Network model for periodically strained graphene

The long-wavelength physics of monolayer graphene in the presence of periodic strain fields has a
natural chiral scattering network description. When the strain field varies slowly compared to the
graphene lattice and the effective magnetic length of the induced valley pseudomagnetic field, the
low-energy physics can be understood in terms of valley-polarized percolating domain-wall modes.
Inspired by a recent experiment, we consider a strain field with threefold rotation and mirror sym-
metries but without twofold rotation symmetry, resulting in a system with the connectivity of
the oriented kagome network. Scattering processes in this network are captured by a symmetry-
constrained phenomenological S matrix. We analyze the phase diagram of the kagome network, and
show that the bulk physics of the strained graphene can be qualitatively captured by the network
when we account for a percolation transition at charge neutrality. We also discuss the limitations
of this approach to properly account for boundary physics.