The valley filter efficiency of monolayer graphene and bilayer graphene line defect model

TL;DR

This study investigates the valley filter efficiency in monolayer and bilayer graphene line defect models, revealing conditions for perfect valley polarization and the effects of disorder and magnetic fields on transport properties.

Contribution

It introduces models for valley filter efficiency in graphene line defects and analyzes their performance under disorder and magnetic fields using transfer matrix methods.

Findings

Line defects over 15 nm act as perfect valley filters under weak disorder.

Backscattering and bulk states reduce valley polarization in diffusive regimes.

Long line defects have low conductance but maintain polarization.

Abstract

In addition to electron charge and spin, novel materials host another degree of freedom, the valley. For a junction composed of valley filter sandwiched by two normal terminals, we focus on the valley efficiency under disorder with two valley filter models based on monolayer and bilayer graphene. Applying the transfer matrix method, valley resolved transmission coefficients are obtained. We find that: i) under weak disorder, when the line defect length is over about $15\rm nm$, it functions as a perfect channel (quantized conductance) and valley filter (totally polarized); ii) in the diffusive regime, combination effects of backscattering and bulk states assisted intervalley transmission enhance the conductance and suppress the valley polarization; iii) for very long line defect, though the conductance is small, polarization is indifferent to length. Under perpendicular magnetics field, the characters of charge and valley transport are only slightly affected. Finally we discuss the efficiency of transport valley polarized current in a hybrid system.