# Image-potential-induced spin-orbit interaction in one-dimensional electron systems

## TL;DR

This paper investigates how image-potential-induced spin-orbit interaction (iSOI) in one-dimensional electron systems affects electron density, correlations, and collective excitations, revealing a density-dependent instability and mode evolution.

## Contribution

It introduces the concept of iSOI in 1D systems, showing its impact on electron interactions and collective modes, including a transition from spin to charge excitations.

## Key findings

- iSOI depends on electron density, causing feedback effects.
- System becomes unstable against density fluctuations at certain conditions.
- One collective mode softens and transitions from spin to charge excitation at critical iSOI.

## Abstract

We study the spin-orbit interaction effects in a one-dimensional electron system that result from the image charges in a nearby metallic gate. The nontrivial property of the image-potential-induced spin-orbit interaction (iSOI) is that it directly depends on the electron density because of which a positive feedback arises between the electron density and the iSOI magnitude. As a result, the system becomes unstable against the density fluctuations under certain conditions. In addition, the iSOI contributes to the electron-electron interaction giving rise to strong changes in electron correlations and collective excitation spectra. We trace the evolution of the spectrum of the collective excitations and their spin-charge structures with the change in the iSOI parameter. One out of two collective modes softens as the iSOI amplitude grows to become unstable at its critical value. Interestingly, this mode evolves from a pure spin excitation to a pure charge one. At the critical point its velocity turns to zero together with the charge stiffness.