Evolution of the quantum Hall bulk spectrum into chiral edge states

T Patlatiuk,A Yacoby,Y Tserkovnyak,C P Scheller,D Hill,D M Zumbühl,K W West,L N Pfeiffer,G Barak

doi:10.1038/s41467-018-06025-3

T Patlatiuk, A Yacoby + Show 7 more

Open Access

https://doi.org/10.1038/s41467-018-06025-3

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Abstract

One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. Here, we use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas. This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. We present consistent analytical and numerical models, inferring the edge states from the well-known bulk spectrum, finding excellent agreement with the experiment—thus providing direct evidence for the bulk to edge correspondence. In addition, we observe various features beyond the single-particle picture, such as Fermi level pinning, exchange-enhanced spin splitting and signatures of edge-state reconstruction.

Highlights

One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum
We observe the chiral nature of edge states, as well as Fermi level pinning effects
Interactions lead to signatures of edge reconstruction and exchange-enhanced spinsplitting at large in-plane magnetic fields. We emphasize that this spectroscopy is done at zero bias, eliminating heating or lifetime effects

Summary

Introduction

One of the most intriguing and fundamental properties of topological systems is the correspondence between the conducting edge states and the gapped bulk spectrum. We use a GaAs cleaved edge quantum wire to perform momentum-resolved spectroscopy of the quantum Hall edge states in a tunnel-coupled 2D electron gas This reveals the momentum and position of the edge states with unprecedented precision and shows the evolution from very low magnetic fields all the way to high fields where depopulation occurs. Accessing the surface states in a topological system separately and independently, has proven to be challenging for a number of reasons, including disorder, insufficient resolution, or remnant bulk conductivity contaminating transport experiments Local probes, such as scanning single electron transistors, could in principle overcome the bulk conductivity problem and have been intensely investigated in the context of quantum Hall systems[4,5,6,7,8,9,10,11,12,13]. We emphasize that this spectroscopy is done at zero bias, eliminating heating or lifetime effects

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