We consider the $\nu =0$ quantum Hall ferromagnetic state of bilayer graphene subject to a kinklike perpendicular electric field, which generates domain walls in the electronic state and low-energy collective modes confined to move along them. In particular, it is shown that two pairs of collective helical modes are formed at opposite sides of the kink, each pair consisting of modes with identical helicities. We derive an effective field-theoretical model of these modes in terms of two weakly coupled anisotropic quantum spin ladders, with parameters tunable through control of the electric and magnetic fields. This yields a rich phase diagram, where, due to the helical nature of the modes, distinct phases possess very different charge conduction properties. Most notably, this system can potentially exhibit a transition from a superfluid to an insulating phase.

• Received 6 September 2013
• Revised 13 November 2013

DOI:https://doi.org/10.1103/PhysRevB.89.121411