The integer quantum Hall effect is a striking example of a macroscopic topological quantum state of matter. Visualizing the effect in space directly is notoriously difficult because most high-quality two-dimensional electron gases (2DEG) are buried at material interfaces. Graphene, a 2D material with excitations that mimic relativistic massless Dirac fermions, instead features a fully exposed 2DEG that is ideal for visualizing quantum Hall physics. Additionally, the recent ability to custom ‘draw’ nanoscale substrate gate potentials in 2D heterostructures has opened the door for creating confined quantum dot (QD) states in a contiguous sheet of graphene. In this talk I will present scanning tunneling microscopy/spectroscopy (STM/S) measurements that explore the interplay between the spatial and magnetic confinement of relativistic Dirac fermions. I will first describe how quasi-bound resonances occur due to relativistic Klein scattering at QD edges. As a magnetic field is applied, and the system enters the quantum Hall regime, I will then show measurements that directly visualize the intricate evolution of the QD resonant states into highly degenerate Landau levels and how electron interactions lead to the subsequent formation of a ‘wedding cake’-like structure due to quantum Hall edge reconstruction.
Watch a video of the talk here.