Spatially inhomogeneous strains in graphene can simulate the effects of valley-dependent magnetic fields. As demonstrated in recent experiments, the realizable magnetic fields are large enough to give rise to well-defined flat pseudo-Landau levels, potentially having counter-propagating edge modes. In the present work we address the conditions under which such edge modes are visible. We find that, whereas armchair edges do not support counter-propagating edge modes, zigzag edges do so, through a novel selective-hybridization mechanism. We then discuss effects of interactions on the stability of counter-propagating 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.
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