Title: Transport Measurements of Correlated States in Graphene Flat Bands
Description: In electronic flat bands the electron kinetic energy is quenched and dominated by interaction and correlated states can emerge. These many-body collective modes are not only interesting enigmas to solve, but may also lead to real-life applications. This thesis studies correlated states in graphene, a tunable system that can be programmed by ex- ternal parameters such as electric field. Two types of graphene flat bands are examined. One, highly degenerate and discreet Landau levels created by external magnetic field. Two, moirè flat bands created by relative crystalline twist between graphene layers. Correlated states are studied with transport measurements. The results were measured in dual-gated graphite/Boron nitride encapsulated graphene heterostructures with very low disorder. The high quality of the heterostructure is showcased by ballistic electron optics including nega- tive refraction across a gate-defined pn junction. In the first type of flat band — a partially filled Landau level — the competition of electrons solid states and fractional quantum Hall liquid manifests as reentrant quantum Hall effect, with a valley and spin hierarchy unique to graphene.

Alternatively, in the flat bands arising from moiré superlattices, we explore two tuning knobs of correlated states. In twisted bilayer graphene, the band width are tuned by changing interlayer hybridization via pressure. The resulting superconducting and correlated insulator states can be restored outside of a narrow range of twist angles near 1.1 degrees. New fermi surfaces also form at commensurate fillings of the flat band with reduced degeneracy. In twisted monolayer-bilayer graphene, we find extraordinary level of control and tunability because of the low symmetry. With perpendicular electric field, the system can alternate among correlated metallic and insulating states, as well as topological magnetic states. The magnetization direction can be switched purely with electrostatic doping at zero magnetic field.