Quantum transport in graphene heterostructures

The two dimensional charge carriers in mono- and bilayer graphene are described by massless and massive chiral Dirac Hamiltonians, respectively. This thesis describes low temperature transport experiments designed to probe the consequences of this basic fact. The first part concerns the effect of the lattice pseudospin, an analog of a relativistic electron spin, on the scattering properties of mono- and bilayer graphene. We fabricate graphene devices with an extremely narrow local gates, and study ballistic carrier transport through the resulting barrier. By analyzing the interference of quasiparticles confined to the region beneath the gate, we are able to determine that charge carriers normally incident to the barrier are transmitted perfectly, a solid state analog of the Klein tunneling of relativistic quantum mechanics. The second part of the work describes the development of hexagonal boron nitride (hBN), an insulating isomorph of graphite, as a substrate and gate dielectric for graphene electronics. We use the enhanced mobility of electrons in h-BN supported graphene to investigate the effect of electronic interactions. We find interactions drive spontaneous breaking of the emergent SU(4) symmetry of the graphene Landau levels, leading to a variety of quantum Hall isospin ferromagnetic (QHIFM) states, which we study using tilted field magnetotransport. At yet higher fields, we observe fractional quantum Hall states which show signatures of the unique symmetries and anisotropies of the graphene QHIFM. The final part of the thesis details a proposal and preliminary experiments to probe isospin ordering in bilayer graphene using capacitance measurements