# Charge and energy fractionalization mechanism in one-dimensional channels

## TL;DR

This paper investigates how injecting single electrons into one-dimensional interacting quantum channels causes charge and energy fractionalization, analyzing the resulting particle-hole pairs and fractional excitations in topological edge states.

## Contribution

It provides a detailed calculation of the nonequilibrium electron distribution function post-injection, elucidating the fractionalization process in counterpropagating channels.

## Key findings

- Charge and energy fractionalization occurs via particle-hole pair creation.
- Full analysis of chiral fractional excitations in counterpropagating channels.
- Proposed methods to measure distributions in topological quantum states.

## Abstract

We study the problem of injecting single electrons into interacting one-dimensional quantum systems, a fundamental building block for electron quantum optics. It is well known that such injection leads to charge and energy fractionalization. We elucidate this concept by calculating the nonequilibrium electron distribution function in the momentum and energy domains after the injection of an energy-resolved electron. Our results shed light on how fractionalization occurs via the creation of particle-hole pairs by the injected electron. In particular, we focus on systems with a pair of counterpropagating channels, and we fully analyze the properties of each chiral fractional excitation which is created by the injection. We suggest possible routes to access their energy and momentum distribution functions in topological quantum Hall or quantum spin-Hall edge states.