# Unrestricted electron bunching at the helical edge

## TL;DR

This paper investigates electron bunching phenomena at the edges of topological insulators caused by magnetic impurities, revealing that larger impurity spins lead to arbitrarily large electron bunching, while spin-1/2 impurities have bounded bunching.

## Contribution

The study provides an exact analytical solution for shot noise due to magnetic impurities of arbitrary spin at topological insulator edges, extending understanding of electron bunching behavior.

## Key findings

- For $S>1/2$, Fano factor can be arbitrarily large.
- For $S=1/2$, Fano factor is bounded between 1 and 2.
- Analytical solution for shot noise with arbitrary impurity spin.

## Abstract

A quantum magnetic impurity of spin $S$ at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary $S$. Our full analytical solution reveals that for $S>\frac{1}{2}$ the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for $S=\frac{1}{2}$ the Fano factor is bounded between $1$ and $2$, generalizing earlier studies.