Decomposition into Propagating and Evanescent Modes of Graphene Ribbons

TL;DR

This paper develops a comprehensive analytical framework for classifying and constructing bulk modes in graphene ribbons, enabling more efficient electronic transport simulations in graphene-based devices.

Contribution

It introduces a complete set of bulk modes for graphene ribbons at arbitrary energies, with explicit analytical expressions and classification into propagating or evanescent modes.

Findings

Derived analytical expressions for bulk modes.

Classified modes into propagating and evanescent.

Demonstrated applications in transport simulations.

Abstract

Bulk modes (BM) are basis solutions to the Schr\"{o}dinger equation and they are useful in a number of physical problems. In the present work, we establish a complete set of BMs for graphene ribbons at arbitrary energy. We derive analytical expressions for these modes and systematically classify them into propagating or evanescent mode. We also demonstrate their uses in efficient electronic transport simulations of graphene-based electronic devices within both the mode-matching method and the Green's function framework. Explicit constructions of Green's functions for infinite and semi-infinite graphene ribbons are presented.