Husimi Maps in Graphene

TL;DR

This paper introduces a Husimi projection method to connect atomistic simulations with Dirac effective theory in graphene, enabling multiscale visualization of quasiparticle behavior and boundary scattering phenomena.

Contribution

The paper develops a Husimi map technique that translates atomistic wavefunctions into semiclassical pictures, bridging microscopic and continuum descriptions in graphene.

Findings

Maps of boundary scattering behavior reveal insights into wavefunction properties.

Boundary conditions influence the emergence of Fano resonances.

Husimi maps help analyze bond currents near resonances.

Abstract

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.