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We present a method for bridging the gap between the Dirac effective field theory and atomistic simulations in graphene based on the Husimi projection, allowing us to depict phenomena in graphene at arbitrary scales. This technique takes the atomistic wavefunction as an input, and produces semiclassical pictures of quasiparticles in the two Dirac valleys. We use the Husimi tech- nique to produce maps of the scattering behavior of boundaries, giving insight into the properties of wavefunctions at energies both close to and far from the Dirac point. Boundary conditions play a significant role to the rise of Fano resonances, which we examine using the Husimi map to deepen our understanding of bond currents near resonance.

We build upon previous work that used coherent states as a measurement of the local phase space and extended the flux operator by adapting the Husimi projection to produce a vector field called the Husimi map. In this article, we extend its definition from continuous systems to lattices. This requires making several adjustments to incorporate effects such as group velocity and multiple bands. Several phenomena which uniquely occur in lattice systems, like group-velocity warping and internal Bragg diffraction, are explained and demonstrated using Husimi maps. We also show that scattering points between bands and valleys can be identified in the divergence of the Husimi map.

We develop the Husimi map for visualizing quantum wavefunctions using coherent states as a measurement of the local phase space to produce a vector field related to the probability flux. Adapted from the Husimi projection, the Husimi map is complimentary to the usual flux map, since they are identical for small coherent states. By improving our understanding of the flux operator and offering a robust and flexible alternative, we show how the Husimi projection can provide a map to the classical dynamics underlying a quantum wavefunction. We demonstrate its capabilities on bound systems with electromagnetic fields, as well as on open systems on and off resonance.