. By scanning the tip with a large voltage applied, we enhance interference effects and see fringes in our images. Simulations agree well with the experimentally obtained images.