Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene

TL;DR

This paper demonstrates that graphene can host atomically sharp edges without edge-state reconstruction, allowing direct probing of universal quantum Hall edge properties and advancing understanding of topological states in 2D materials.

Contribution

It provides experimental evidence that graphene's edges can be atomically sharp, enabling control and direct study of quantum Hall edge states without reconstruction.

Findings

Atomically sharp edges in graphene are achievable without edge-state reconstruction.

Bulk Landau levels evolve into edge states at sharp zigzag edges.

Graphene's edge-state structure can be directly controlled and studied.

Abstract

The quantum-Hall-effect (QHE) occurs in topologically-ordered states of two-dimensional (2d) electron-systems in which an insulating bulk-state coexists with protected 1d conducting edge-states. Owing to a unique topologically imposed edge-bulk correspondence these edge-states are endowed with universal properties such as fractionally-charged quasiparticles and interference-patterns, which make them indispensable components for QH-based quantum-computation and other applications. The precise edge-bulk correspondence, conjectured theoretically in the limit of sharp edges, is difficult to realize in conventional semiconductor-based electron systems where soft boundaries lead to edge-state reconstruction. Using scanning-tunneling microscopy and spectroscopy to follow the spatial evolution of bulk Landau-levels towards a zigzag edge of graphene supported above a graphite substrate we demonstrate that in this system it is possible to realize atomically sharp edges with no edge-state reconstruction. Our results single out graphene as a system where the edge-state structure can be controlled and the universal properties directly probed.