Graphene, a two-dimensional honeycomb lattice of carbon atoms, has become the hottest platform for condensed matter physics and a promising next generation electronic material. The band structures of single-, bi- and tri-layer graphene differ dramatically, yet all host chiral charge carriers with competing symmetries (such as spin, valley and orbital) that may be broken spontaneously or by an external field. In this thesis we present comprehensive transport studies on double-gated single-, bi- and tri-layer graphene, which lead to further insight into single particle and many-body physics in this fascinating 2D system.

A prevailing motif in these studies was the use of suspended structures with the aim to eliminate extrinsic factors such as disorder, which obscure intrinsic physical phenomena. Our efforts were most successful with dual gated suspended bilayer graphene where an unprecedented sample quality was achieved.

These studies are discussed in chapters six through nine. First, we focus on the observation of a spontaneous zero conductance gap at the charge neutrality point with zero out of plane electric and magnetic fields. By applying fields this gap can be closed with an electric field of either polarity, and grows monotonically with increasing magnetic field. These findings provide insight into the underlying symmetries of this correlated electron phenomena.

Secondly, we performed a systematic study using several devices of the minimum conductivity at charge neutrality. These devices fall into one group with finite, and another with zero minimum conductivity. Because the second group consists of only high quality samples we surmise this insulating state is intrinsic. By tuning temperature we found this gapped insulating state has a critical temperature suggesting a phase transition between insulating and conducting states. Additionally, the transition is tuned by disorder, out-of-plane electric field, or carrier density, suggesting a quantum phase transition.

Lastly, we study broken symmetry QH states at finite carrier density in the presence of zero and finite out of plane electric field. We find minute electric fields, which are commonly induced in single gated samples, significantly affect the broken symmetry states. Hence this study with zero electric field is the first genuine measurement of these states.

The wide range of applications and promising possibilities of stacked 2D materials highlight the importance of studying heterostructures. The works presented in this dissertation tell a comprehensive story about the heterostructure composed of graphene and hexagonal boron nitride (hBN). Through the use of established characterization techniques such as transport and scanning tunneling microscopy, we will explore phenomena in the graphene/hBN heterostructure from the bottom up in three vertical stages. Stage 1 is the bottommost part of the heterostructure and deals with the accumulation of charged defects in hBN induced by an exposure to high electric fields. Stage 2 focuses on the graphene/hBN interface and how these layered materials work together to enable the corralling of relativistic charge carriers. Finally, stage 3 probes the exposed surface of a double-layered graphene system which is decoupled from hBN while still benefiting from its structural support. The interplay between these materials yields high quality and atomically resolved tunneling spectroscopy results that suggest the emergence of correlated phenomena in naturally occurring double-layered graphene.