Atomistic deconstruction of current flow in graphene based hetero-junctions

We describe the numerical modeling of current flow in graphene heterojunctions, within the Keldysh Landauer Non-equilibrium Green's function (NEGF) formalism. By implementing a $k$-space approach along the transverse modes, coupled with partial matrix inversion using the Recursive Green's function Algorithm (RGFA), we can simulate on an atomistic scale current flow across devices approaching experimental dimensions. We use the numerical platform to deconstruct current flow in graphene, compare with experimental results on conductance, conductivity and quantum Hall, and deconstruct the physics of electron `optics' and pseudospintronics in graphene $p-n$ junctions. We also demonstrate how to impose exact open boundary conditions along the edges to minimize spurious edge reflections.