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 the S matrix gains an appropriate energy dependence. We also discuss the limitations of this

approach to properly account for boundary physics.