Theory of the valley-valve effect in graphene nanoribbons

TL;DR

This paper explains how a potential step in zigzag-edged graphene nanoribbons causes intrinsic intervalley scattering, affecting conductance and the valley-valve effect, with a model linking localized edge states to the number of carbon atoms across the ribbon.

Contribution

It introduces a theoretical model showing that potential steps induce intervalley scattering via localized edge states, explaining the valley-valve effect's dependence on ribbon width parity.

Findings

Conductance depends on the number of carbon atoms across the ribbon.

Intervalley scattering occurs regardless of the smoothness of the potential step.

The conductance formula explains the parity dependence of the valley-valve effect.

Abstract

A potential step in a graphene nanoribbon with zigzag edges is shown to be an intrinsic source of intervalley scattering -- no matter how smooth the step is on the scale of the lattice constant a. The valleys are coupled by a pair of localized states at the opposite edges, which act as an attractor/repellor for edge states propagating in valley K/K'. The relative displacement Delta along the ribbon of the localized states determines the conductance G. Our result G=(e^{2}/h)[1-\cos(N\pi+2\pi\Delta/3a)] explains why the ``valley-valve'' effect (the blocking of the current by a p-n junction) depends on the parity of the number N of carbon atoms across the ribbon.