The Quantum Hall Transition in Real Space: From Localized to Extended States

TL;DR

This study uses scanning tunneling spectroscopy at low temperatures and high magnetic fields to directly observe the evolution of electronic wave functions during the integer quantum Hall transition, revealing localized to extended state changes.

Contribution

First direct real-space observation of the quantum Hall transition showing the evolution from localized to extended states at the microscopic level.

Findings

Localized drift states in insulating phases

Extended drift states at the quantum critical point

Localized quantum tunneling points near extended states

Abstract

Using scanning tunneling spectroscopy in ultra-high vacuum at low temperature (T = 0.3 K) and high magnetic fields (B < 12 T), we directly probe electronic wave functions across an integer quantum Hall transition. In accordance with theoretical predictions, we observe the evolution from localized drift states in the insulating phases to branched extended drift states at the quantum critical point. The observed microscopic behavior close to the extended state indicates points of localized quantum tunneling, which are considered to be decisive for a quantitative description of the transition.