Electric conduction as a signature of magnetic phases in graphene

The emergence of magnetic ordering in two-dimensional electron systems in the quantum Hall regime is a remarkable consequence of interaction effects. Most prominently, these systems exhibit an intimate relation between spin and charge excitations enforced by a topological constraint. As a result, the nature of magnetic phases and transitions between them can be manifested in electric transport.

A particularly interesting realization of this phenomenon is observed in undoped graphene, where owing to the presence of a valley isospin in addition to the real spin, a rich variety of magnetic phases can be formed. A transition between distinct phases may then be signified by large magneto-conductance. Indeed, recent experimental results indicate that graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle. This behavior is attributed to a quantum phase transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk quantum Hall state at filling factor zero. I will discuss a theoretical model which accounts for this behavior. A key ingredient in this theory is the formation of charge-carrying collective edge modes, which undergo a dramatic change in character through the magnetic phase transition in the bulk. The electric transport properties of the system, being dominated by these modes, thus encode the distinct magnetic phases and their fluctuations near criticality.