  Spatially varying strain patterns can qualitatively alter the electronic
properties of graphene, acting as effective valley-dependent magnetic fields
and giving rise to pseudo-Landau-level (PLL) quantization. Here, we show that
the strain-induced magnetic field is one component of an SU(2) non-Abelian
gauge field within the low-energy theory of graphene, and identify the other
two components as period-3 charge-density waves. We show that these
density-waves, if spatially varied, give rise to PLL quantization. We also
argue that strain-induced magnetic fields can induce density-wave order in
graphene, thus dynamically gapping out the lowest PLL; moreover, the ordering
should generically be accompanied by dislocations. We discuss experimental
signatures of these effects.
