Quantum Hall plateau transition in graphene with spatially correlated random hopping

TL;DR

This study reveals that spatially correlated ripples in graphene significantly alter the quantum Hall plateau transition, leading to an anomalous fixed point due to preserved chiral symmetry and suppressed scattering.

Contribution

It demonstrates that spatial correlation in random hopping induces a fixed point in the quantum Hall transition in graphene, highlighting the role of chiral symmetry.

Findings

Criticality changes to an anomalous fixed point with correlated ripples.

Chiral symmetry preservation suppresses scattering between K and K' points.

Results suggest a fixed point for chiral symmetric Dirac fermions in clean graphene.

Abstract

We investigate how the criticality of the quantum Hall plateau transition in disordered graphene differs from those in the ordinary quantum Hall systems, based on the honeycomb lattice with ripples modeled as random hoppings. The criticality of the graphene-specific n=0 Landau level is found to change dramatically to an anomalous, almost exact fixed point as soon as we make the random hopping spatially correlated over a few bond lengths. We attribute this to the preserved chiral symmetry and suppressed scattering between K and K' points in the Brillouin zone. The results suggest that a fixed point for random Dirac fermions with chiral symmetry can be realized in free-standing, clean graphene with ripples.