Symmetries and the conductance of graphene nanoribbons with long-range disorder

TL;DR

This paper investigates how symmetries affect the conductance of graphene nanoribbons with long-range disorder, revealing different localization behaviors based on edge type and valley mixing.

Contribution

It uncovers the role of hidden pseudovalley structures and symmetry breaking in determining conductance and localization in disordered graphene nanoribbons.

Findings

Metallic armchair nanoribbons exhibit a perfectly conducting channel.

Semiconducting armchair nanoribbons show ordinary localization.

Weak localization is suppressed in certain ribbon types without valley mixing.

Abstract

We study the conductance of graphene nanoribbons with long-range disorder. Due to the absence of intervalley scattering from the disorder potential, time-reversal symmetry (TRS) can be effectively broken even without a magnetic field, depending on the type of ribbon edge. Even though armchair edges generally mix valleys, we show that metallic armchair nanoribbons possess a hidden pseudovalley structure and effectively broken TRS. In contrast, semiconducting armchair nanoribbons inevitably mix valleys and restore TRS. As a result, in strong disorder metallic armchair ribbons exhibit a perfectly conducting channel, but semiconducting armchair ribbons ordinary localization. TRS is also effectively broken in zigzag nanoribbons in the absence of valley mixing. However, we show that intervalley scattering in zigzag ribbons is significantly enhanced and TRS is restored even for smooth disorder, if the Fermi energy is smaller than the potential amplitude. The symmetry properties of disordered nanoribbons are also reflected in their conductance in the diffusive regime. In particular, we find suppression of weak localization and an enhancement of conductance fluctuations in metallic armchair and zigzag ribbons without valley mixing. In contrast, semiconducting armchair and zigzag ribbons with valley mixing exhibit weak localization behavior.