Two dimensional materials constitute an exciting and unusually tunable platform for investigation of both fundamental phenomena and electronic applications. Here I will present our results on transport measurements on high mobility few-layer graphene and phosphorene devices. In bilayer and trilayer graphene devices with mobility as high as 400,000 cm2/V, we observe intrinsic gapped states at the charge neutrality point, arising from electronic interactions. This state is identified to be a layer antiferromagnetic state with broken time reversal symmetry. In another few-layer graphene system, ABA-stacked trilayer graphene consists of multiple Dirac bands, where crystal symmetry protects the spin degenerate counter-propagating edge modes resulting in σxx = 4e2/h. At even higher magnetic fields, the crystal symmetry is broken in by electron-electron interactions and the n=0 quantum Hall state develops an insulating phase with non-monotonic dependence on temperature and magnetic field. Our findings indicate the role of crystal and spin symmetry in generation of topological phases in multiple Dirac bands. At finite doping, we explore the tunable integer and fractional quantum Hall states and Landau level crossings in these few-layer systems. Finally, I will present our recent results on quantum oscillations and weak localization in air-stable, few-layer phosphorene devices. Our results underscore the fascinating many-body physics in these 2D membranes.
