Electrical Parameters for Planar Transport in Graphene and 2-D Materials

TL;DR

This paper revisits classical electrodynamics to develop new mathematical tools and definitions for electrical parameters in 2-D materials like graphene, including a new divergence theorem and modified Gauss law.

Contribution

It introduces a new line integral, divergence theorem, and definitions for flux, electric vector potential, and displacement in 2-D materials, advancing the theoretical framework for planar transport.

Findings

Derived a new divergence theorem applicable in 2-D

Formulated a modified Gauss law for 2-D materials

Defined conduction and displacement currents in 2-D systems

Abstract

Classical electrodynamics has been revisited with a view to recast the electrical parameters for planar transport in 2-dimensional (2-D) materials like graphene. In this attempt a new line integral, named transverse line integral, with extensive applications in 2-D, is defined. Since the existing divergence theorem in not applicable in 2-D, we introduced a new divergence theorem. A new definition for the in-plane flux of any 2-D vector is introduced. A new vector named electric vector potential is defined and Gauss law is modified in terms of the 2-D flux of the new vector. The new Gauss law in presence of dielectric is obtained and a new electric displacement vector is defined for the 2-D materials. The conduction and displacement current densities in 2-D are defined. Resistance and resistivity in 2-D materials are discussed. The continuity equation for planar transport is derived.