Sensory Organ like Response of Zigzag Edge Graphene Nanoribbons

TL;DR

This paper models the nonlinear density and spin responses of zigzag edge graphene nanoribbons to external edge potentials and magnetic fields, revealing Weber-Fechner law-like behavior and system size dependence, validated by tight binding calculations.

Contribution

It introduces an analytical continuum Dirac model for edge responses in graphene nanoribbons, highlighting nonlinear behavior and size effects, with validation through tight binding methods.

Findings

Response depends logarithmically on edge potential

Response varies with nanoribbon width

Analytical results validated by tight binding calculations

Abstract

Using a continuum Dirac theory, we study the density and spin response of zigzag edge terminated graphene ribbons subjected to edge potentials and Zeeman fields. Our analytical calculations of the density and spin responses of the closed system (fixed particle number) to the static edge fields, show a highly nonlinear Weber-Fechner type behavior where the response depends logarithmically on the edge potential. The dependence of the response on the size of the system (e.g. width of a nanoribbon) is also uncovered. Zigzag edge graphene nanoribbons, therefore, provide a realization of response of organs such as the eye and ear that obey Weber-Fechner law. We validate our analytical results with tight binding calculations. These results are crucial in understanding important effects of electron-electron interactions in graphene nanoribbons such as edge magnetism etc., and also suggest possibilities for device applications of graphene nanoribbons.