# Waveform measurement of charge- and spin-density wave packets in a Tomonaga-Luttinger liquid

## TL;DR

This paper reports the first direct waveform measurements of charge and spin wave packets in a Tomonaga-Luttinger liquid, demonstrating spin-charge separation and controllability of 1D electron dynamics in quantum Hall edge channels.

## Contribution

It introduces a time domain measurement technique for observing waveforms of charge and spin excitations in a TL liquid, revealing spin-charge separation directly.

## Key findings

- Confirmed spatial separation of charge and spin wave packets over 200 μm
- Demonstrated control of 1D electron dynamics via electric environment tuning
- Provided direct waveform evidence of spin-charge separation in a TL liquid

## Abstract

In contrast to a free electron system, a Tomonaga-Luttinger (TL) liquid in a one dimensional (1D) electron system hosts charge and spin excitations as independent entities. When an electron wave packet is injected into a TL liquid, it transforms into wave packets carrying either charge or spin that propagate at different group velocities and move away from each other. This process, known as spin-charge separation, is the hallmark of TL physics. While the existence of these TL eigenmodes has been identified in momentum- or frequency-resolved measurements, their waveforms, which are a direct manifestation of 1D electron dynamics, have been long awaited to be measured. In this study, we present a time domain measurement for the spin-charge-separation process in an asymmetric chiral TL liquid comprising quantum Hall (QH) edge channels. We measure the waveforms of both charge and spin excitations by combining a spin filter with a time-resolved charge detector. Spatial separation of charge- and spin-wave packets over a distance exceeding 200 um was confirmed. In addition, we found that the 1D electron dynamics can be controlled by tuning the electric environment. These experimental results provide fundamental information about non-equilibrium phenomena in actual 1D electron systems.

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Source: https://tomesphere.com/paper/1703.04833