Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutr
ality point. In a quantizing magnetic field electron interactions can cause spontaneous symmetry breaking within the spin and valley degrees of freedom, resulting in quantum Hall states (QHS) with complex order. Here we report fractional quantum Hall states (FQHS) in bilayer graphene which show phase transitions that can be tuned by a transverse electric field. This result provides a model platform to study the role of symmetry breaking in emergent states with distinct topological order.
The most celebrated property of the quantum spin Hall effect is the presence of spin-polarized counter-propagating edge states. This novel edge state configuration has also been predicted to occur in graphene when spin-split electron- and hole-like L
andau levels are forced to cross at the edge of the sample. In particular, a quantum spin Hall analogue has been predicted at { u}=0 in bilayer graphene if the ground state is a spin ferromagnet. Previous studies have demonstrated that the bilayer { u}=0 state is an insulator in a perpendicular magnetic field, though the exact nature of this state has not been identified. Here we present measurements of the { u}=0 state in a dual-gated bilayer graphene device in tilted magnetic field. The application of an in-plane magnetic field and perpendicular electric field allows us to map out a full phase diagram of the { u}=0 state as a function of experimentally tunable parameters. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of order 4e^2/h, consistent with predictions for the ferromagnet.
We report a multiband transport study of bilayer graphene at high carrier densities. Employing a poly(ethylene)oxide-CsClO$_4$ solid polymer electrolyte gate we demonstrate the filling of the high energy subbands in bilayer graphene samples at carrie
r densities $|n|geq2.4times 10^{13}$ cm$^{-2}$. We observe a sudden increase of resistance and the onset of a second family of Shubnikov de Haas (SdH) oscillations as these high energy subbands are populated. From simultaneous Hall and magnetoresistance measurements together with SdH oscillations in the multiband conduction regime, we deduce the carrier densities and mobilities for the higher energy bands separately and find the mobilities to be at least a factor of two higher than those in the low energy bands.
