Electric and magnetic waveguides in graphene: quantum and classical

TL;DR

This paper explores electric and magnetic waveguides in graphene and their classical analogs, analyzing symmetries and wave behavior through analytical solutions and visualizations in quantum and classical contexts.

Contribution

It provides an analytical approach to solving the Dirac-Weyl equation for waveguides in graphene, highlighting symmetry considerations and comparing quantum and classical waveguide features.

Findings

Identified symmetry conditions influencing waveguide behavior

Derived analytical solutions for square-profile waveguides

Visualized quantum and classical wave properties through graphics

Abstract

Electric and magnetic waveguides are considered in planar Dirac materials like graphene as well as their classical version for relativistic particles of zero mass and electric charge. In order to solve the Dirac-Weyl equation analytically, we have assumed the displacement symmetry of the system along a direction. In these conditions we have examined the rest of symmetries relevant each type, magnetic or electric system, which will determine their similarities and differences. We have worked out waveguides with square profile in detail to show up some of the most interesting features also in quantum and classical complementary contexts. All the results have been visualized along a series of representative graphics showing explicitly the main properties for both types of waveguides.