Dynamics of electrons and explicit solutions of Dirac-Weyl systems

TL;DR

This paper constructs broad classes of explicit, non-singular solutions for Dirac-Weyl systems relevant to graphene, advancing the understanding of their dynamics with new solution methods.

Contribution

It introduces a novel approach to explicitly solve Dirac-Weyl systems, expanding the known solution space significantly.

Findings

Constructed wider classes of solutions than previously known

Proved solutions and potentials are free of singularities

Provided various illustrative examples

Abstract

Explicit solutions of Dirac-Weyl system, which is essential in graphene studies, are constructed using our recent approach to the construction of solutions of dynamical systems. The obtained classes of solutions are much wider than the ones, which were considered before. It is proved that neither constructed potentials nor corresponding solutions have singularities. Various examples are provided.