Network model for periodically strained graphene

TL;DR

This paper models the low-energy physics of periodically strained graphene using a chiral scattering network, revealing a percolation transition and the importance of symmetry constraints in understanding its phase diagram.

Contribution

It introduces a kagome network model with symmetry-constrained scattering matrices to describe strained graphene's valley-polarized modes and analyzes its phase diagram.

Findings

The network captures the bulk physics of strained graphene.

A percolation transition occurs at charge neutrality.

Limitations exist in modeling boundary physics.

Abstract

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 symmetries 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.