  Single-layer graphenes subject to periodic lateral strains are artificial
crystals that can support boundary spectra with an intrinsic polarity. These
are analyzed by comparing the effects of periodic magnetic fields and
strain-induced pseudomagnetic fields that respectively break and preserve
time-reversal symmetry. In the former case, a Chern classification of the
superlattice minibands with zero total magnetic flux enforces {\it single}
counter-propagating modes traversing each bulk gap on opposite boundaries of a
nanoribbon. For the pseudomagnetic field, pairs of counter-propagating modes
migrate to the {\it same} boundary where they provide well-developed
valley-helical transport channels on a single zigzag edge. We discuss possible
schemes for implementing this situation and their experimental signatures.
