Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum-Hall Edge States

TL;DR

This paper presents time-of-flight measurements of single-electron wave packets in quantum-Hall edge states, revealing their velocity dependence on magnetic field and estimating the edge potential.

Contribution

It introduces a method to measure electron arrival times and velocities in quantum-Hall edge states, providing new insights into their dynamics and potential landscape.

Findings

Electron velocity follows a 1/B dependence consistent with E×B drift.

Edge potential estimated from energy dependence of velocity.

Demonstrated a technique for time-resolved electron detection in quantum Hall systems.

Abstract

We report time-of-flight measurements on electrons travelling in quantum-Hall edge states. Hot-electron wave packets are emitted one per cycle into edge states formed along a depleted sample boundary. The electron arrival time is detected by driving a detector barrier with a square wave that acts as a shutter. By adding an extra path using a deflection barrier, we measure a delay in the arrival time, from which the edge-state velocity $v$ is deduced. We find that $v$ follows $1/B$ dependence, in good agreement with the $\vec{E} \times \vec{B}$ drift. The edge potential is estimated from the energy-dependence of $v$ using a harmonic approximation.