# Topological classification of shot noise on fractional quantum Hall edges

## TL;DR

This paper demonstrates that shot noise measurements can electrically classify the topological nature of fractional quantum Hall edges, revealing three universality classes based on thermal transport behavior.

## Contribution

It introduces a method to classify edge topologies via shot noise, linking electrical measurements to thermal transport regimes in fractional quantum Hall systems.

## Key findings

- Shot noise falls into three topological classes: vanishing, algebraically decaying, or constant.
- Electrical transport remains ballistic across all classes.
- Thermal transport varies: ballistic, diffusive, or antiballistic.

## Abstract

Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited from the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport appears more challenging. Here, we show that the shot noise generated on the edge provides a fully electrical method to probe the edge structure. In the incoherent regime, the noise falls into three topologically distinct universality classes: charge transport is always ballistic while thermal transport is either ballistic, diffusive, or "antiballistic". Correspondingly, the noise either vanishes, decays algebraically or is constant up to exponentially small corrections in the edge length.