Nonequilibrium electron spectroscopy of Luttinger liquids

TL;DR

This paper demonstrates how nonequilibrium electron spectroscopy can probe energy relaxation and collective excitations in Luttinger liquids, revealing power-law distributions and plasmon emission effects in strongly correlated one-dimensional systems.

Contribution

It introduces a method to use high-energy electron injection spectroscopy to study energy relaxation in Luttinger liquids, linking spectral features to collective plasmon modes.

Findings

Electron distribution near injection energy follows a power law with an exponent depending on the Luttinger parameter.

Energy relaxation is primarily due to plasmon emission in the Luttinger liquid.

In chiral Luttinger liquids, the distribution function increases linearly with distance from the injection energy.

Abstract

Understanding the effects of nonequilibrium on strongly interacting quantum systems is a challenging problem in condensed matter physics. In dimensions greater than one, interacting electrons can often be understood within Fermi-liquid theory where low-energy excitations are weakly interacting quasiparticles. On the contrary, electrons in one dimension are known to form a strongly-correlated phase of matter called a Luttinger liquid (LL), whose low-energy excitations are collective density waves, or plasmons, of the electron gas. Here we show that spectroscopy of locally injected high-energy electrons can be used to probe energy relaxation in the presence of such strong correlations. For detection energies near the injection energy, the electron distribution is described by a power law whose exponent depends in a continuous way on the Luttinger parameter, and energy relaxation can be attributed to plasmon emission. For a chiral LL as realized at the edge of a fractional quantum Hall state, the distribution function grows linearly with the distance to the injection energy, independent of filling fraction.