Quantum Electronic Transport in Mesoscopic Graphene Devices

Abstract

Graphene provides a rich platform for the study of interaction-induced broken symmetry states due to the presence of spin and sublattice symmetries that can be controllably broken with external electric and magnetic fields. At high magnetic fields and low temperatures, where quantum effects dominate, we map out the phase diagram of broken symmetry quantum Hall states in suspended bilayer graphene. Application of a perpendicular electric field breaks the sublattice (or layer) symmetry, allowing identification of distinct layer-polarized and canted antiferromagnetic v=0 states. At low fields, a new spontaneous broken-symmetry state emerges, which we explore using transport measurements. The large energy gaps associated with the v=0 state and electric field induced insulating states in bilayer graphene offer an opportunity for tunable bandgap engineering. We use local electrostatic gating to create quantum confined devices in graphene, including quantum point contacts and gate-defined quantum dots. The final part of this thesis focuses on proximity induced superconductivity in graphene Josephson junctions. We directly visualize current flow in a graphene Josephson junction using superconducting interferometry. The key to our approach involves reconstruction of the real-space current density from magnetic interference using Fourier methods. We observe that current is confined to the crystal boundaries near the Dirac point and that edge and bulk currents coexist at higher Fermi energies. These results are consistent with the existence of "fiber-optic" edge modes at the Dirac point, which we model theoretically. Our techniques also open the door to fast spatial imaging of current distributions along more complicated networks of domains in larger crystals.