Spatially inhomogeneous strains in graphene can simulate the effects of valley-dependent magnetic fields. As demonstrated in recent experiments [N. Levy et al., Science 329, 544 (2010) and K. K. Gomes et al., Nature (London) 483, 306 (2012)], the realizable magnetic fields are large enough to give rise to well-defined flat pseudo-Landau levels, potentially having counterpropagating edge modes. In this work, we address the conditions under which such edge modes are visible. We find that, whereas armchair edges do not support counterpropagating edge modes, zigzag edges do so, through a selective-hybridization mechanism. We then discuss effects of interactions on the stability of counterpropagating edge modes and find that, for the experimentally relevant case of Coulomb interactions, interactions typically decrease the stability of the edge modes. Finally, we generalize our analysis to address the case of spontaneous valley polarization, which is expected to occur in charge-neutral strained graphene [P. Ghaemi et al., Phys. Rev. Lett. 108, 266801 (2012) and D. A. Abanin and D. A. Pesin, Phys. Rev. Lett. 109, 066802 (2012)] .

• Received 17 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.155422