Topology, symmetry, and edge states in graphene heterostructures

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as nanowires. Recently, a new method has emerged with the recognition that gapped symmetry-protected topological (SPT) phases can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties such as the locking of spin and momentum. I will describe our recent experimental realization of such helical states on the edge of a graphene flake subjected to very large magnetic fields. In contrast to its time-reversal-symmetric cousin, the graphene quantum spin Hall state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the applied field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with a tunable bandgap and an associated spin texture.