Observation of ballistic upstream modes at fractional quantum Hall edges of graphene

TL;DR

This study detects upstream modes at fractional quantum Hall edges in graphene through noise measurements, revealing ballistic energy transport and advancing understanding of edge state dynamics in quantum Hall systems.

Contribution

It provides the first direct noise-based evidence of upstream modes in fractional quantum Hall states in graphene, demonstrating their ballistic nature and contrasting with previous diffusive observations.

Findings

Upstream modes are present in hole-conjugate fractional QH states.

Upstream energy transport is ballistic, not diffusive.

Noise magnitude is proportional to injected current and independent of length.

Abstract

The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream'' modes, moving against the direction of charge current flow, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here we report on noise measurements at the edges of fractional QH (FQH) phases realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at $L= 4\,\mu$m or $10\,\mu$m away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for ``hole-conjugate'' FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remaining independent of length together with a remarkable agreement with our theoretical analysis demonstrates the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems. Our investigation opens the door to the study of upstream transport in more complex geometries and in edges of non-Abelian phases in graphene.