  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 neutrality 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.
