Person:

Klales, Anna

We discover and characterise strong quantum scars, or quantum eigenstates resembling classical periodic orbits, in two-dimensional quantum wells perturbed by local impurities. These scars are not explained by ordinary scar theory, which would require the existence of short, moderately unstable periodic orbits in the perturbed system. Instead, they are supported by classical resonances in the unperturbed system and the resulting quantum near-degeneracy. Even in the case of a large number of randomly scattered impurities, the scars prefer distinct orientations that extremise the overlap with the impurities. We demonstrate that these preferred orientations can be used for highly efficient transport of quantum wave packets across the perturbed potential landscape. Assisted by the scars, wave-packet recurrences are significantly stronger than in the unperturbed system. Together with the controllability of the preferred orientations, this property may be very useful for quantum transport applications.

Electrons in graphene can travel for several microns without scattering at low temperatures, and their motion becomes ballistic, following classical trajectories. When a magnetic field B is applied perpendicular to the plane, electrons follow cyclotron orbits. Magnetic focusing occurs when electrons injected from one narrow contact focus onto a second contact located an integer number of cyclotron diameters away. By tuning the magnetic field B and electron density n in the graphene layer, we observe magnetic focusing peaks. We use a cooled scanning gate microscope to image cyclotron trajectories in graphene at 4.2 K. The tip creates a local change in density that casts a shadow by deflecting electrons flowing nearby; an image of flow can be obtained by measuring the transmission between contacts as the tip is raster scanned across the sample. On the first magnetic focusing peak, we image a cyclotron orbit that extends from one contact to the other. In addition, we study the geometry of orbits deflected into the second point contact by the tip.