Dirac-Schrodinger transformations in contacted graphene structures

TL;DR

This paper investigates how boundary conditions at contacts influence electron transmission in graphene, proposing that optical experiments on photonic crystals could help identify the correct boundary conditions at graphene-electrode interfaces.

Contribution

It introduces a framework for understanding boundary conditions at graphene contacts and suggests experimental methods to determine them.

Findings

Boundary conditions significantly affect electron transmission.

Optical experiments on photonic crystals can identify proper boundary conditions.

Theoretical analysis of Dirac-Schrodinger interface transformations.

Abstract

At an interface between contacts and graphene, the mathematical equation that governs the propagation of electrons transforms from the Schrodinger to the Dirac equation. The condition of current probability conservation at such an interface does not determine uniquely the boundary conditions for the quantum wavefunction. We discuss the possible form of boundary conditions, determine its influence on the transmission coefficient of a contacted graphene structure and suggest that optical experiments on photonic crystals with Dirac points can help identifying, under certain circumstances, the proper boundary condition at graphene- electrode interfaces.