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

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 $1\mathrm{/}B$ dependence, in good agreement with the $\vec{E} \times \vec{B}$drift\mathrm{.}Theedgepotentialisestimatedfromtheenergy-dependenceof$v$ using a harmonic approximation.